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@@ -133,7 +133,7 @@
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<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
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@@ -143,7 +143,7 @@
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<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
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<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
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</label>
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@@ -3276,7 +3276,23 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
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<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 爬楼梯最小代价：动态规划 */</span>
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<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">cost</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span>
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<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
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<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="k">return</span> <span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
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<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="p">}</span>
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<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 初始化 dp 表，用于存储子问题的解</span>
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<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="c1">// 初始状态：预设最小子问题的解</span>
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<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
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<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">=</span> <span class="mi">2</span>
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<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
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<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">])</span> <span class="o">+</span> <span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
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<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="p">}</span>
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<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
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<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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@@ -3388,7 +3404,18 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
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<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 爬楼梯最小代价：状态压缩后的动态规划 */</span>
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<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">cost</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span>
|
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<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
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<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="k">return</span> <span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
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<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="p">}</span>
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<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="kd">var</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="p">=</span> <span class="p">(</span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
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<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="p">=</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="bp">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
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<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="p">}</span>
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<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="k">return</span> <span class="n">b</span>
|
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<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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@@ -3548,7 +3575,25 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
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<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 带约束爬楼梯：动态规划 */</span>
|
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<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span> <span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
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<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="k">return</span> <span class="n">n</span>
|
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<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="p">}</span>
|
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<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="c1">// 初始化 dp 表，用于存储子问题的解</span>
|
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<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="mi">3</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="c1">// 初始状态：预设最小子问题的解</span>
|
||||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
|
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<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="p">=</span> <span class="mi">0</span>
|
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<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="mi">0</span>
|
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<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
|
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<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
|
||||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
@@ -133,7 +133,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -143,7 +143,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -3374,7 +3374,22 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最小路径和：暴力搜索 */</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="c1">// 若为左上角单元格，则终止搜索</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="k">if</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">0</span><span class="p">,</span> <span class="n">j</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="k">return</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 若行列索引越界，则返回 +∞ 代价</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">j</span> <span class="o"><</span> <span class="mi">0</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="k">return</span> <span class="p">.</span><span class="bp">max</span>
|
||||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="c1">// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价</span>
|
||||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="kd">let</span> <span class="nv">left</span> <span class="p">=</span> <span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="n">grid</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="kd">let</span> <span class="nv">up</span> <span class="p">=</span> <span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="n">grid</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="c1">// 返回从左上角到 (i, j) 的最小路径代价</span>
|
||||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="k">return</span> <span class="bp">min</span><span class="p">(</span><span class="kr">left</span><span class="p">,</span> <span class="n">up</span><span class="p">)</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3523,7 +3538,27 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 最小路径和：记忆化搜索 */</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span> <span class="n">mem</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="c1">// 若为左上角单元格，则终止搜索</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="k">if</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">0</span><span class="p">,</span> <span class="n">j</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="k">return</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="c1">// 若行列索引越界，则返回 +∞ 代价</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">j</span> <span class="o"><</span> <span class="mi">0</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="k">return</span> <span class="p">.</span><span class="bp">max</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="c1">// 若已有记录，则直接返回</span>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a> <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a> <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a> <span class="c1">// 左边和上边单元格的最小路径代价</span>
|
||||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a> <span class="kd">let</span> <span class="nv">left</span> <span class="p">=</span> <span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="n">grid</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a> <span class="kd">let</span> <span class="nv">up</span> <span class="p">=</span> <span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="n">grid</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="c1">// 记录并返回左上角到 (i, j) 的最小路径代价</span>
|
||||
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="kr">left</span><span class="p">,</span> <span class="n">up</span><span class="p">)</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a> <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3677,7 +3712,29 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 最小路径和：动态规划 */</span>
|
||||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span> <span class="nf">minPathSumDP</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">grid</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="bp">count</span>
|
||||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">m</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="c1">// 状态转移：首行</span>
|
||||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="c1">// 状态转移：首列</span>
|
||||
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a> <span class="c1">// 状态转移：其余行列</span>
|
||||
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3866,7 +3923,28 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 最小路径和：状态压缩后的动态规划 */</span>
|
||||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">func</span> <span class="nf">minPathSumDPComp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">grid</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a> <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="bp">count</span>
|
||||
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">m</span><span class="p">)</span>
|
||||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a> <span class="c1">// 状态转移：首行</span>
|
||||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="c1">// 状态转移：其余行</span>
|
||||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a> <span class="c1">// 状态转移：首列</span>
|
||||
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a> <span class="c1">// 状态转移：其余列</span>
|
||||
<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
@@ -133,7 +133,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -143,7 +143,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -3262,7 +3262,32 @@ dp[i, j] = dp[i-1, j-1]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 编辑距离：动态规划 */</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">String</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="c1">// 状态转移：首行首列</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="n">i</span>
|
||||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="n">j</span>
|
||||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="c1">// 状态转移：其余行列</span>
|
||||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="k">if</span> <span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="p">==</span> <span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a> <span class="c1">// 若两字符相等，则直接跳过此两字符</span>
|
||||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a> <span class="c1">// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1</span>
|
||||
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3490,7 +3515,35 @@ dp[i, j] = dp[i-1, j-1]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 编辑距离：状态压缩后的动态规划 */</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">String</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="c1">// 状态转移：首行</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="n">j</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="c1">// 状态转移：其余行</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a> <span class="c1">// 状态转移：首列</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a> <span class="kd">var</span> <span class="nv">leftup</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1">// 暂存 dp[i-1, j-1]</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="n">i</span>
|
||||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a> <span class="c1">// 状态转移：其余列</span>
|
||||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a> <span class="kd">let</span> <span class="nv">temp</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="k">if</span> <span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="p">==</span> <span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a> <span class="c1">// 若两字符相等，则直接跳过此两字符</span>
|
||||
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="n">leftup</span>
|
||||
<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a> <span class="c1">// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1</span>
|
||||
<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span> <span class="n">leftup</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a> <span class="n">leftup</span> <span class="p">=</span> <span class="n">temp</span> <span class="c1">// 更新为下一轮的 dp[i-1, j-1]</span>
|
||||
<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
@@ -133,7 +133,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -143,7 +143,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
|
||||
@@ -133,7 +133,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -143,7 +143,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -3323,9 +3323,31 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_backtrack.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_backtrack.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 回溯 */</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">state</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="c1">// 当爬到第 n 阶时，方案数量加 1</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="k">if</span> <span class="n">state</span> <span class="p">==</span> <span class="n">n</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 遍历所有选择</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="k">for</span> <span class="n">choice</span> <span class="k">in</span> <span class="n">choices</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="c1">// 剪枝：不允许越过第 n 阶</span>
|
||||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="k">if</span> <span class="n">state</span> <span class="o">+</span> <span class="n">choice</span> <span class="o">></span> <span class="n">n</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="k">break</span>
|
||||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span> <span class="n">choices</span><span class="p">,</span> <span class="n">state</span><span class="p">:</span> <span class="n">state</span> <span class="o">+</span> <span class="n">choice</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="p">}</span>
|
||||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a>
|
||||
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="cm">/* 爬楼梯：回溯 */</span>
|
||||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="kd">func</span> <span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="kd">let</span> <span class="nv">choices</span> <span class="p">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span> <span class="c1">// 可选择向上爬 1 或 2 阶</span>
|
||||
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a> <span class="kd">let</span> <span class="nv">state</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 从第 0 阶开始爬</span>
|
||||
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
|
||||
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1">// 使用 res[0] 记录方案数量</span>
|
||||
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span> <span class="n">choices</span><span class="p">,</span> <span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a> <span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3477,9 +3499,21 @@ dp[i] = dp[i-1] + dp[i-2]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 搜索 */</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="c1">// 已知 dp[1] 和 dp[2] ，返回之</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="k">if</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="k">return</span> <span class="n">i</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="kd">let</span> <span class="nv">count</span> <span class="p">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="k">return</span> <span class="bp">count</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="p">}</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="cm">/* 爬楼梯：搜索 */</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="kd">func</span> <span class="nf">climbingStairsDFS</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3642,9 +3676,29 @@ dp[i] = dp[i-1] + dp[i-2]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
|
||||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 记忆化搜索 */</span>
|
||||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a> <span class="c1">// 已知 dp[1] 和 dp[2] ，返回之</span>
|
||||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="k">if</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="k">return</span> <span class="n">i</span>
|
||||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="c1">// 若存在记录 dp[i] ，则直接返回之</span>
|
||||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
|
||||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="kd">let</span> <span class="nv">count</span> <span class="p">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">)</span> <span class="o">+</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="c1">// 记录 dp[i]</span>
|
||||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">=</span> <span class="bp">count</span>
|
||||
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="k">return</span> <span class="bp">count</span>
|
||||
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="p">}</span>
|
||||
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a>
|
||||
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="cm">/* 爬楼梯：记忆化搜索 */</span>
|
||||
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="kd">func</span> <span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a> <span class="c1">// mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录</span>
|
||||
<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a> <span class="kd">var</span> <span class="nv">mem</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a> <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3777,7 +3831,22 @@ dp[i] = dp[i-1] + dp[i-2]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 爬楼梯：动态规划 */</span>
|
||||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">func</span> <span class="nf">climbingStairsDP</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a> <span class="k">return</span> <span class="n">n</span>
|
||||
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a> <span class="c1">// 初始化 dp 表，用于存储子问题的解</span>
|
||||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a> <span class="c1">// 初始状态：预设最小子问题的解</span>
|
||||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">=</span> <span class="mi">2</span>
|
||||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
|
||||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3891,7 +3960,18 @@ dp[i] = dp[i-1] + dp[i-2]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
|
||||
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kd">func</span> <span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a> <span class="k">return</span> <span class="n">n</span>
|
||||
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a> <span class="kd">var</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a> <span class="kd">var</span> <span class="nv">b</span> <span class="p">=</span> <span class="mi">2</span>
|
||||
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="p">=</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span>
|
||||
<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a> <span class="k">return</span> <span class="n">b</span>
|
||||
<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
@@ -133,7 +133,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -143,7 +143,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -3312,7 +3312,22 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 0-1 背包：暴力搜索 */</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="c1">// 若已选完所有物品或背包无容量，则返回价值 0</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="k">if</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">c</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="k">return</span> <span class="mi">0</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 若超过背包容量，则只能不放入背包</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">c</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="k">return</span> <span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="c1">// 计算不放入和放入物品 i 的最大价值</span>
|
||||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="kd">let</span> <span class="nv">no</span> <span class="p">=</span> <span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="kd">let</span> <span class="nv">yes</span> <span class="p">=</span> <span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="c1">// 返回两种方案中价值更大的那一个</span>
|
||||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="k">return</span> <span class="bp">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span> <span class="n">yes</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3460,7 +3475,27 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 0-1 背包：记忆化搜索 */</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">mem</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="c1">// 若已选完所有物品或背包无容量，则返回价值 0</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="k">if</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">c</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="k">return</span> <span class="mi">0</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="c1">// 若已有记录，则直接返回</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="c1">// 若超过背包容量，则只能不放入背包</span>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a> <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">c</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a> <span class="k">return</span> <span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a> <span class="c1">// 计算不放入和放入物品 i 的最大价值</span>
|
||||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a> <span class="kd">let</span> <span class="nv">no</span> <span class="p">=</span> <span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a> <span class="kd">let</span> <span class="nv">yes</span> <span class="p">=</span> <span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="p">&</span><span class="n">mem</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="c1">// 记录并返回两种方案中价值更大的那一个</span>
|
||||
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span> <span class="n">yes</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a> <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3602,7 +3637,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 0-1 背包：动态规划 */</span>
|
||||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span> <span class="nf">knapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">cap</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">c</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="c1">// 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3807,7 +3860,23 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 0-1 背包：状态压缩后的动态规划 */</span>
|
||||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">func</span> <span class="nf">knapsackDPComp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a> <span class="c1">// 倒序遍历</span>
|
||||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="n">cap</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a> <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o"><=</span> <span class="n">c</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
@@ -133,7 +133,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -143,7 +143,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
|
||||
@@ -133,7 +133,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -143,7 +143,7 @@
|
||||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
|
||||
|
||||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||||
</label>
|
||||
|
||||
|
||||
@@ -3306,7 +3306,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 完全背包：动态规划 */</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">cap</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">c</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="c1">// 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3465,7 +3483,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 完全背包：状态压缩后的动态规划 */</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">cap</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">c</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="c1">// 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a> <span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3500,7 +3536,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
<p>背包问题是一大类动态规划问题的代表，其拥有很多的变种，例如零钱兑换问题。</p>
|
||||
<div class="admonition question">
|
||||
<p class="admonition-title">Question</p>
|
||||
<p>给定 <span class="arithmatex">\(n\)</span> 种硬币，第 <span class="arithmatex">\(i\)</span> 个硬币的面值为 <span class="arithmatex">\(coins[i - 1]\)</span> ，为目标金额 <span class="arithmatex">\(amt\)</span> ，<strong>每种硬币可以重复选取</strong>，问能够凑出目标金额的最少硬币个数。如果无法凑出目标金额则返回 <span class="arithmatex">\(-1\)</span> 。</p>
|
||||
<p>给定 <span class="arithmatex">\(n\)</span> 种硬币，第 <span class="arithmatex">\(i\)</span> 个硬币的面值为 <span class="arithmatex">\(coins[i - 1]\)</span> ，目标金额为 <span class="arithmatex">\(amt\)</span> ，<strong>每种硬币可以重复选取</strong>，问能够凑出目标金额的最少硬币个数。如果无法凑出目标金额则返回 <span class="arithmatex">\(-1\)</span> 。</p>
|
||||
</div>
|
||||
<p>如下图所示，凑出 <span class="arithmatex">\(11\)</span> 元最少需要 <span class="arithmatex">\(3\)</span> 枚硬币，方案为 <span class="arithmatex">\(1 + 2 + 5 = 11\)</span> 。</p>
|
||||
<p><img alt="零钱兑换问题的示例数据" src="../unbounded_knapsack_problem.assets/coin_change_example.png" /></p>
|
||||
@@ -3651,7 +3687,30 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 零钱兑换：动态规划 */</span>
|
||||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span> <span class="nf">coinChangeDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="kd">let</span> <span class="nv">MAX</span> <span class="p">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="c1">// 状态转移：首行首列</span>
|
||||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">amt</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">MAX</span>
|
||||
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="c1">// 状态转移：其余行列</span>
|
||||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">amt</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="c1">// 若超过背包容量，则不选硬币 i</span>
|
||||
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a> <span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="p">?</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="p">:</span> <span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -3856,7 +3915,27 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 零钱兑换：状态压缩后的动态规划 */</span>
|
||||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">func</span> <span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a> <span class="kd">let</span> <span class="nv">MAX</span> <span class="p">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="n">MAX</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="mi">0</span>
|
||||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a> <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">amt</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="c1">// 若超过背包容量，则不选硬币 i</span>
|
||||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a> <span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="p">?</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="p">:</span> <span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -4026,7 +4105,29 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 零钱兑换 II：动态规划 */</span>
|
||||
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kd">func</span> <span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a> <span class="c1">// 初始化首列</span>
|
||||
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a> <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">amt</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a> <span class="c1">// 若超过背包容量，则不选硬币 i</span>
|
||||
<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a> <span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
|
||||
<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span>
|
||||
<a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -4170,7 +4271,26 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 零钱兑换 II：状态压缩后的动态规划 */</span>
|
||||
<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">func</span> <span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a> <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="n">amt</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a> <span class="c1">// 若超过背包容量，则不选硬币 i</span>
|
||||
<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a> <span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
|
||||
<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span>
|
||||
<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
Reference in New Issue
Block a user