deploy

chapter_dynamic_programming/dp_problem_features/index.html

@@ -3740,7 +3740,7 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 <a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></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="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></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="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
 <a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>    <span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
-<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></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>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">3</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></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>
 <a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>    <span class="p">}</span>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
@@ -3974,7 +3974,7 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 <a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>        <span class="k">return</span> <span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
 <a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>    <span class="p">}</span>
 <a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></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>
-<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></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>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">3</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></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>
 <a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>    <span class="p">}</span>
 <a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a>    <span class="k">return</span> <span class="n">b</span>
@@ -4242,7 +4242,7 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
 <a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></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>
 <a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></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>
 <a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></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-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></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-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">3</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></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-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></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-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a>    <span class="p">}</span>

chapter_dynamic_programming/dp_solution_pipeline/index.html

@@ -4452,16 +4452,16 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 <a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></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-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></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-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a>    <span class="c1">// 状态转移：首行</span>
-<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></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-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a>    <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">m</span> <span class="p">{</span>
 <a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></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-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a>    <span class="p">}</span>
 <a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a>    <span class="c1">// 状态转移：首列</span>
-<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></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-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></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-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a>    <span class="p">}</span>
 <a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a>    <span class="c1">// 状态转移：其余行和列</span>
-<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></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-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></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-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a>        <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">m</span> <span class="p">{</span>
 <a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></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-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a>        <span class="p">}</span>
 <a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a>    <span class="p">}</span>
@@ -4814,15 +4814,15 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 <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-41-9" 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="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">m</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-41-13" 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="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">n</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-41-17" 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="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">m</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>

chapter_dynamic_programming/edit_distance_problem/index.html

@@ -3815,15 +3815,15 @@ dp[i, j] = dp[i-1, j-1]
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></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-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></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-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="c1">// 状态转移：首行首列</span>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></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-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></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-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>    <span class="p">}</span>
-<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></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-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>    <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">m</span> <span class="p">{</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></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-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>    <span class="p">}</span>
 <a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a>    <span class="c1">// 状态转移：其余行和列</span>
-<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></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-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></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-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>        <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">m</span> <span class="p">{</span>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></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-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>                <span class="c1">// 若两字符相等，则直接跳过此两字符</span>
 <a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></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>
@@ -4242,16 +4242,16 @@ dp[i, j] = dp[i-1, j-1]
 <a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></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-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></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-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>    <span class="c1">// 状态转移：首行</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></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-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a>    <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">m</span> <span class="p">{</span>
 <a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></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-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a>    <span class="p">}</span>
 <a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>    <span class="c1">// 状态转移：其余行</span>
-<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></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-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a>        <span class="c1">// 状态转移：首列</span>
 <a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></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-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></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-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a>        <span class="c1">// 状态转移：其余列</span>
-<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></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-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a>        <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">m</span> <span class="p">{</span>
 <a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></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-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></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-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a>                <span class="c1">// 若两字符相等，则直接跳过此两字符</span>

chapter_dynamic_programming/intro_to_dynamic_programming/index.html

@@ -4661,7 +4661,7 @@ dp[i] = dp[i-1] + dp[i-2]
 <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-41-12" 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="mi">3</span> <span class="p">...</span> <span class="n">n</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>
@@ -4880,7 +4880,7 @@ dp[i] = dp[i-1] + dp[i-2]
 <a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a>    <span class="p">}</span>
 <a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a>    <span class="kd">var</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">1</span>
 <a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a>    <span class="kd">var</span> <span class="nv">b</span> <span class="p">=</span> <span class="mi">2</span>
-<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></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-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a>    <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">3</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></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-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a>    <span class="p">}</span>
 <a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a>    <span class="k">return</span> <span class="n">b</span>

chapter_dynamic_programming/knapsack_problem/index.html

@@ -4356,8 +4356,8 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a>    <span class="c1">// 初始化 dp 表</span>
 <a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></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-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a>    <span class="c1">// 状态转移</span>
-<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></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-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></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-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a>        <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">cap</span> <span class="p">{</span>
 <a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></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">&gt;</span> <span class="n">c</span> <span class="p">{</span>
 <a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a>                <span class="c1">// 若超过背包容量，则不选物品 i</span>
 <a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></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>
@@ -4728,9 +4728,9 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <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-41-7" 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="mi">1</span> <span class="p">...</span> <span class="n">n</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-41-9" 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="p">(</span><span class="mi">1</span> <span class="p">...</span> <span class="n">cap</span><span class="p">).</span><span class="n">reversed</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">&lt;=</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>

chapter_dynamic_programming/unbounded_knapsack_problem/index.html

@@ -3961,8 +3961,8 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="c1">// 初始化 dp 表</span>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></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-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="c1">// 状态转移</span>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></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-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></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-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>        <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">cap</span> <span class="p">{</span>
 <a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></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">&gt;</span> <span class="n">c</span> <span class="p">{</span>
 <a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>                <span class="c1">// 若超过背包容量，则不选物品 i</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></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>
@@ -4281,8 +4281,8 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>    <span class="c1">// 初始化 dp 表</span>
 <a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></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-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>    <span class="c1">// 状态转移</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></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-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></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-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a>        <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">cap</span> <span class="p">{</span>
 <a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></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">&gt;</span> <span class="n">c</span> <span class="p">{</span>
 <a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>                <span class="c1">// 若超过背包容量，则不选物品 i</span>
 <a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></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>
@@ -4622,12 +4622,12 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 <a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a>    <span class="c1">// 初始化 dp 表</span>
 <a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></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-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a>    <span class="c1">// 状态转移：首行首列</span>
-<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></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-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a>    <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">amt</span> <span class="p">{</span>
 <a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></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-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a>    <span class="p">}</span>
 <a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a>    <span class="c1">// 状态转移：其余行和列</span>
-<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></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-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></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-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a>        <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">amt</span> <span class="p">{</span>
 <a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></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">&gt;</span> <span class="n">a</span> <span class="p">{</span>
 <a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a>                <span class="c1">// 若超过目标金额，则不选硬币 i</span>
 <a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></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>
@@ -5021,8 +5021,8 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 <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-41-9" 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="mi">1</span> <span class="p">...</span> <span class="n">n</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="mi">1</span> <span class="p">...</span> <span class="n">amt</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">&gt;</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">// 若超过目标金额，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>
@@ -5353,12 +5353,12 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 <a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a>    <span class="c1">// 初始化 dp 表</span>
 <a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></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-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a>    <span class="c1">// 初始化首列</span>
-<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></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-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
 <a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></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-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a>    <span class="p">}</span>
 <a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a>    <span class="c1">// 状态转移</span>
-<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></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-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></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-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a>        <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">amt</span> <span class="p">{</span>
 <a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></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">&gt;</span> <span class="n">a</span> <span class="p">{</span>
 <a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a>                <span class="c1">// 若超过目标金额，则不选硬币 i</span>
 <a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></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>
@@ -5673,8 +5673,8 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 <a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></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-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></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-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a>    <span class="c1">// 状态转移</span>
-<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></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-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></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-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
+<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a>        <span class="k">for</span> <span class="n">a</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">amt</span> <span class="p">{</span>
 <a id="__codelineno-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></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">&gt;</span> <span class="n">a</span> <span class="p">{</span>
 <a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a>                <span class="c1">// 若超过目标金额，则不选硬币 i</span>
 <a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></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>