This commit is contained in:
krahets
2023-09-03 19:14:50 +08:00
parent 7c23f8439d
commit 42edb18ac1
10 changed files with 199 additions and 112 deletions
@@ -3751,9 +3751,40 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fractional_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="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</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">fractionalKnapsack</span><span class="p">}</span>
<div class="highlight"><span class="filename">fractional_knapsack.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 物品 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span> <span class="nc">Item</span> <span class="p">{</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="kd">var</span> <span class="nv">w</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 物品重量</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="kd">var</span> <span class="nv">v</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 物品价值</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="kd">init</span><span class="p">(</span><span class="n">w</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="kc">self</span><span class="p">.</span><span class="n">w</span> <span class="p">=</span> <span class="n">w</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="kc">self</span><span class="p">.</span><span class="n">v</span> <span class="p">=</span> <span class="n">v</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="p">}</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* 分数背包:贪心 */</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kd">func</span> <span class="nf">fractionalKnapsack</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">-&gt;</span> <span class="nb">Double</span> <span class="p">{</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="c1">// 创建物品列表,包含两个属性:重量、价值</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="kd">var</span> <span class="nv">items</span> <span class="p">=</span> <span class="n">zip</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="bp">map</span> <span class="p">{</span> <span class="n">Item</span><span class="p">(</span><span class="n">w</span><span class="p">:</span> <span class="nv">$0</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nv">$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="c1">// 按照单位价值 item.v / item.w 从高到低进行排序</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a> <span class="n">items</span><span class="p">.</span><span class="bp">sort</span><span class="p">(</span><span class="n">by</span><span class="p">:</span> <span class="p">{</span> <span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">v</span><span class="p">)</span> <span class="o">/</span> <span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">w</span><span class="p">))</span> <span class="o">&lt;</span> <span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">v</span><span class="p">)</span> <span class="o">/</span> <span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">w</span><span class="p">))</span> <span class="p">})</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="c1">// 循环贪心选择</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="kd">var</span> <span class="nv">res</span> <span class="p">=</span> <span class="mf">0.0</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a> <span class="kd">var</span> <span class="nv">cap</span> <span class="p">=</span> <span class="n">cap</span>
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a> <span class="k">for</span> <span class="n">item</span> <span class="k">in</span> <span class="n">items</span> <span class="p">{</span>
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a> <span class="k">if</span> <span class="n">item</span><span class="p">.</span><span class="n">w</span> <span class="o">&lt;=</span> <span class="n">cap</span> <span class="p">{</span>
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a> <span class="c1">// 若剩余容量充足,则将当前物品整个装进背包</span>
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a> <span class="n">res</span> <span class="o">+=</span> <span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span>
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a> <span class="n">cap</span> <span class="o">-=</span> <span class="n">item</span><span class="p">.</span><span class="n">w</span>
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a> <span class="c1">// 若剩余容量不足,则将当前物品的一部分装进背包</span>
<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a> <span class="n">res</span> <span class="o">+=</span> <span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span> <span class="o">/</span> <span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">)</span> <span class="o">*</span> <span class="nb">Double</span><span class="p">(</span><span class="n">cap</span><span class="p">)</span>
<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a> <span class="c1">// 已无剩余容量,因此跳出循环</span>
<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a> <span class="k">break</span>
<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a> <span class="p">}</span>
<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a> <span class="p">}</span>
<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a> <span class="k">return</span> <span class="n">res</span>
<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="p">}</span>
</code></pre></div>
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@@ -3648,7 +3648,25 @@
</code></pre></div>
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<div class="highlight"><span class="filename">coin_change_greedy.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">coinChangeGreedy</span><span class="p">}</span>
<div class="highlight"><span class="filename">coin_change_greedy.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 零钱兑换:贪心 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">coinChangeGreedy</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">-&gt;</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">// 假设 coins 列表有序</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="kd">var</span> <span class="nv">amt</span> <span class="p">=</span> <span class="n">amt</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 循环进行贪心选择,直到无剩余金额</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="k">while</span> <span class="n">amt</span> <span class="o">&gt;</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="c1">// 找到小于且最接近剩余金额的硬币</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="k">while</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="o">&amp;&amp;</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">amt</span> <span class="p">{</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="n">i</span> <span class="o">-=</span> <span class="mi">1</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">// 选择 coins[i]</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="n">amt</span> <span class="o">-=</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</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="c1">// 若未找到可行方案,则返回 -1</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="k">return</span> <span class="n">amt</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="o">-</span><span class="mi">1</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
</code></pre></div>
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+20 -1
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@@ -3704,7 +3704,26 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
</code></pre></div>
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<div class="tabbed-block">
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
<div class="highlight"><span class="filename">max_capacity.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最大容量:贪心 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">maxCapacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-&gt;</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">// 初始化 i, j 分列数组两端</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="kd">var</span> <span class="nv">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="n">ht</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="c1">// 初始最大容量为 0</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="kd">var</span> <span class="nv">res</span> <span class="p">=</span> <span class="mi">0</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 循环贪心选择,直至两板相遇</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="p">{</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="c1">// 更新最大容量</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="kd">let</span> <span class="nv">cap</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="n">res</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">cap</span><span class="p">)</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="c1">// 向内移动短板</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="k">if</span> <span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</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="p">}</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="k">return</span> <span class="n">res</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="p">}</span>
</code></pre></div>
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<div class="tabbed-block">
@@ -3676,7 +3676,26 @@ n = 3 a + b
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<div class="tabbed-block">
<div class="highlight"><span class="filename">max_product_cutting.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">maxProductCutting</span><span class="p">}</span>
<div class="highlight"><span class="filename">max_product_cutting.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最大切分乘积:贪心 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">maxProductCutting</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">-&gt;</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">// 当 n &lt;= 3 时,必须切分出一个 1</span>
<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="o">&lt;=</span> <span class="mi">3</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">1</span> <span class="o">*</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="p">}</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 贪心地切分出 3 ,a 为 3 的个数,b 为余数</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="kd">let</span> <span class="nv">a</span> <span class="p">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">3</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="kd">let</span> <span class="nv">b</span> <span class="p">=</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">3</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="k">if</span> <span class="n">b</span> <span class="p">==</span> <span class="mi">1</span> <span class="p">{</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="c1">// 当余数为 1 时,将一对 1 * 3 转化为 2 * 2</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="k">return</span> <span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="p">}</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="k">if</span> <span class="n">b</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="c1">// 当余数为 2 时,不做处理</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="k">return</span> <span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</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="c1">// 当余数为 0 时,不做处理</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="k">return</span> <span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="p">}</span>
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