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@@ -62,17 +62,15 @@
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@@ -3894,7 +3892,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
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<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
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<div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</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="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</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="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""完全背包：动态规划"""</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
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<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="c1"># 初始化 dp 表</span>
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@@ -3960,16 +3958,16 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
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<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">UnboundedKnapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
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<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
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<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
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<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
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<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 状态转移</span>
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<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选物品 i</span>
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<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">];</span>
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<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">];</span>
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<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
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<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]);</span>
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<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
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<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="p">}</span>
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@@ -4004,23 +4002,23 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 完全背包：动态规划 */</span>
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<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
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<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="c1">// 初始化 dp 表</span>
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<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>
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<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="c1">// 状态转移</span>
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<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>
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<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">></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>
|
||||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a> <span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-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="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-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="p">}</span>
|
||||
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><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="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </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="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><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="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -4106,7 +4104,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 完全背包：动态规划 */</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
|
||||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
@@ -4118,7 +4116,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
|
||||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
|
||||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
|
||||
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -4260,7 +4258,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span> <span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</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="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</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="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w"> </span><span class="sd">"""完全背包：空间优化后的动态规划"""</span>
|
||||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
|
||||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a> <span class="c1"># 初始化 dp 表</span>
|
||||
@@ -4327,16 +4325,16 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">UnboundedKnapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
|
||||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><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="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </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="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><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="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
|
||||
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">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="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]);</span>
|
||||
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">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="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
|
||||
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -4368,23 +4366,23 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 完全背包：空间优化后的动态规划 */</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="kd">var</span> <span class="nv">dp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">n</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">...</span> <span class="n">cap</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">c</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="c1">// 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a> <span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </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="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span>
|
||||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
|
||||
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -4460,7 +4458,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 完全背包：空间优化后的动态规划 */</span>
|
||||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
|
||||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
@@ -4472,7 +4470,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
||||
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
|
||||
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">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="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
|
||||
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">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="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
|
||||
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -4640,7 +4638,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span> <span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w"> </span><span class="sd">"""零钱兑换：动态规划"""</span>
|
||||
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
|
||||
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a> <span class="n">MAX</span> <span class="o">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
@@ -4719,26 +4717,26 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 零钱兑换：动态规划 */</span>
|
||||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="c1">// 状态转移：首行首列</span>
|
||||
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w"> </span><span class="c1">// 状态转移：其余行和列</span>
|
||||
<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -4777,28 +4775,28 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 零钱兑换：动态规划 */</span>
|
||||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">func</span> <span class="nf">coinChangeDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a> <span class="kd">let</span> <span class="nv">MAX</span> <span class="p">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></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-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a> <span class="c1">// 状态转移：首行首列</span>
|
||||
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></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-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></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-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a> <span class="c1">// 状态转移：其余行和列</span>
|
||||
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></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-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></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-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a> <span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a> <span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="p">?</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="p">:</span> <span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">MAX</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="c1">// 状态转移：首行首列</span>
|
||||
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w"> </span><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="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">MAX</span>
|
||||
<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w"> </span><span class="c1">// 状态转移：其余行和列</span>
|
||||
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </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="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -4889,7 +4887,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 零钱兑换：动态规划 */</span>
|
||||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">fn</span> <span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
|
||||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
@@ -4906,7 +4904,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -5101,7 +5099,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span> <span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">"""零钱兑换：空间优化后的动态规划"""</span>
|
||||
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
|
||||
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a> <span class="n">MAX</span> <span class="o">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
@@ -5174,24 +5172,24 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 零钱兑换：空间优化后的动态规划 */</span>
|
||||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="n">Array</span><span class="p">.</span><span class="n">Fill</span><span class="p">(</span><span class="n">dp</span><span class="p">,</span><span class="w"> </span><span class="n">MAX</span><span class="p">);</span>
|
||||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -5227,25 +5225,25 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 零钱兑换：空间优化后的动态规划 */</span>
|
||||
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kd">func</span> <span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a> <span class="kd">let</span> <span class="nv">MAX</span> <span class="p">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></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-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></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-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></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-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></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-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a> <span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a> <span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="p">?</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="p">:</span> <span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">MAX</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="n">MAX</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -5323,7 +5321,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 零钱兑换：空间优化后的动态规划 */</span>
|
||||
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">fn</span> <span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
|
||||
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
@@ -5338,7 +5336,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
||||
<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -5486,7 +5484,7 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span> <span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w"> </span><span class="sd">"""零钱兑换 II：动态规划"""</span>
|
||||
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
|
||||
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a> <span class="c1"># 初始化 dp 表</span>
|
||||
@@ -5563,20 +5561,20 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeIIDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
|
||||
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="c1">// 初始化首列</span>
|
||||
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]];</span>
|
||||
<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
|
||||
<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -5615,27 +5613,27 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 零钱兑换 II：动态规划 */</span>
|
||||
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="kd">func</span> <span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></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-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a> <span class="c1">// 初始化首列</span>
|
||||
<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></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-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></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-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></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-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></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-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a> <span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a> <span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
|
||||
<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span>
|
||||
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w"> </span><span class="c1">// 初始化首列</span>
|
||||
<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w"> </span><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="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span>
|
||||
<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span>
|
||||
<a id="__codelineno-61-23" name="__codelineno-61-23" href="#__codelineno-61-23"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -5723,7 +5721,7 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 零钱兑换 II：动态规划 */</span>
|
||||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="k">fn</span> <span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
|
||||
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
@@ -5870,7 +5868,7 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="8:14"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><input id="__tabbed_8_14" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label><label for="__tabbed_8_14">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="k">def</span> <span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</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="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="w"> </span><span class="sd">"""零钱兑换 II：空间优化后的动态规划"""</span>
|
||||
<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
|
||||
<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a> <span class="c1"># 初始化 dp 表</span>
|
||||
@@ -5940,17 +5938,17 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeIIDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
|
||||
<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-11" name="__codelineno-73-11" href="#__codelineno-73-11"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
|
||||
<a id="__codelineno-73-13" name="__codelineno-73-13" href="#__codelineno-73-13"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-73-14" name="__codelineno-73-14" href="#__codelineno-73-14"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-73-15" name="__codelineno-73-15" href="#__codelineno-73-15"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]];</span>
|
||||
<a id="__codelineno-73-15" name="__codelineno-73-15" href="#__codelineno-73-15"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
|
||||
<a id="__codelineno-73-16" name="__codelineno-73-16" href="#__codelineno-73-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-73-17" name="__codelineno-73-17" href="#__codelineno-73-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-73-18" name="__codelineno-73-18" href="#__codelineno-73-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -5984,24 +5982,24 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 零钱兑换 II：空间优化后的动态规划 */</span>
|
||||
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kd">func</span> <span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a> <span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></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-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></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-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a> <span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></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-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></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-75-10" name="__codelineno-75-10" href="#__codelineno-75-10"></a> <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="n">a</span> <span class="p">{</span>
|
||||
<a id="__codelineno-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></a> <span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-75-12" name="__codelineno-75-12" href="#__codelineno-75-12"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-75-13" name="__codelineno-75-13" href="#__codelineno-75-13"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||
<a id="__codelineno-75-14" name="__codelineno-75-14" href="#__codelineno-75-14"></a> <span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-75-15" name="__codelineno-75-15" href="#__codelineno-75-15"></a> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
|
||||
<a id="__codelineno-75-16" name="__codelineno-75-16" href="#__codelineno-75-16"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-75-17" name="__codelineno-75-17" href="#__codelineno-75-17"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-75-18" name="__codelineno-75-18" href="#__codelineno-75-18"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-75-19" name="__codelineno-75-19" href="#__codelineno-75-19"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span>
|
||||
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
|
||||
<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w"> </span><span class="c1">// 状态转移</span>
|
||||
<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-75-10" name="__codelineno-75-10" href="#__codelineno-75-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></a><span class="w"> </span><span class="c1">// 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-75-12" name="__codelineno-75-12" href="#__codelineno-75-12"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
|
||||
<a id="__codelineno-75-13" name="__codelineno-75-13" href="#__codelineno-75-13"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-75-14" name="__codelineno-75-14" href="#__codelineno-75-14"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-75-15" name="__codelineno-75-15" href="#__codelineno-75-15"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span>
|
||||
<a id="__codelineno-75-16" name="__codelineno-75-16" href="#__codelineno-75-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-75-17" name="__codelineno-75-17" href="#__codelineno-75-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-75-18" name="__codelineno-75-18" href="#__codelineno-75-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-75-19" name="__codelineno-75-19" href="#__codelineno-75-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span>
|
||||
<a id="__codelineno-75-20" name="__codelineno-75-20" href="#__codelineno-75-20"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
@@ -6076,7 +6074,7 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 零钱兑换 II：空间优化后的动态规划 */</span>
|
||||
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">fn</span> <span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
|
||||
<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
|
||||
<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||||
@@ -6450,5 +6448,7 @@ aria-label="页脚"
|
||||
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
|
||||
|
||||
|
||||
<script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
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||||
<script id="init-glightbox">const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});
|
||||
document$.subscribe(() => { lightbox.reload() });
|
||||
</script></body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user