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<h2 class="post-title" itemprop="name headline">Leetcode 377: Combination Sum IV
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<h3 id="题目描述"><a href="#题目描述" class="headerlink" title="题目描述"></a>题目描述</h3><p>给定一个由正整数组成且不存在重复数字的数组，找出和为给定目标正整数的组合的个数。<br><a id="more"></a></p>
<h3 id="示例"><a href="#示例" class="headerlink" title="示例"></a>示例</h3><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line">nums = [1, 2, 3]</span><br><span class="line">target = 4</span><br><span class="line"></span><br><span class="line">所有可能的组合为：</span><br><span class="line">(1, 1, 1, 1)</span><br><span class="line">(1, 1, 2)</span><br><span class="line">(1, 2, 1)</span><br><span class="line">(1, 3)</span><br><span class="line">(2, 1, 1)</span><br><span class="line">(2, 2)</span><br><span class="line">(3, 1)</span><br><span class="line"></span><br><span class="line">请注意，顺序不同的序列被视作不同的组合。</span><br><span class="line"></span><br><span class="line">因此输出为 7。</span><br></pre></td></tr></table></figure>
<h3 id="解题思路"><a href="#解题思路" class="headerlink" title="解题思路"></a>解题思路</h3><p>这是一个比较典型的动态规划问题。假设数组中元素为3个：m, n, k。那么我们可以知道任何一个数num，即dp[num] = dp[num - m] + dp[num - n] + dp[num - k]。<br>比如示例中，dp[4] = dp[3] + dp[2] + dp[1]，而dp[3] = dp[2] + dp[1] + dp[0]，这儿的dp[0] = 1。所以我们从dp[0]一次往后计算，即可得到dp[target]。</p>
<h3 id="解题代码"><a href="#解题代码" class="headerlink" title="解题代码"></a>解题代码</h3><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">combinationSum4</span><span class="params">(<span class="keyword">int</span>[] nums, <span class="keyword">int</span> target)</span> </span>{</span><br><span class="line"> <span class="keyword">int</span>[] dp = <span class="keyword">new</span> <span class="keyword">int</span>[target+<span class="number">1</span>];</span><br><span class="line"> dp[<span class="number">0</span>] = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">1</span>; i < dp.length; i++) {</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> ele : nums) {</span><br><span class="line"> <span class="keyword">if</span> (i - ele >= <span class="number">0</span>) dp[i] += dp[i-ele];</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> dp[target];</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
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