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tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><h1>找到数组中重复的数字</h1><h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="题目描述">题目描述<a href="#题目描述" class="hash-link" aria-label="Direct link to 题目描述" title="Direct link to 题目描述"></a></h2><p>找出数组中重复的数字。</p><p>在一个长度为 n 的数组 nums 里的所有数字都在 0 ~ n-1 的范围内。数组中某些数字是重复的，但不知道有几个数字重复了，也不知道每个数字重复了几次。请找出数组中任意一个重复的数字。</p><p>示例：</p><div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">输入：[2, 3, 1, 0, 2, 5, 3]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">输出：2 或 3</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg class="copyButtonIcon_y97N" viewBox="0 0 24 24"><path d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg class="copyButtonSuccessIcon_LjdS" viewBox="0 0 24 24"><path d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="解法一-哈希表">解法一： 哈希表<a href="#解法一-哈希表" class="hash-link" aria-label="Direct link to 解法一： 哈希表" title="Direct link to 解法一： 哈希表"></a></h2><p><a href="https://codesandbox.io/s/hzfe-suan-fa-shu-zu-zhong-chong-fu-shu-zi-ha-xi-biao-forked-p8df3?file=/index.html" target="_blank" rel="noopener noreferrer">在线链接</a></p><p>从题目中分析，只需要找到任意一个重复的数字，那么可以利用哈希表，用数字的值作为 key 去存储，如果遇到已经存在的 key，则直接返回，这样就找到了重复的数字。</p><h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="算法步骤">算法步骤<a href="#算法步骤" class="hash-link" aria-label="Direct link to 算法步骤" title="Direct link to 算法步骤"></a></h3><ol><li>声明哈希表用来保存遍历的值。</li><li>开始遍历数组。</li><li>获取当前值，判断值是否已经存在，若存在，则返回结果并结束循环；若不存在，则继续下一步。</li><li>储存当前值进哈希表。</li><li>处理数组下一位，重复直到遍历完成。</li></ol><div class="language-javascript codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-javascript codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">/**</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @param {number[]} nums</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @return {number}</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">const</span><span class="token plain"> </span><span class="token function-variable function" style="color:#d73a49">findRepeatNumber</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">function</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token parameter">nums</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">// 定义 hash 表</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">let</span><span class="token plain"> map </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">new</span><span class="token plain"> </span><span class="token class-name">Map</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">let</span><span class="token plain"> i </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">while</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34"><</span><span class="token plain"> nums</span><span class="token punctuation" style="color:#393A34">.</span><span class="token property-access">length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">// 如果存在当前数字，那么直接结束循环，返回当前数字</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">map</span><span class="token punctuation" style="color:#393A34">.</span><span class="token method function property-access" style="color:#d73a49">has</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> map</span><span class="token punctuation" style="color:#393A34">.</span><span class="token method function property-access" style="color:#d73a49">get</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">// 储存已经遍历过的值</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> map</span><span class="token punctuation" style="color:#393A34">.</span><span class="token method function property-access" style="color:#d73a49">set</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> i</span><span class="token operator" style="color:#393A34">++</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg class="copyButtonIcon_y97N" viewBox="0 0 24 24"><path d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg class="copyButtonSuccessIcon_LjdS" viewBox="0 0 24 24"><path d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="复杂度分析">复杂度分析<a href="#复杂度分析" class="hash-link" aria-label="Direct link to 复杂度分析" title="Direct link to 复杂度分析"></a></h3><ul><li>时间复杂度 O(N)：遍历一遍数组既可完成。</li><li>空间复杂度 O(N)：需要声明哈希表进行存储。</li></ul><h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="解法二-原地交换">解法二： 原地交换<a href="#解法二-原地交换" class="hash-link" aria-label="Direct link to 解法二： 原地交换" title="Direct link to 解法二： 原地交换"></a></h2><p><a href="https://codesandbox.io/s/hzfe-suan-fa-shu-zu-zhong-chong-fu-shu-zi-yuan-di-jiao-huan-forked-bxsby?file=/index.html" target="_blank" rel="noopener noreferrer">在线链接</a></p><p>我们可以把数组的值，交换到与该值相等的索引的位置。如果交换时发现，该索引的位置已经存在与当前值相等的值，则结束操作并返回当前值。</p><h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="算法步骤-1">算法步骤<a href="#算法步骤-1" class="hash-link" aria-label="Direct link to 算法步骤" title="Direct link to 算法步骤"></a></h3><ol><li>遍历数组。</li><li>判断当前值和索引是否相等，如果是，直接跳过处理下一个元素，不是，则进行下一步。</li><li>判断需要交换的索引位置的值，是否和当前值相等，如果是，则返回当前值并结束，不是，则进行下一步。</li><li>将当前值和对应索引位置的元素进行交换。</li><li>依次处理完全部元素。</li></ol><div class="language-javascript codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-javascript codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">/**</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @param {number[]} nums</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @return {number}</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">const</span><span class="token plain"> </span><span class="token function-variable function" style="color:#d73a49">findRepeatNumber</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">function</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token parameter">nums</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">let</span><span class="token plain"> i </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">while</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34"><</span><span class="token plain"> nums</span><span class="token punctuation" style="color:#393A34">.</span><span class="token property-access">length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">// 如果当前值等于索引，那么直接跳过</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">===</span><span class="token plain"> i</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> i</span><span class="token operator" style="color:#393A34">++</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">continue</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">// 如果需要交换的索引位置已经存在相同值，直接结束，返回当前值</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">===</span><span class="token plain"> nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">// 交换当前值，和对应索引存在的值</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">nums</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">i</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg class="copyButtonIcon_y97N" viewBox="0 0 24 24"><path d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg class="copyButtonSuccessIcon_LjdS" viewBox="0 0 24 24"><path d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="复杂度分析-1">复杂度分析<a href="#复杂度分析-1" class="hash-link" aria-label="Direct link to 复杂度分析" title="Direct link to 复杂度分析"></a></h3><ul><li>时间复杂度 O(N)：每个元素最多被移动 2 次。</li><li>空间复杂度 O(1)：不需要额外的空间完成。</li></ul><h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考资料">参考资料<a href="#参考资料" class="hash-link" aria-label="Direct link to 参考资料" title="Direct link to 参考资料"></a></h2><ol><li><a href="https://book.douban.com/subject/6966465/" target="_blank" rel="noopener noreferrer">剑指 offer</a></li></ol></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages navigation"><a class="pagination-nav__link pagination-nav__link--prev" href="/awesome-interview/book4/coding-apply-call-bind"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">编码：实现 apply/call/bind</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#题目描述" class="table-of-contents__link toc-highlight">题目描述</a></li><li><a href="#解法一-哈希表" class="table-of-contents__link toc-highlight">解法一： 哈希表</a><ul><li><a href="#算法步骤" class="table-of-contents__link toc-highlight">算法步骤</a></li><li><a href="#复杂度分析" class="table-of-contents__link toc-highlight">复杂度分析</a></li></ul></li><li><a 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