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Missing Number · Issue #268 · grandyang/leetcode · GitHub</title> <meta name="route-pattern" content="/_view_fragments/issues/show/:user_id/:repository/:id/issue_layout(.:format)" data-turbo-transient> <meta name="route-controller" content="voltron_issues_fragments" data-turbo-transient> <meta name="route-action" content="issue_layout" data-turbo-transient> <meta name="current-catalog-service-hash" content="81bb79d38c15960b92d99bca9288a9108c7a47b18f2423d0f6438c5b7bcd2114"> <meta name="request-id" content="8EF8:372A2A:46715:5B40D:67EAEAC4" data-pjax-transient="true"/><meta name="html-safe-nonce" content="da4e0fe921d2c5a3845a2d83b1d63c5c13b3509ff1ce286fd6b2257d074f5387" data-pjax-transient="true"/><meta name="visitor-payload" content="eyJyZWZlcnJlciI6IiIsInJlcXVlc3RfaWQiOiI4RUY4OjM3MkEyQTo0NjcxNTo1QjQwRDo2N0VBRUFDNCIsInZpc2l0b3JfaWQiOiIxNDMzNjcwMTAxMDExOTgzMDQ0IiwicmVnaW9uX2VkZ2UiOiJzb3V0aGVhc3Rhc2lhIiwicmVnaW9uX3JlbmRlciI6InNvdXRoZWFzdGFzaWEifQ==" data-pjax-transient="true"/><meta name="visitor-hmac" content="7469ef24b868cacb4a8721997b205d058171562952713ae4713a95547b8fb5ca" data-pjax-transient="true"/> <meta name="hovercard-subject-tag" content="issue:450388133" data-turbo-transient> <meta name="github-keyboard-shortcuts" content="repository,issues,copilot" data-turbo-transient="true" /> <meta name="selected-link" value="repo_issues" data-turbo-transient> <link rel="assets" href="https://github.githubassets.com/"> <meta name="google-site-verification" content="Apib7-x98H0j5cPqHWwSMm6dNU4GmODRoqxLiDzdx9I"> <meta name="octolytics-url" content="https://collector.github.com/github/collect" /> <meta name="analytics-location" content="/<user-name>/<repo-name>/voltron/issues_fragments/issue_layout" data-turbo-transient="true" /> <meta name="user-login" content=""> <meta name="viewport" content="width=device-width"> <meta name="description" content="Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array. For example, Given nums = [0, 1, 3] return 2. Note : Your algorithm should run in linear runtime complexity. Could you ..."> <link rel="search" type="application/opensearchdescription+xml" href="/opensearch.xml" title="GitHub"> <link rel="fluid-icon" href="https://github.com/fluidicon.png" title="GitHub"> <meta property="fb:app_id" content="1401488693436528"> <meta name="apple-itunes-app" content="app-id=1477376905, app-argument=https://github.com/_view_fragments/issues/show/grandyang/leetcode/268/issue_layout" /> <meta name="twitter:image" content="https://opengraph.githubassets.com/9ad33ca67a6f8a26fcfee576f42380bce7b660da5e7b6b29a8311b64a86ca3bb/grandyang/leetcode/issues/268" /><meta name="twitter:site" content="@github" /><meta name="twitter:card" content="summary_large_image" /><meta name="twitter:title" content="[LeetCode] 268. Missing Number · Issue #268 · grandyang/leetcode" /><meta name="twitter:description" content="Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array. For example, Given nums = [0, 1, 3] return 2. Note : Your algorithm should run ..." /> <meta property="og:image" content="https://opengraph.githubassets.com/9ad33ca67a6f8a26fcfee576f42380bce7b660da5e7b6b29a8311b64a86ca3bb/grandyang/leetcode/issues/268" /><meta property="og:image:alt" content="Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array. For example, Given nums = [0, 1, 3] return 2. Note : Your algorithm should run ..." /><meta property="og:image:width" content="1200" /><meta property="og:image:height" content="600" /><meta property="og:site_name" content="GitHub" /><meta property="og:type" content="object" /><meta property="og:title" content="[LeetCode] 268. Missing Number · Issue #268 · grandyang/leetcode" /><meta property="og:url" content="https://github.com/grandyang/leetcode/issues/268" /><meta property="og:description" content="Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array. For example, Given nums = [0, 1, 3] return 2. 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data-target="react-app.embeddedData">{"payload":{"preloaded_records":{},"preloadedQueries":[{"queryId":"3dddeeb0bc5f88ccaca7204fa97a09b8","queryName":"IssueViewerViewQuery","variables":{"id":"repository","number":268,"owner":"grandyang","repo":"leetcode"},"result":{"data":{"repository":{"isOwnerEnterpriseManaged":false,"issue":{"id":"MDU6SXNzdWU0NTAzODgxMzM=","updatedAt":"2021-04-08T07:06:09Z","title":"[LeetCode] 268. Missing Number","number":268,"repository":{"nameWithOwner":"grandyang/leetcode","id":"MDEwOlJlcG9zaXRvcnkxODk0NDQ0MjM=","name":"leetcode","owner":{"__typename":"User","login":"grandyang","id":"MDQ6VXNlcjg1NTMwMTA=","url":"https://github.com/grandyang"},"isArchived":false,"isPrivate":false,"databaseId":189444423,"slashCommandsEnabled":false,"viewerCanInteract":false,"viewerInteractionLimitReasonHTML":"","planFeatures":{"maximumAssignees":10},"visibility":"PUBLIC","pinnedIssues":{"totalCount":0},"viewerCanPinIssues":false,"issueTypes":null},"titleHTML":"[LeetCode] 268. Missing Number","url":"https://github.com/grandyang/leetcode/issues/268","viewerCanUpdateNext":false,"issueType":null,"state":"OPEN","stateReason":null,"duplicateOf":null,"linkedPullRequests":{"nodes":[]},"subIssuesSummary":{"total":0,"completed":0},"__isLabelable":"Issue","labels":{"edges":[],"pageInfo":{"endCursor":null,"hasNextPage":false}},"__isNode":"Issue","assignees":{"nodes":[]},"milestone":null,"databaseId":450388133,"viewerDidAuthor":false,"locked":false,"author":{"__typename":"User","__isActor":"User","login":"grandyang","id":"MDQ6VXNlcjg1NTMwMTA=","profileUrl":"https://github.com/grandyang","avatarUrl":"https://avatars.githubusercontent.com/u/8553010?u=e77fff8485af7a0dd7160048240bf9272e4be8cf\u0026v=4"},"__isComment":"Issue","body":" \n\nGiven an array containing _n_ distinct numbers taken from `0, 1, 2, ..., n`, find the one that is missing from the array.\n\nFor example, \nGiven _nums_ = `[0, 1, 3]` return `2`. \n\n**Note** : \nYour algorithm should run in linear runtime complexity. Could you implement it using only constant extra space complexity? \n\n \n\n这道题给我们n个数字，是0到n之间的数但是有一个数字去掉了，让我们寻找这个数字，要求线性的时间复杂度和常数级的空间复杂度。那么最直观的一个方法是用等差数列的求和公式求出0到n之间所有的数字之和，然后再遍历数组算出给定数字的累积和，然后做减法，差值就是丢失的那个数字，参见代码如下：\n\n \n\n解法一：\n \n \n class Solution {\n public:\n int missingNumber(vector\u003cint\u003e\u0026 nums) {\n int sum = 0, n = nums.size();\n for (auto \u0026a : nums) {\n sum += a;\n }\n return 0.5 * n * (n + 1) - sum;\n }\n };\n\n \n\n这题还有一种解法，使用位操作Bit Manipulation来解的，用到了异或操作的特性，相似的题目有[Single Number 单独的数字,](http://www.cnblogs.com/Given%20an%20array%20of%20integers,%20every%20element%20appears%20three%20times%20except%20for%20one.%20Find%20that%20single%20one.%20%20Note:%20Your%20algorithm%20should%20have%20a%20linear%20runtime%20complexity.%20Could%20you%20implement%20it%20without%20using%20extra%20memory) [Single Number II 单独的数字之二](http://www.cnblogs.com/grandyang/p/4263927.html)和[Single Number III 单独的数字之三](http://www.cnblogs.com/grandyang/p/4741122.html)。那么思路是既然0到n之间少了一个数，我们将这个少了一个数的数组合0到n之间完整的数组异或一下，那么相同的数字都变为0了，剩下的就是少了的那个数字了，参加代码如下：\n\n \n\n解法二：\n \n \n class Solution {\n public:\n int missingNumber(vector\u003cint\u003e\u0026 nums) {\n int res = 0;\n for (int i = 0; i \u003c nums.size(); ++i) {\n res ^= (i + 1) ^ nums[i];\n }\n return res;\n }\n };\n\n \n\n这道题还可以用二分查找法来做，我们首先要对数组排序，然后我们用二分查找法算出中间元素的下标，然后用元素值和下标值之间做对比，如果元素值大于下标值，则说明缺失的数字在左边，此时将right赋为mid，反之则将left赋为mid+1。那么看到这里，作为读者的你可能会提出，排序的时间复杂度都不止O(n)，何必要多此一举用二分查找，还不如用上面两种方法呢。对，你说的没错，但是在面试的时候，有可能人家给你的数组就是排好序的，那么此时用二分查找法肯定要优于上面两种方法，所以这种方法最好也要掌握以下~\n\n \n\n解法三：\n \n \n class Solution {\n public:\n int missingNumber(vector\u003cint\u003e\u0026 nums) {\n sort(nums.begin(), nums.end());\n int left = 0, right = nums.size();\n while (left \u003c right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] \u003e mid) right = mid;\n else left = mid + 1;\n }\n return right;\n }\n };\n\n \n\n在CareerCup中有一道类似的题，[5.7 Find Missing Integer 查找丢失的数](http://www.cnblogs.com/grandyang/p/4747429.html)，但是那道题不让我们直接访问整个int数字，而是只能访问其二进制表示数中的某一位，强行让我们使用位操作Bit Manipulation来解题，也是蛮有意思的一道题。\n\n \n\n[LeetCode All in One 题目讲解汇总(持续更新中...)](http://www.cnblogs.com/grandyang/p/4606334.html)\n","bodyHTML":"\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003eGiven an array containing \u003cem\u003en\u003c/em\u003e distinct numbers taken from \u003ccode class=\"notranslate\"\u003e0, 1, 2, ..., n\u003c/code\u003e, find the one that is missing from the array.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFor example,\u003cbr\u003e\nGiven \u003cem\u003enums\u003c/em\u003e = \u003ccode class=\"notranslate\"\u003e[0, 1, 3]\u003c/code\u003e return \u003ccode class=\"notranslate\"\u003e2\u003c/code\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eNote\u003c/strong\u003e :\u003cbr\u003e\nYour algorithm should run in linear runtime complexity. Could you implement it using only constant extra space complexity?\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e这道题给我们n个数字，是0到n之间的数但是有一个数字去掉了，让我们寻找这个数字，要求线性的时间复杂度和常数级的空间复杂度。那么最直观的一个方法是用等差数列的求和公式求出0到n之间所有的数字之和，然后再遍历数组算出给定数字的累积和，然后做减法，差值就是丢失的那个数字，参见代码如下：\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e解法一：\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"class Solution {\npublic:\n int missingNumber(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int sum = 0, n = nums.size();\n for (auto \u0026amp;a : nums) {\n sum += a;\n }\n return 0.5 * n * (n + 1) - sum;\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int missingNumber(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int sum = 0, n = nums.size();\n for (auto \u0026amp;a : nums) {\n sum += a;\n }\n return 0.5 * n * (n + 1) - sum;\n }\n};\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e这题还有一种解法，使用位操作Bit Manipulation来解的，用到了异或操作的特性，相似的题目有\u003ca href=\"http://www.cnblogs.com/Given%20an%20array%20of%20integers,%20every%20element%20appears%20three%20times%20except%20for%20one.%20Find%20that%20single%20one.%20%20Note:%20Your%20algorithm%20should%20have%20a%20linear%20runtime%20complexity.%20Could%20you%20implement%20it%20without%20using%20extra%20memory\" rel=\"nofollow\"\u003eSingle Number 单独的数字,\u003c/a\u003e \u003ca href=\"http://www.cnblogs.com/grandyang/p/4263927.html\" rel=\"nofollow\"\u003eSingle Number II 单独的数字之二\u003c/a\u003e和\u003ca href=\"http://www.cnblogs.com/grandyang/p/4741122.html\" rel=\"nofollow\"\u003eSingle Number III 单独的数字之三\u003c/a\u003e。那么思路是既然0到n之间少了一个数，我们将这个少了一个数的数组合0到n之间完整的数组异或一下，那么相同的数字都变为0了，剩下的就是少了的那个数字了，参加代码如下：\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e解法二：\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"class Solution {\npublic:\n int missingNumber(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int res = 0;\n for (int i = 0; i \u0026lt; nums.size(); ++i) {\n res ^= (i + 1) ^ nums[i];\n }\n return res;\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int missingNumber(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int res = 0;\n for (int i = 0; i \u0026lt; nums.size(); ++i) {\n res ^= (i + 1) ^ nums[i];\n }\n return res;\n }\n};\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e这道题还可以用二分查找法来做，我们首先要对数组排序，然后我们用二分查找法算出中间元素的下标，然后用元素值和下标值之间做对比，如果元素值大于下标值，则说明缺失的数字在左边，此时将right赋为mid，反之则将left赋为mid+1。那么看到这里，作为读者的你可能会提出，排序的时间复杂度都不止O(n)，何必要多此一举用二分查找，还不如用上面两种方法呢。对，你说的没错，但是在面试的时候，有可能人家给你的数组就是排好序的，那么此时用二分查找法肯定要优于上面两种方法，所以这种方法最好也要掌握以下~\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e解法三：\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"class Solution {\npublic:\n int missingNumber(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n sort(nums.begin(), nums.end());\n int left = 0, right = nums.size();\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] \u0026gt; mid) right = mid;\n else left = mid + 1;\n }\n return right;\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int missingNumber(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n sort(nums.begin(), nums.end());\n int left = 0, right = nums.size();\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] \u0026gt; mid) right = mid;\n else left = mid + 1;\n }\n return right;\n }\n};\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e在CareerCup中有一道类似的题，\u003ca href=\"http://www.cnblogs.com/grandyang/p/4747429.html\" rel=\"nofollow\"\u003e5.7 Find Missing Integer 查找丢失的数\u003c/a\u003e，但是那道题不让我们直接访问整个int数字，而是只能访问其二进制表示数中的某一位，强行让我们使用位操作Bit Manipulation来解题，也是蛮有意思的一道题。\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"http://www.cnblogs.com/grandyang/p/4606334.html\" rel=\"nofollow\"\u003eLeetCode All in One 题目讲解汇总(持续更新中...)\u003c/a\u003e\u003c/p\u003e","bodyVersion":"bb5978b2e72d5fec50c1c9b6c81a7df464e4894b90035ebb3791dc22179ed85b","createdAt":"2019-05-30T16:18:11Z","__isReactable":"Issue","reactionGroups":[{"content":"THUMBS_UP","viewerHasReacted":false,"reactors":{"totalCount":1,"nodes":[{"__typename":"User","login":"wailaifeike","__isNode":"User","id":"MDQ6VXNlcjM5NjY4OTIz"}]}},{"content":"THUMBS_DOWN","viewerHasReacted":false,"reactors":{"totalCount":0,"nodes":[]}},{"content":"LAUGH","viewerHasReacted":false,"reactors":{"totalCount":0,"nodes":[]}},{"content":"HOORAY","viewerHasReacted":false,"reactors":{"totalCount":0,"nodes":[]}},{"content":"CONFUSED","viewerHasReacted":false,"reactors":{"totalCount":0,"nodes":[]}},{"content":"HEART","viewerHasReacted":false,"reactors":{"totalCount":0,"nodes":[]}},{"content":"ROCKET","viewerHasReacted":false,"reactors":{"totalCount":0,"nodes":[]}},{"content":"EYES","viewerHasReacted":false,"reactors":{"totalCount":0,"nodes":[]}}],"viewerCanUpdateMetadata":false,"viewerCanComment":false,"viewerCanAssign":false,"viewerCanLabel":false,"__isIssueOrPullRequest":"Issue","projectItemsNext":{"edges":[],"pageInfo":{"endCursor":null,"hasNextPage":false}},"viewerCanSetMilestone":false,"isPinned":false,"viewerCanDelete":false,"viewerCanTransfer":false,"viewerCanConvertToDiscussion":false,"viewerCanLock":false,"viewerCanType":false,"frontTimelineItems":{"pageInfo":{"hasNextPage":false,"endCursor":"Y3Vyc29yOnYyOpPPAAABcYCWh6gCqjEwMjk4MTAwNTE="},"totalCount":1,"edges":[{"node":{"__typename":"CrossReferencedEvent","__isIssueTimelineItems":"CrossReferencedEvent","__isTimelineEvent":"CrossReferencedEvent","databaseId":1029810051,"createdAt":"2020-04-16T01:24:41Z","actor":{"__typename":"User","login":"Woodyiiiiiii","id":"MDQ6VXNlcjM2Mzk1NzIx","__isActor":"User","avatarUrl":"https://avatars.githubusercontent.com/u/36395721?s=64\u0026u=811035d29ef9c27fb9a968bbcb6d8debf6173ee1\u0026v=4"},"source":{"__typename":"Issue","__isNode":"Issue","id":"MDU6SXNzdWU2MDA2ODIzODU="},"willCloseTarget":false,"referencedAt":"2020-04-16T01:24:41Z","target":{"__typename":"Issue","repository":{"id":"MDEwOlJlcG9zaXRvcnkxODk0NDQ0MjM="},"__isNode":"Issue","id":"MDU6SXNzdWU0NTAzODgxMzM="},"innerSource":{"__typename":"Issue","__isReferencedSubject":"Issue","id":"MDU6SXNzdWU2MDA2ODIzODU=","issueTitleHTML":"LeetCode 268. 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Missing Number</bdi></a><span class="Box-sc-g0xbh4-0 iQfnYL prc-Text-Text-0ima0">#268</span></div><div class="Box-sc-g0xbh4-0 jGasrR"></div></div><div><div class="Box-sc-g0xbh4-0 cQpCwc"><button data-component="IconButton" type="button" class="prc-Button-ButtonBase-c50BI prc-Button-IconButton-szpyj" data-loading="false" data-no-visuals="true" data-size="medium" data-variant="invisible" aria-describedby=":R77i9b:-loading-announcement" aria-labelledby=":R7i9b:"><svg aria-hidden="true" focusable="false" class="octicon octicon-copy" viewBox="0 0 16 16" width="16" height="16" fill="currentColor" display="inline-block" overflow="visible" style="vertical-align:text-bottom"><path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 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data-testid="github-avatar"/></a></div><div class="Box-sc-g0xbh4-0 koxHLL ActivityHeader-module__narrowViewportWrapper--Hjl75"><div class="Box-sc-g0xbh4-0 dqmClk"><a class="Box-sc-g0xbh4-0 cRhwji prc-Link-Link-85e08" href="https://github.com/grandyang" data-hovercard-url="/users/grandyang/hovercard" data-testid="issue-body-header-author">grandyang</a></div><div class="Box-sc-g0xbh4-0 bJQcYY ActivityHeader-module__footer--FVHp7"><span>opened </span><a class="Box-sc-g0xbh4-0 bjFvWy prc-Link-Link-85e08" href="https://github.com/grandyang/leetcode/issues/268#issue-450388133" data-testid="issue-body-header-link"><relative-time sx="[object Object]" class="sc-aXZVg gcWyXp">on May 30, 2019</relative-time></a></div></div><div class="Box-sc-g0xbh4-0 kgTqOk ActivityHeader-module__narrowViewportWrapper--Hjl75"><div class="Box-sc-g0xbh4-0 izrTon ActivityHeader-module__edits--LwHTE"></div><div class="Box-sc-g0xbh4-0 kpoUe"><div class="Box-sc-g0xbh4-0 ezcJRX"></div><div class="Box-sc-g0xbh4-0 dnyPuu"><button data-component="IconButton" type="button" aria-haspopup="true" aria-expanded="false" tabindex="0" class="prc-Button-ButtonBase-c50BI prc-Button-IconButton-szpyj" data-loading="false" data-no-visuals="true" data-size="small" data-variant="invisible" aria-describedby=":R15bd5db:-loading-announcement" aria-labelledby=":Rv5bd5db:" id=":R15bd5db:"><svg aria-hidden="true" focusable="false" class="octicon octicon-kebab-horizontal" viewBox="0 0 16 16" width="16" height="16" fill="currentColor" display="inline-block" overflow="visible" style="vertical-align:text-bottom"><path d="M8 9a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3ZM1.5 9a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3Zm13 0a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3Z"></path></svg></button><span class="prc-TooltipV2-Tooltip-cYMVY" data-direction="s" aria-hidden="true" id=":Rv5bd5db:">Issue body actions</span></div></div></div></div></div><div class="IssueBodyViewer-module__IssueBody--MXyFt"><div data-testid="markdown-body" data-team-hovercards-enabled="true" class="markdown-body" data-turbolinks="false"><div class="Box-sc-g0xbh4-0 markdown-body NewMarkdownViewer-module__safe-html-box--cRsz0"><p dir="auto"> </p> <p dir="auto">Given an array containing <em>n</em> distinct numbers taken from <code class="notranslate">0, 1, 2, ..., n</code>, find the one that is missing from the array.</p> <p dir="auto">For example,<br> Given <em>nums</em> = <code class="notranslate">[0, 1, 3]</code> return <code class="notranslate">2</code>.</p> <p dir="auto"><strong>Note</strong> :<br> Your algorithm should run in linear runtime complexity. Could you implement it using only constant extra space complexity?</p> <p dir="auto"> </p> <p dir="auto">这道题给我们n个数字，是0到n之间的数但是有一个数字去掉了，让我们寻找这个数字，要求线性的时间复杂度和常数级的空间复杂度。那么最直观的一个方法是用等差数列的求和公式求出0到n之间所有的数字之和，然后再遍历数组算出给定数字的累积和，然后做减法，差值就是丢失的那个数字，参见代码如下：</p> <p dir="auto"> </p> <p dir="auto">解法一：</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="class Solution { public: int missingNumber(vector<int>& nums) { int sum = 0, n = nums.size(); for (auto &a : nums) { sum += a; } return 0.5 * n * (n + 1) - sum; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int missingNumber(vector<int>& nums) { int sum = 0, n = nums.size(); for (auto &a : nums) { sum += a; } return 0.5 * n * (n + 1) - sum; } }; </code></pre></div> <p dir="auto"> </p> <p dir="auto">这题还有一种解法，使用位操作Bit Manipulation来解的，用到了异或操作的特性，相似的题目有<a href="http://www.cnblogs.com/Given%20an%20array%20of%20integers,%20every%20element%20appears%20three%20times%20except%20for%20one.%20Find%20that%20single%20one.%20%20Note:%20Your%20algorithm%20should%20have%20a%20linear%20runtime%20complexity.%20Could%20you%20implement%20it%20without%20using%20extra%20memory" rel="nofollow">Single Number 单独的数字,</a> <a href="http://www.cnblogs.com/grandyang/p/4263927.html" rel="nofollow">Single Number II 单独的数字之二</a>和<a href="http://www.cnblogs.com/grandyang/p/4741122.html" rel="nofollow">Single Number III 单独的数字之三</a>。那么思路是既然0到n之间少了一个数，我们将这个少了一个数的数组合0到n之间完整的数组异或一下，那么相同的数字都变为0了，剩下的就是少了的那个数字了，参加代码如下：</p> <p dir="auto"> </p> <p dir="auto">解法二：</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="class Solution { public: int missingNumber(vector<int>& nums) { int res = 0; for (int i = 0; i < nums.size(); ++i) { res ^= (i + 1) ^ nums[i]; } return res; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int missingNumber(vector<int>& nums) { int res = 0; for (int i = 0; i < nums.size(); ++i) { res ^= (i + 1) ^ nums[i]; } return res; } }; </code></pre></div> <p dir="auto"> </p> <p dir="auto">这道题还可以用二分查找法来做，我们首先要对数组排序，然后我们用二分查找法算出中间元素的下标，然后用元素值和下标值之间做对比，如果元素值大于下标值，则说明缺失的数字在左边，此时将right赋为mid，反之则将left赋为mid+1。那么看到这里，作为读者的你可能会提出，排序的时间复杂度都不止O(n)，何必要多此一举用二分查找，还不如用上面两种方法呢。对，你说的没错，但是在面试的时候，有可能人家给你的数组就是排好序的，那么此时用二分查找法肯定要优于上面两种方法，所以这种方法最好也要掌握以下~</p> <p dir="auto"> </p> <p dir="auto">解法三：</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="class Solution { public: int missingNumber(vector<int>& nums) { sort(nums.begin(), nums.end()); int left = 0, right = nums.size(); while (left < right) { int mid = left + (right - left) / 2; if (nums[mid] > mid) right = mid; else left = mid + 1; } return right; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int missingNumber(vector<int>& nums) { sort(nums.begin(), nums.end()); int left = 0, right = nums.size(); while (left < right) { int mid = left + (right - left) / 2; if (nums[mid] > mid) right = mid; else left = mid + 1; } return right; } }; </code></pre></div> <p dir="auto"> </p> <p dir="auto">在CareerCup中有一道类似的题，<a href="http://www.cnblogs.com/grandyang/p/4747429.html" rel="nofollow">5.7 Find Missing Integer 查找丢失的数</a>，但是那道题不让我们直接访问整个int数字，而是只能访问其二进制表示数中的某一位，强行让我们使用位操作Bit Manipulation来解题，也是蛮有意思的一道题。</p> <p dir="auto"> </p> <p dir="auto"><a href="http://www.cnblogs.com/grandyang/p/4606334.html" rel="nofollow">LeetCode All in One 题目讲解汇总(持续更新中...)</a></p></div></div><div class="IssueBodyViewer-module__IssueBodyTaskList--r4XEH"><div role="toolbar" aria-label="Reactions" class="d-flex gap-1 flex-wrap"><span role="tooltip" aria-label="wailaifeike" id=":R6il5db:" class="Tooltip__TooltipBase-sc-17tf59c-0 dNXcPh tooltipped-ne tooltipped-align-left-2 tooltipped-multiline"><button type="button" 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data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon m-2"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none m-2"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> <template id="snippet-clipboard-copy-button-unpositioned"> <div class="zeroclipboard-container"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn btn-invisible js-clipboard-copy m-2 p-0 d-flex flex-justify-center flex-items-center" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> </div> <div id="js-global-screen-reader-notice" class="sr-only mt-n1" aria-live="polite" aria-atomic="true" ></div> <div id="js-global-screen-reader-notice-assertive" class="sr-only mt-n1" aria-live="assertive" aria-atomic="true"></div> </body> </html>