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[LeetCode] 540. Single Element in a Sorted Array · Issue #540 · grandyang/leetcode · GitHub
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Single Element in a Sorted Array · Issue #540 · 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="DD6A:384AF5:13A2DF5:1818238:67E7B8C1" data-pjax-transient="true"/><meta name="html-safe-nonce" content="a7c7ddf55594a2c5945ef48320d650f1e89ef72e75d14467a920fd99ec5fa8d3" data-pjax-transient="true"/><meta name="visitor-payload" content="eyJyZWZlcnJlciI6IiIsInJlcXVlc3RfaWQiOiJERDZBOjM4NEFGNToxM0EyREY1OjE4MTgyMzg6NjdFN0I4QzEiLCJ2aXNpdG9yX2lkIjoiMzM4NzY2NTQ1MDg1MjEzNzE1MyIsInJlZ2lvbl9lZGdlIjoic291dGhlYXN0YXNpYSIsInJlZ2lvbl9yZW5kZXIiOiJzb3V0aGVhc3Rhc2lhIn0=" data-pjax-transient="true"/><meta name="visitor-hmac" content="f584670203555f5425c0a7803adfd2bf578fa97bf4b1271afa5734a678a0a7b1" data-pjax-transient="true"/> <meta name="hovercard-subject-tag" content="issue:450390572" 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 a sorted array consisting of only integers where every element appears twice except for one element which appears once. 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data-data-router-enabled="false" > <script type="application/json" data-target="react-app.embeddedData">{"payload":{"preloaded_records":{},"preloadedQueries":[{"queryId":"3dddeeb0bc5f88ccaca7204fa97a09b8","queryName":"IssueViewerViewQuery","variables":{"id":"repository","number":540,"owner":"grandyang","repo":"leetcode"},"result":{"data":{"repository":{"isOwnerEnterpriseManaged":false,"issue":{"id":"MDU6SXNzdWU0NTAzOTA1NzI=","updatedAt":"2021-04-08T07:15:49Z","title":"[LeetCode] 540. Single Element in a Sorted Array","number":540,"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] 540. Single Element in a Sorted Array","url":"https://github.com/grandyang/leetcode/issues/540","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":450390572,"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 a sorted array consisting of only integers where every element appears twice except for one element which appears once. Find this single element that appears only once.\n\nExample 1:\n \n \n Input: [1,1,2,3,3,4,4,8,8]\n Output: 2\n \n\n \n\nExample 2:\n \n \n Input: [3,3,7,7,10,11,11]\n Output: 10\n \n\n \n\nNote: Your solution should run in O(log n) time and O(1) space.\n\n \n\n这道题给我们了一个有序数组，说是所有的元素都出现了两次，除了一个元素，让我们找到这个元素。如果没有时间复杂度的限制，我们可以用多种方法来做，最straightforward的解法就是用个双指针，每次检验两个，就能找出落单的。也可以像[Single Number](http://www.cnblogs.com/grandyang/p/4130577.html)里的方法那样，将所有数字亦或起来，相同的数字都会亦或成0，剩下就是那个落单的数字。那么由于有了时间复杂度的限制，需要为O(logn)，而数组又是有序的，不难想到要用二分搜索法来做。二分搜索法的难点在于折半了以后，如何判断将要去哪个分支继续搜索，而这道题确实判断条件不明显，比如下面两个例子：\n\n1 1 2 2 3\n\n1 2 2 3 3\n\n这两个例子初始化的时候left=0, right=4一样，mid算出来也一样为2，但是他们要去的方向不同，如何区分出来呢？仔细观察我们可以发现，如果当前数字出现两次的话，我们可以通过数组的长度跟当前位置的关系，计算出右边和当前数字不同的数字的总个数，如果是偶数个，说明落单数左半边，反之则在右半边。有了这个规律就可以写代码了，为啥我们直接就能跟mid+1比呢，不怕越界吗？当然不会，因为left如何跟right相等，就不会进入循环，所以mid一定会比right小，一定会有mid+1存在。当然mid是有可能为0的，所以此时当mid和mid+1的数字不等时，我们直接返回mid的数字就可以了，参见代码如下：\n\n \n\n解法一：\n \n \n class Solution {\n public:\n int singleNonDuplicate(vector\u003cint\u003e\u0026 nums) {\n int left = 0, right = nums.size() - 1, n = nums.size();\n while (left \u003c right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] == nums[mid + 1]) {\n if ((n - 1 - mid) % 2 == 1) right = mid;\n else left = mid + 1;\n } else {\n if (mid == 0 || nums[mid] != nums[mid - 1]) return nums[mid];\n if ((n - 1 - mid) % 2 == 0) right = mid;\n else left = mid + 1;\n }\n }\n return nums[left];\n }\n };\n\n \n\n下面这种解法是对上面的分支进行合并，使得代码非常的简洁。使用到了亦或1这个小技巧，为什么要亦或1呢，原来我们可以将坐标两两归为一对，比如0和1，2和3，4和5等等。而亦或1可以直接找到你的小伙伴，比如对于2，亦或1就是3，对于3，亦或1就是2。如果你和你的小伙伴相等了，说明落单数在右边，如果不等，说明在左边，这方法，太叼了有木有，参见代码如下：\n\n \n\n解法二：\n \n \n class Solution {\n public:\n int singleNonDuplicate(vector\u003cint\u003e\u0026 nums) {\n int left = 0, right = nums.size() - 1;\n while (left \u003c right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] == nums[mid ^ 1]) left = mid + 1;\n else right = mid;\n }\n return nums[left];\n }\n };\n\n \n\n下面这种解法其实跟上面的方法其实有些类似，虽然没有亦或1，但是将right缩小了一倍，但是在比较的时候，是比较mid*2和mid*2+1的关系的，这样还是能正确的比较原本应该相等的两个小伙伴的值的，其实核心思路和上面一样，参见代码如下：\n\n \n\n解法三：\n \n \n class Solution {\n public:\n int singleNonDuplicate(vector\u003cint\u003e\u0026 nums) {\n int left = 0, right = nums.size() / 2;\n while (left \u003c right) {\n int mid = left + (right - left) / 2;\n if (nums[mid * 2] == nums[mid * 2 + 1]) left = mid + 1;\n else right = mid;\n }\n return nums[left * 2];\n }\n };\n\n \n\n下面这种方法其实跟解法二很像，没有用亦或1，但是对mid进行了处理，强制使其成为小伙伴对儿中的第一个位置，然后跟另一个小伙伴比较大小，参见代码如下：\n\n \n\n解法四：\n \n \n class Solution {\n public:\n int singleNonDuplicate(vector\u003cint\u003e\u0026 nums) {\n int left = 0, right = nums.size() - 1;\n while (left \u003c right) {\n int mid = left + (right - left) / 2;\n if (mid % 2 == 1) --mid;\n if (nums[mid] == nums[mid + 1]) left = mid + 2;\n else right = mid;\n }\n return nums[left];\n }\n };\n\n \n\n参考资料：\n\n\u003chttps://discuss.leetcode.com/topic/83310/short-compare-nums-i-with-nums-i-1\u003e\n\n\u003chttps://discuss.leetcode.com/topic/82235/java-code-by-using-binary-search-o-log-n\u003e\n\n\u003chttps://discuss.leetcode.com/topic/82332/java-binary-search-o-log-n-shorter-than-others\u003e\n\n\u003chttps://discuss.leetcode.com/topic/87424/java-binary-search-short-7l-o-log-n-w-explanations\u003e\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 a sorted array consisting of only integers where every element appears twice except for one element which appears once. Find this single element that appears only once.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExample 1:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"Input: [1,1,2,3,3,4,4,8,8]\nOutput: 2\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eInput: [1,1,2,3,3,4,4,8,8]\nOutput: 2\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExample 2:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"Input: [3,3,7,7,10,11,11]\nOutput: 10\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eInput: [3,3,7,7,10,11,11]\nOutput: 10\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003eNote: Your solution should run in O(log n) time and O(1) space.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e这道题给我们了一个有序数组，说是所有的元素都出现了两次，除了一个元素，让我们找到这个元素。如果没有时间复杂度的限制，我们可以用多种方法来做，最straightforward的解法就是用个双指针，每次检验两个，就能找出落单的。也可以像\u003ca href=\"http://www.cnblogs.com/grandyang/p/4130577.html\" rel=\"nofollow\"\u003eSingle Number\u003c/a\u003e里的方法那样，将所有数字亦或起来，相同的数字都会亦或成0，剩下就是那个落单的数字。那么由于有了时间复杂度的限制，需要为O(logn)，而数组又是有序的，不难想到要用二分搜索法来做。二分搜索法的难点在于折半了以后，如何判断将要去哪个分支继续搜索，而这道题确实判断条件不明显，比如下面两个例子：\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e1 1 2 2 3\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e1 2 2 3 3\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e这两个例子初始化的时候left=0, right=4一样，mid算出来也一样为2，但是他们要去的方向不同，如何区分出来呢？仔细观察我们可以发现，如果当前数字出现两次的话，我们可以通过数组的长度跟当前位置的关系，计算出右边和当前数字不同的数字的总个数，如果是偶数个，说明落单数左半边，反之则在右半边。有了这个规律就可以写代码了，为啥我们直接就能跟mid+1比呢，不怕越界吗？当然不会，因为left如何跟right相等，就不会进入循环，所以mid一定会比right小，一定会有mid+1存在。当然mid是有可能为0的，所以此时当mid和mid+1的数字不等时，我们直接返回mid的数字就可以了，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 singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() - 1, n = nums.size();\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] == nums[mid + 1]) {\n if ((n - 1 - mid) % 2 == 1) right = mid;\n else left = mid + 1;\n } else {\n if (mid == 0 || nums[mid] != nums[mid - 1]) return nums[mid];\n if ((n - 1 - mid) % 2 == 0) right = mid;\n else left = mid + 1;\n }\n }\n return nums[left];\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() - 1, n = nums.size();\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] == nums[mid + 1]) {\n if ((n - 1 - mid) % 2 == 1) right = mid;\n else left = mid + 1;\n } else {\n if (mid == 0 || nums[mid] != nums[mid - 1]) return nums[mid];\n if ((n - 1 - mid) % 2 == 0) right = mid;\n else left = mid + 1;\n }\n }\n return nums[left];\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下面这种解法是对上面的分支进行合并，使得代码非常的简洁。使用到了亦或1这个小技巧，为什么要亦或1呢，原来我们可以将坐标两两归为一对，比如0和1，2和3，4和5等等。而亦或1可以直接找到你的小伙伴，比如对于2，亦或1就是3，对于3，亦或1就是2。如果你和你的小伙伴相等了，说明落单数在右边，如果不等，说明在左边，这方法，太叼了有木有，参见代码如下：\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 singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() - 1;\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] == nums[mid ^ 1]) left = mid + 1;\n else right = mid;\n }\n return nums[left];\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() - 1;\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid] == nums[mid ^ 1]) left = mid + 1;\n else right = mid;\n }\n return nums[left];\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下面这种解法其实跟上面的方法其实有些类似，虽然没有亦或1，但是将right缩小了一倍，但是在比较的时候，是比较mid\u003cem\u003e2和mid\u003c/em\u003e2+1的关系的，这样还是能正确的比较原本应该相等的两个小伙伴的值的，其实核心思路和上面一样，参见代码如下：\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 singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() / 2;\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid * 2] == nums[mid * 2 + 1]) left = mid + 1;\n else right = mid;\n }\n return nums[left * 2];\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() / 2;\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (nums[mid * 2] == nums[mid * 2 + 1]) left = mid + 1;\n else right = mid;\n }\n return nums[left * 2];\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下面这种方法其实跟解法二很像，没有用亦或1，但是对mid进行了处理，强制使其成为小伙伴对儿中的第一个位置，然后跟另一个小伙伴比较大小，参见代码如下：\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e \u003c/p\u003e\n\u003cp dir=\"auto\"\u003e解法四：\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"class Solution {\npublic:\n int singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() - 1;\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (mid % 2 == 1) --mid;\n if (nums[mid] == nums[mid + 1]) left = mid + 2;\n else right = mid;\n }\n return nums[left];\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int singleNonDuplicate(vector\u0026lt;int\u0026gt;\u0026amp; nums) {\n int left = 0, right = nums.size() - 1;\n while (left \u0026lt; right) {\n int mid = left + (right - left) / 2;\n if (mid % 2 == 1) --mid;\n if (nums[mid] == nums[mid + 1]) left = mid + 2;\n else right = mid;\n }\n return nums[left];\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参考资料：\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://discuss.leetcode.com/topic/83310/short-compare-nums-i-with-nums-i-1\" rel=\"nofollow\"\u003ehttps://discuss.leetcode.com/topic/83310/short-compare-nums-i-with-nums-i-1\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://discuss.leetcode.com/topic/82235/java-code-by-using-binary-search-o-log-n\" rel=\"nofollow\"\u003ehttps://discuss.leetcode.com/topic/82235/java-code-by-using-binary-search-o-log-n\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://discuss.leetcode.com/topic/82332/java-binary-search-o-log-n-shorter-than-others\" rel=\"nofollow\"\u003ehttps://discuss.leetcode.com/topic/82332/java-binary-search-o-log-n-shorter-than-others\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://discuss.leetcode.com/topic/87424/java-binary-search-short-7l-o-log-n-w-explanations\" rel=\"nofollow\"\u003ehttps://discuss.leetcode.com/topic/87424/java-binary-search-short-7l-o-log-n-w-explanations\u003c/a\u003e\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 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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 a sorted array consisting of only integers where every element appears twice except for one element which appears once. Find this single element that appears only once.</p> <p dir="auto">Example 1:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="Input: [1,1,2,3,3,4,4,8,8] Output: 2"><pre class="notranslate"><code class="notranslate">Input: [1,1,2,3,3,4,4,8,8] Output: 2 </code></pre></div> <p dir="auto"> </p> <p dir="auto">Example 2:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="Input: [3,3,7,7,10,11,11] Output: 10"><pre class="notranslate"><code class="notranslate">Input: [3,3,7,7,10,11,11] Output: 10 </code></pre></div> <p dir="auto"> </p> <p dir="auto">Note: Your solution should run in O(log n) time and O(1) space.</p> <p dir="auto"> </p> <p dir="auto">这道题给我们了一个有序数组，说是所有的元素都出现了两次，除了一个元素，让我们找到这个元素。如果没有时间复杂度的限制，我们可以用多种方法来做，最straightforward的解法就是用个双指针，每次检验两个，就能找出落单的。也可以像<a href="http://www.cnblogs.com/grandyang/p/4130577.html" rel="nofollow">Single Number</a>里的方法那样，将所有数字亦或起来，相同的数字都会亦或成0，剩下就是那个落单的数字。那么由于有了时间复杂度的限制，需要为O(logn)，而数组又是有序的，不难想到要用二分搜索法来做。二分搜索法的难点在于折半了以后，如何判断将要去哪个分支继续搜索，而这道题确实判断条件不明显，比如下面两个例子：</p> <p dir="auto">1 1 2 2 3</p> <p dir="auto">1 2 2 3 3</p> <p dir="auto">这两个例子初始化的时候left=0, right=4一样，mid算出来也一样为2，但是他们要去的方向不同，如何区分出来呢？仔细观察我们可以发现，如果当前数字出现两次的话，我们可以通过数组的长度跟当前位置的关系，计算出右边和当前数字不同的数字的总个数，如果是偶数个，说明落单数左半边，反之则在右半边。有了这个规律就可以写代码了，为啥我们直接就能跟mid+1比呢，不怕越界吗？当然不会，因为left如何跟right相等，就不会进入循环，所以mid一定会比right小，一定会有mid+1存在。当然mid是有可能为0的，所以此时当mid和mid+1的数字不等时，我们直接返回mid的数字就可以了，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 singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() - 1, n = nums.size(); while (left < right) { int mid = left + (right - left) / 2; if (nums[mid] == nums[mid + 1]) { if ((n - 1 - mid) % 2 == 1) right = mid; else left = mid + 1; } else { if (mid == 0 || nums[mid] != nums[mid - 1]) return nums[mid]; if ((n - 1 - mid) % 2 == 0) right = mid; else left = mid + 1; } } return nums[left]; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() - 1, n = nums.size(); while (left < right) { int mid = left + (right - left) / 2; if (nums[mid] == nums[mid + 1]) { if ((n - 1 - mid) % 2 == 1) right = mid; else left = mid + 1; } else { if (mid == 0 || nums[mid] != nums[mid - 1]) return nums[mid]; if ((n - 1 - mid) % 2 == 0) right = mid; else left = mid + 1; } } return nums[left]; } }; </code></pre></div> <p dir="auto"> </p> <p dir="auto">下面这种解法是对上面的分支进行合并，使得代码非常的简洁。使用到了亦或1这个小技巧，为什么要亦或1呢，原来我们可以将坐标两两归为一对，比如0和1，2和3，4和5等等。而亦或1可以直接找到你的小伙伴，比如对于2，亦或1就是3，对于3，亦或1就是2。如果你和你的小伙伴相等了，说明落单数在右边，如果不等，说明在左边，这方法，太叼了有木有，参见代码如下：</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 singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() - 1; while (left < right) { int mid = left + (right - left) / 2; if (nums[mid] == nums[mid ^ 1]) left = mid + 1; else right = mid; } return nums[left]; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() - 1; while (left < right) { int mid = left + (right - left) / 2; if (nums[mid] == nums[mid ^ 1]) left = mid + 1; else right = mid; } return nums[left]; } }; </code></pre></div> <p dir="auto"> </p> <p dir="auto">下面这种解法其实跟上面的方法其实有些类似，虽然没有亦或1，但是将right缩小了一倍，但是在比较的时候，是比较mid<em>2和mid</em>2+1的关系的，这样还是能正确的比较原本应该相等的两个小伙伴的值的，其实核心思路和上面一样，参见代码如下：</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 singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() / 2; while (left < right) { int mid = left + (right - left) / 2; if (nums[mid * 2] == nums[mid * 2 + 1]) left = mid + 1; else right = mid; } return nums[left * 2]; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() / 2; while (left < right) { int mid = left + (right - left) / 2; if (nums[mid * 2] == nums[mid * 2 + 1]) left = mid + 1; else right = mid; } return nums[left * 2]; } }; </code></pre></div> <p dir="auto"> </p> <p dir="auto">下面这种方法其实跟解法二很像，没有用亦或1，但是对mid进行了处理，强制使其成为小伙伴对儿中的第一个位置，然后跟另一个小伙伴比较大小，参见代码如下：</p> <p dir="auto"> </p> <p dir="auto">解法四：</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="class Solution { public: int singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() - 1; while (left < right) { int mid = left + (right - left) / 2; if (mid % 2 == 1) --mid; if (nums[mid] == nums[mid + 1]) left = mid + 2; else right = mid; } return nums[left]; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int singleNonDuplicate(vector<int>& nums) { int left = 0, right = nums.size() - 1; while (left < right) { int mid = left + (right - left) / 2; if (mid % 2 == 1) --mid; if (nums[mid] == nums[mid + 1]) left = mid + 2; else right = mid; } return nums[left]; } }; </code></pre></div> <p dir="auto"> </p> <p dir="auto">参考资料：</p> <p dir="auto"><a href="https://discuss.leetcode.com/topic/83310/short-compare-nums-i-with-nums-i-1" rel="nofollow">https://discuss.leetcode.com/topic/83310/short-compare-nums-i-with-nums-i-1</a></p> <p dir="auto"><a href="https://discuss.leetcode.com/topic/82235/java-code-by-using-binary-search-o-log-n" rel="nofollow">https://discuss.leetcode.com/topic/82235/java-code-by-using-binary-search-o-log-n</a></p> <p dir="auto"><a 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width="16" 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>