{"id":738,"date":"2017-11-04T23:55:23","date_gmt":"2017-11-05T06:55:23","guid":{"rendered":"http:\/\/zxi.mytechroad.com\/blog\/?p=738"},"modified":"2018-04-19T08:36:32","modified_gmt":"2018-04-19T15:36:32","slug":"leetcode-169-majority-element","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/divide-and-conquer\/leetcode-169-majority-element\/","title":{"rendered":"\u82b1\u82b1\u9171  LeetCode 169. Majority Element"},"content":{"rendered":"<p><iframe loading=\"lazy\" title=\"\u82b1\u82b1\u9171 LeetCode 169. Majority Element - \u5237\u9898\u627e\u5de5\u4f5c EP101\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/LPIvL-jvGdA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>\u9898\u76ee\u5927\u610f\uff1a\u7ed9\u4f60\u4e00\u4e2a\u6570\u7ec4\uff0c\u5176\u4e2d\u4e00\u4e2a\u6570\u51fa\u73b0\u8d85\u8fc7n\/2\u6b21\uff0c\u95ee\u4f60\u51fa\u73b0\u6b21\u6570\u6700\u591a\u7684\u90a3\u4e2a\u6570\u662f\u4ec0\u4e48\uff1f<\/p>\n<p><strong>Problem:<\/strong><\/p>\n<p>Given an array of size\u00a0<i>n<\/i>, find the majority element. The majority element is the element that appears\u00a0<b>more than<\/b>\u00a0<code>\u230a n\/2 \u230b<\/code>\u00a0times.<\/p>\n<p>You may assume that the array is non-empty and the majority element always exist in the array.<\/p>\n<p><strong>Ideas:<\/strong><\/p>\n<p><a href=\"http:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/11\/169-ep101.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-743\" src=\"http:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/11\/169-ep101.png\" alt=\"\" width=\"960\" height=\"540\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/11\/169-ep101.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/11\/169-ep101-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/11\/169-ep101-768x432.png 768w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/11\/169-ep101-624x351.png 624w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/a><\/p>\n<p><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script><\/p>\n<p><ins class=\"adsbygoogle\" style=\"display: block; text-align: center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-2404451723245401\" data-ad-slot=\"7983117522\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<p><strong>Solution 1:<\/strong><\/p>\n<p>Hash table O(n) \/ O(n)<\/p>\n<pre class=\"lang:c++ decode:true\">\/\/ Author: Huahua\r\n\/\/ Runtime : 23 ms\r\nclass Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        unordered_map&lt;int, int&gt; count;\r\n        const int n = nums.size();\r\n        for (const int num : nums)\r\n            if (++count[num] &gt; n \/ 2) return num;\r\n        return -1;\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n<p><strong>Solution 2:<\/strong><\/p>\n<p>BST O(nlogk) \/ O(n)<\/p>\n<pre class=\"lang:c++ decode:true \">\/\/ Author: Huahua\r\n\/\/ Runtime : 19 ms\r\nclass Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        map&lt;int, int&gt; count;\r\n        const int n = nums.size();\r\n        for (const int num : nums)\r\n            if (++count[num] &gt; n \/ 2) return num;\r\n        return -1;\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n<p><strong>Solution 3:<\/strong><\/p>\n<p>Randomization O(n) \/ O(1)<\/p>\n<pre class=\"lang:c++ decode:true \">\/\/ Author: Huahua\r\n\/\/ Runtime: 19 ms\r\nclass Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        srand(time(nullptr));\r\n        const int n = nums.size();\r\n        while (true) {\r\n            const int index = rand() % n;\r\n            const int majority = nums[index];\r\n            int count = 0;\r\n            for (const int num : nums)\r\n                if (num == majority &amp;&amp; ++count &gt; n\/2) return num;\r\n        }\r\n        return -1;\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n<p><strong>Solution 4:<\/strong><\/p>\n<p>Bit voting\u00a0O(n) \/ O(1)<\/p>\n<pre class=\"lang:c++ decode:true\">class Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        const int n = nums.size();\r\n        int majority = 0;        \r\n        for (int i = 0; i &lt; 32; ++i) {\r\n            int mask = 1 &lt;&lt; i;\r\n            int count = 0;\r\n            for (const int num : nums)\r\n                if ((num &amp; mask) &amp;&amp; (++count &gt; n \/2)) {\r\n                    majority |= mask;\r\n                    break;\r\n                }\r\n        }\r\n        return majority;\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n<p><strong>Solution 5:<\/strong><\/p>\n<p>Moore Voting\u00a0O(n) \/ O(1)<\/p>\n<pre class=\"lang:c++ decode:true\">class Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        int majority = nums.front();\r\n        int count = 0;\r\n        \r\n        for (const int num : nums) {\r\n            if (num == majority) ++count;\r\n            else if (--count == 0) {\r\n                count = 1;\r\n                majority = num;\r\n            }\r\n        }\r\n        \r\n        return majority;\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n<p>Solution 6:<\/p>\n<p>Full sorting\u00a0O(nlogn) \/ O(1)<\/p>\n<pre class=\"lang:c++ decode:true \">class Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        std::sort(nums.begin(), nums.end());\r\n        return nums[nums.size()\/2];\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n<p>Solution 7:<\/p>\n<p>Partial sorting\u00a0O(n) \/ O(1)<\/p>\n<pre class=\"lang:c++ decode:true \">class Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        nth_element(nums.begin(), nums.begin() + nums.size() \/ 2, nums.end());\r\n        return nums[nums.size() \/ 2];\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n<p>Solution 8:<\/p>\n<p>Divide and conquer\u00a0O(nlogn) \/ O(logn)<\/p>\n<pre class=\"lang:c++ decode:true\">class Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        return majorityElement(nums, 0, nums.size() - 1);\r\n    }\r\nprivate:\r\n    int majorityElement(const vector&lt;int&gt;&amp; nums, int l, int r) {\r\n        if (l == r) return nums[l];\r\n        const int m = l + (r - l) \/ 2;\r\n        const int ml = majorityElement(nums, l, m);\r\n        const int mr = majorityElement(nums, m + 1, r);\r\n        if (ml == mr) return ml;\r\n        return count(nums.begin() + l, nums.begin() + r + 1, ml) &gt;\r\n               count(nums.begin() + l, nums.begin() + r + 1, mr)\r\n               ? ml : mr;\r\n    }\r\n};<\/pre>\n<p>Divide and conquer\u00a0O(nlogn) \/ O(logn)<\/p>\n<pre class=\"lang:c++ decode:true \">class Solution {\r\npublic:\r\n    int majorityElement(vector&lt;int&gt;&amp; nums) {\r\n        return majorityElement(nums, 0, nums.size() - 1).first;\r\n    }\r\nprivate:\r\n    pair&lt;int, int&gt; majorityElement(const vector&lt;int&gt;&amp; nums, int l, int r) {\r\n        if (l == r) return {nums[l], 1};\r\n        int mid = l + (r - l) \/ 2;\r\n        auto ml = majorityElement(nums, l, mid);\r\n        auto mr = majorityElement(nums, mid + 1, r);\r\n        if (ml.first == mr.first) return { ml.first, ml.second + mr.second };\r\n        if (ml.second &gt; mr.second)\r\n            return { ml.first, ml.second + count(nums.begin() + mid + 1, nums.begin() + r + 1, ml.first) };\r\n        else\r\n            return { mr.first, mr.second + count(nums.begin() + l, nums.begin() + mid + 1, mr.first) };\r\n    }\r\n};<\/pre>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9898\u76ee\u5927\u610f\uff1a\u7ed9\u4f60\u4e00\u4e2a\u6570\u7ec4\uff0c\u5176\u4e2d\u4e00\u4e2a\u6570\u51fa\u73b0\u8d85\u8fc7n\/2\u6b21\uff0c\u95ee\u4f60\u51fa\u73b0\u6b21\u6570\u6700\u591a\u7684\u90a3\u4e2a\u6570\u662f\u4ec0\u4e48\uff1f Problem: Given an array of size\u00a0n, find the majority element. The majority element is the element that appears\u00a0more than\u00a0\u230a n\/2 \u230b\u00a0times. You may assume&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[126,43,163,70],"tags":[16,197],"class_list":["post-738","post","type-post","status-publish","format-standard","hentry","category-bit","category-divide-and-conquer","category-easy","category-hashtable","tag-bit","tag-voting","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/738","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=738"}],"version-history":[{"count":10,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/738\/revisions"}],"predecessor-version":[{"id":2639,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/738\/revisions\/2639"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=738"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=738"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}