{"id":643,"date":"2017-10-19T22:05:56","date_gmt":"2017-10-20T05:05:56","guid":{"rendered":"http:\/\/zxi.mytechroad.com\/blog\/?p=643"},"modified":"2018-09-03T10:11:57","modified_gmt":"2018-09-03T17:11:57","slug":"leetcode-149-max-points-on-a-line","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/geometry\/leetcode-149-max-points-on-a-line\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 149. Max Points on a Line"},"content":{"rendered":"<p><iframe loading=\"lazy\" title=\"\u82b1\u82b1\u9171 LeetCode 149. Max Points on a Line - \u5237\u9898\u627e\u5de5\u4f5c EP92\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/7FPL7nAi9aM?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><strong>Problem:<\/strong><\/p>\n<div class=\"question-description\">\n<p>Given\u00a0<i>n<\/i>\u00a0points on a 2D plane, find the maximum number of points that lie on the same straight line.<\/p>\n<\/div>\n<p><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script><br \/>\n<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>Idea:<\/strong><\/p>\n<p><a href=\"http:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/10\/149-ep92.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-647\" src=\"http:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/10\/149-ep92.png\" alt=\"\" width=\"960\" height=\"540\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/10\/149-ep92.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/10\/149-ep92-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/10\/149-ep92-768x432.png 768w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2017\/10\/149-ep92-624x351.png 624w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/a><\/p>\n<p>count by slope<\/p>\n<p>Time complexity: O(n^2)<\/p>\n<p>Space complexity: O(n)<\/p>\n<h1><strong>Solution:<\/strong><\/h1>\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++ \/ pair<\/h2>\n<div class=\"tabcontent\">\n\n<pre class=\"lang:c++ decode:true\">\/\/ Author: Huahua\r\n\/\/ Running time: 6 ms\r\nclass Solution {\r\npublic:\r\n    int maxPoints(vector&lt;Point&gt;&amp; points) {\r\n        int n = points.size();        \r\n        int ans = 0;\r\n        for (int i = 0; i &lt; n; ++i) {\r\n            std::map&lt;std::pair&lt;int,int&gt;, int&gt; count;\r\n            int same_points = 1;\r\n            int max_points = 0;\r\n            for (int j = i + 1; j &lt; n; ++j) {\r\n                const Point&amp; p1 = points[i];\r\n                const Point&amp; p2 = points[j];\r\n                if (p1.x == p2.x &amp;&amp; p1.y == p2.y)\r\n                    ++same_points;\r\n                else\r\n                    max_points = max(max_points, ++count[getSlope(p1, p2)]);\r\n            }\r\n            ans = max(ans, same_points + max_points);             \r\n        }\r\n        return ans;\r\n    }\r\nprivate:\r\n    \/\/ slope dy\/dx : &lt;dy, dx&gt;\r\n    std::pair&lt;int, int&gt; getSlope(const Point&amp; p1, const Point&amp; p2) {\r\n        const int dx = p2.x - p1.x;\r\n        const int dy = p2.y - p1.y;\r\n        \r\n        \/\/ horizontal line\r\n        if (dy == 0) return { p1.y, 0 };\r\n        \/\/ vertical line\r\n        if (dx == 0) return { 0, p1.x };\r\n        \r\n        const int d = gcd(dx, dy);\r\n        return { dy \/ d, dx \/ d };\r\n    }\r\n    \r\n    int gcd(int m, int n) {\r\n        return n == 0 ? m : gcd(n, m % n);\r\n    }\r\n};<\/pre>\n\n<\/div><h2 class=\"tabtitle\">C++ \/ long<\/h2>\n<div class=\"tabcontent\">\n\n<pre class=\"lang:c++ decode:true \">\/\/ Author: Huahua\r\n\/\/ Running time: 4 ms\r\nclass Solution {\r\npublic:\r\n  int maxPoints(vector&lt;Point&gt;&amp; points) {\r\n    int n = points.size();        \r\n    int ans = 0;\r\n    for (int i = 0; i &lt; n; ++i) {\r\n      unordered_map&lt;long, int&gt; count;\r\n      int same_points = 1;\r\n      int max_points = 0;\r\n      const Point&amp; p1 = points[i];\r\n      for (int j = i + 1; j &lt; n; ++j) {                \r\n        const Point&amp; p2 = points[j];\r\n        if (p1.x == p2.x &amp;&amp; p1.y == p2.y)\r\n          ++same_points;\r\n        else\r\n          max_points = max(max_points, ++count[getSlope(p1, p2)]);\r\n      }\r\n      ans = max(ans, same_points + max_points);             \r\n    }\r\n    return ans;\r\n  }\r\nprivate:\r\n  \/\/ slope dy\/dx : dy &lt;&lt; 32 | dx\r\n  long getSlope(const Point&amp; p1, const Point&amp; p2) {\r\n    const int dx = p2.x - p1.x;\r\n    const int dy = p2.y - p1.y;\r\n\r\n    \/\/ horizontal line\r\n    if (dy == 0) return static_cast&lt;long&gt;(p1.y) &lt;&lt; 32 | 0;\r\n    \/\/ vertical line\r\n    if (dx == 0) return static_cast&lt;long&gt;(0)&lt;&lt; 32 | p1.x;\r\n\r\n    const int d = __gcd(dx, dy);\r\n    return static_cast&lt;long&gt;(dy \/ d) &lt;&lt; 32 | (dx \/ d);\r\n  }\r\n};<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problem: Given\u00a0n\u00a0points on a 2D plane, find the maximum number of points that lie on the same straight line. Idea: count by slope Time complexity:&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[127,165],"tags":[217,135,136],"class_list":["post-643","post","type-post","status-publish","format-standard","hentry","category-geometry","category-hard","tag-hard","tag-line","tag-point","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/643","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=643"}],"version-history":[{"count":8,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/643\/revisions"}],"predecessor-version":[{"id":3827,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/643\/revisions\/3827"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}