{"id":5280,"date":"2019-07-11T08:45:23","date_gmt":"2019-07-11T15:45:23","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=5280"},"modified":"2019-07-11T08:45:33","modified_gmt":"2019-07-11T15:45:33","slug":"leetcode-391-perfect-rectangle","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/geometry\/leetcode-391-perfect-rectangle\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 391. Perfect Rectangle"},"content":{"rendered":"\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\u82b1\u82b1\u9171 LeetCode 391. Perfect Rectangle - \u5237\u9898\u627e\u5de5\u4f5c EP255\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/8JM_dyOu_JY?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>\n<\/div><\/figure>\n\n\n\n<p>Given N axis-aligned rectangles where N &gt; 0, determine if they all together form an exact cover of a rectangular region.<\/p>\n\n\n\n<p>Each rectangle is represented as a bottom-left point and a top-right point. For example, a unit square is represented as [1,1,2,2]. (coordinate of bottom-left point is (1, 1) and top-right point is (2, 2)).<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/assets.leetcode.com\/uploads\/2018\/10\/22\/rectangle_perfect.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Example 1:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">rectangles = [\n  [1,1,3,3],\n  [3,1,4,2],\n  [3,2,4,4],\n  [1,3,2,4],\n  [2,3,3,4]\n]\n\nReturn true. All 5 rectangles together form an exact cover of a rectangular region.\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/assets.leetcode.com\/uploads\/2018\/10\/22\/rectangle_separated.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Example 2:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">rectangles = [\n  [1,1,2,3],\n  [1,3,2,4],\n  [3,1,4,2],\n  [3,2,4,4]\n]\n\nReturn false. Because there is a gap between the two rectangular regions.\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/assets.leetcode.com\/uploads\/2018\/10\/22\/rectangle_hole.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Example 3:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">rectangles = [\n  [1,1,3,3],\n  [3,1,4,2],\n  [1,3,2,4],\n  [3,2,4,4]\n]\n\nReturn false. Because there is a gap in the top center.\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/assets.leetcode.com\/uploads\/2018\/10\/22\/rectangle_intersect.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Example 4:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">rectangles = [\n  [1,1,3,3],\n  [3,1,4,2],\n  [1,3,2,4],\n  [2,2,4,4]\n]\n\nReturn false. Because two of the rectangles overlap with each other.\n<\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solution: Counting corner points<\/strong><\/h2>\n\n\n\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"c++\">\n\/\/ Author: Huahua\nclass Solution {\npublic:\n  bool isRectangleCover(vector<vector<int>>& rectangles) {\n    set<pair<int, int>> corners;\n    int area = 0;\n    for (const auto& rect : rectangles) {            \n      pair<int, int> p1{rect[0], rect[1]};\n      pair<int, int> p2{rect[2], rect[1]};\n      pair<int, int> p3{rect[2], rect[3]};\n      pair<int, int> p4{rect[0], rect[3]};\n      for (const auto& p : {p1, p2, p3, p4}) {        \n        const auto& ret = corners.insert(p);\n        if (!ret.second) corners.erase(ret.first);\n      }\n      area += (p3.first - p1.first) * (p3.second - p1.second);\n    }\n    if (corners.size() != 4) return false;\n    const auto& p1 = *begin(corners);\n    const auto& p3 = *rbegin(corners);    \n    return area == (p3.first - p1.first) * (p3.second - p1.second);\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Given N axis-aligned rectangles where N &gt; 0, determine if they all together form an exact cover of a rectangular region. Each rectangle is represented&#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],"tags":[284,217,82],"class_list":["post-5280","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-geometry","tag-hard","tag-hashtable","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5280","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=5280"}],"version-history":[{"count":2,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5280\/revisions"}],"predecessor-version":[{"id":5282,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5280\/revisions\/5282"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=5280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=5280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=5280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}