{"id":8734,"date":"2021-11-20T13:32:11","date_gmt":"2021-11-20T21:32:11","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=8734"},"modified":"2021-11-20T13:32:48","modified_gmt":"2021-11-20T21:32:48","slug":"leetcode-2001-number-of-pairs-of-interchangeable-rectangles","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/hashtable\/leetcode-2001-number-of-pairs-of-interchangeable-rectangles\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 2001. Number of Pairs of Interchangeable Rectangles"},"content":{"rendered":"\n

You are given n<\/code> rectangles represented by a 0-indexed<\/strong> 2D integer array rectangles<\/code>, where rectangles[i] = [widthi<\/sub>, heighti<\/sub>]<\/code> denotes the width and height of the ith<\/sup><\/code> rectangle.<\/p>\n\n\n\n

Two rectangles i<\/code> and j<\/code> (i < j<\/code>) are considered interchangeable<\/strong> if they have the same<\/strong> width-to-height ratio. More formally, two rectangles are interchangeable<\/strong> if widthi<\/sub>\/heighti<\/sub> == widthj<\/sub>\/heightj<\/sub><\/code> (using decimal division, not integer division).<\/p>\n\n\n\n

Return the number<\/strong> of pairs of interchangeable<\/strong> rectangles in <\/em>rectangles<\/code>.<\/p>\n\n\n\n

Example 1:<\/strong><\/p>\n\n\n\n

Input:<\/strong> rectangles = [[4,8],[3,6],[10,20],[15,30]]\nOutput:<\/strong> 6\nExplanation:<\/strong> The following are the interchangeable pairs of rectangles by index (0-indexed):\n- Rectangle 0 with rectangle 1: 4\/8 == 3\/6.\n- Rectangle 0 with rectangle 2: 4\/8 == 10\/20.\n- Rectangle 0 with rectangle 3: 4\/8 == 15\/30.\n- Rectangle 1 with rectangle 2: 3\/6 == 10\/20.\n- Rectangle 1 with rectangle 3: 3\/6 == 15\/30.\n- Rectangle 2 with rectangle 3: 10\/20 == 15\/30.\n<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> rectangles = [[4,5],[7,8]]\nOutput:<\/strong> 0\nExplanation:<\/strong> There are no interchangeable pairs of rectangles.\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • n == rectangles.length<\/code><\/li>
  • 1 <= n <= 105<\/sup><\/code><\/li>
  • rectangles[i].length == 2<\/code><\/li>
  • 1 <= widthi<\/sub>, heighti<\/sub> <= 105<\/sup><\/code><\/li><\/ul>\n\n\n\n
    Solution: Hashtable<\/strong><\/h2>\n\n\n\n
    Use aspect ratio as the key.<\/p>\n\n\n\n
    Time complexity: O(n)
    Space complexity: O(n)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  long long interchangeableRectangles(vector>& rectangles) {\n    long long ans  = 0;\n    unordered_map m;\n    for (const auto& r : rectangles) {\n      long long d = gcd(r[0], r[1]);\n      ans += m[((r[0] \/ d) << 20) | (r[1] \/ d)]++;\n    }\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
    You are given n rectangles represented by a 0-indexed 2D integer array rectangles, where rectangles[i] = [widthi, heighti] denotes the width and height of the ith rectangle. Two rectangles i and j (i < j) are considered interchangeable if they…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[70],"tags":[82,177],"class_list":["post-8734","post","type-post","status-publish","format-standard","hentry","category-hashtable","tag-hashtable","tag-medium","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/8734","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=8734"}],"version-history":[{"count":2,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/8734\/revisions"}],"predecessor-version":[{"id":8736,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/8734\/revisions\/8736"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=8734"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=8734"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=8734"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}