{"id":9280,"date":"2021-12-30T02:37:20","date_gmt":"2021-12-30T10:37:20","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=9280"},"modified":"2021-12-30T02:44:42","modified_gmt":"2021-12-30T10:44:42","slug":"leetcode-1925-count-square-sum-triples","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/math\/leetcode-1925-count-square-sum-triples\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1925. Count Square Sum Triples"},"content":{"rendered":"\n

A square triple<\/strong> (a,b,c)<\/code> is a triple where a<\/code>, b<\/code>, and c<\/code> are integers<\/strong> and a2<\/sup> + b2<\/sup> = c2<\/sup><\/code>.<\/p>\n\n\n\n

Given an integer n<\/code>, return the number of square triples<\/strong> such that <\/em>1 <= a, b, c <= n<\/code>.<\/p>\n\n\n\n

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

Input:<\/strong> n = 5\nOutput:<\/strong> 2\nExplanation<\/strong>: The square triples are (3,4,5) and (4,3,5).\n<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> n = 10\nOutput:<\/strong> 4\nExplanation<\/strong>: The square triples are (3,4,5), (4,3,5), (6,8,10), and (8,6,10).\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • 1 <= n <= 250<\/code><\/li><\/ul>\n\n\n\n
    Solution: Enumerate a & b<\/strong><\/h2>\n\n\n\n
    Brute force enumerates a & b & c, which takes O(n3<\/sup>). Just need to enumerate a & b and validate c.<\/p>\n\n\n\n
    Time complexity: O(n2<\/sup>)
    Space complexity: O(1)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int countTriples(int n) {\n    int ans = 0;\n    for (int a = 1; a <= n; ++a)\n      for (int b = 1; b <= n; ++b) {\n        int c = sqrt(a * a + b * b);\n        if (c <= n && c * c == a * a + b * b) ++ans;        \n      }\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n\n\n\n
    <\/p>\n","protected":false},"excerpt":{"rendered":"
    A square triple (a,b,c) is a triple where a, b, and c are integers and a2 + b2 = c2. Given an integer n, return the number of square triples such that 1 <= a, b, c <= n. Example 1: Input:…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[31],"class_list":["post-9280","post","type-post","status-publish","format-standard","hentry","category-math","tag-math","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9280","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=9280"}],"version-history":[{"count":2,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9280\/revisions"}],"predecessor-version":[{"id":9282,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9280\/revisions\/9282"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=9280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=9280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=9280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}