{"id":8195,"date":"2021-03-06T09:17:45","date_gmt":"2021-03-06T17:17:45","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=8195"},"modified":"2021-03-06T09:20:17","modified_gmt":"2021-03-06T17:20:17","slug":"leetcode-1780-check-if-number-is-a-sum-of-powers-of-three","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/math\/leetcode-1780-check-if-number-is-a-sum-of-powers-of-three\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1780. Check if Number is a Sum of Powers of Three"},"content":{"rendered":"\n

Given an integer n<\/code>, return true<\/code> if it is possible to represent <\/em>n<\/code> as the sum of distinct powers of three.<\/em> Otherwise, return false<\/code>.<\/p>\n\n\n\n

An integer y<\/code> is a power of three if there exists an integer x<\/code> such that y == 3x<\/sup><\/code>.<\/p>\n\n\n\n

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

Input:<\/strong> n = 12\nOutput:<\/strong> true\nExplanation:<\/strong> 12 = 31<\/sup> + 32<\/sup>\n<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> n = 91\nOutput:<\/strong> true\nExplanation:<\/strong> 91 = 30<\/sup> + 32<\/sup> + 34<\/sup>\n<\/pre>\n\n\n\n
Example 3:<\/strong><\/p>\n\n\n\n
Input:<\/strong> n = 21\nOutput:<\/strong> false\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • 1 <= n <= 107<\/sup><\/code><\/li><\/ul>\n\n\n\n
    Solution: Greedy + Math<\/p>\n\n\n\n
    Find the largest 3^x that <= n, subtract that from n and repeat the process.
    x should be monotonically decreasing, otherwise we have duplicate terms.
    e.g. 12 = 32<\/sup> + 31<\/sup> true
    e.g. 21 = 32<\/sup><\/span><\/strong> + 32<\/sup><\/span><\/strong>+ 31<\/sup> false<\/p>\n\n\n\n
    Time complexity: O(logn?)
    Space complexity: O(1)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  bool checkPowersOfThree(int n) {\n    int last = INT_MAX;\n    while (n) {\n      int p = 0;\n      int cur = 1;\n      while (cur * 3 <= n) {\n        cur *= 3;\n        ++p;\n      }\n      if (p == last) return false;\n      last = p;    \n      n -= cur;\n    }\n    return true;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
    Given an integer n, return true if it is possible to represent n as the sum of distinct powers of three. Otherwise, return false. An integer y is a power of three if there…<\/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":[88,31,177],"class_list":["post-8195","post","type-post","status-publish","format-standard","hentry","category-math","tag-greedy","tag-math","tag-medium","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/8195","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=8195"}],"version-history":[{"count":3,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/8195\/revisions"}],"predecessor-version":[{"id":8199,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/8195\/revisions\/8199"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=8195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=8195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=8195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}