{"id":5912,"date":"2019-12-01T23:21:33","date_gmt":"2019-12-02T07:21:33","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=5912"},"modified":"2019-12-01T23:21:52","modified_gmt":"2019-12-02T07:21:52","slug":"leetcode-1277-count-square-submatrices-with-all-ones","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/dynamic-programming\/leetcode-1277-count-square-submatrices-with-all-ones\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1277. Count Square Submatrices with All Ones"},"content":{"rendered":"\n

Given a m * n<\/code> matrix of ones and zeros, return how many square<\/strong> submatrices have all ones.<\/p>\n\n\n\n

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

Input:<\/strong> matrix =\n[\n  [0,1,1,1],\n  [1,1,1,1],\n  [0,1,1,1]\n]\nOutput:<\/strong> 15\nExplanation:<\/strong> \nThere are 10<\/strong> squares of side 1.\nThere are 4<\/strong> squares of side 2.\nThere is  1<\/strong> square of side 3.\nTotal number of squares = 10 + 4 + 1 = 15<\/strong>.\n<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> matrix = \n[\n  [1,0,1],\n  [1,1,0],\n  [1,1,0]\n]\nOutput:<\/strong> 7\nExplanation:<\/strong> \nThere are 6<\/strong> squares of side 1.  \nThere is 1<\/strong> square of side 2. \nTotal number of squares = 6 + 1 = 7<\/strong>.\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • 1 <= arr.length <= 300<\/code><\/li>
  • 1 <= arr[0].length <= 300<\/code><\/li>
  • 0 <= arr[i][j] <= 1<\/code><\/li><\/ul>\n\n\n\n
    Solution: DP<\/strong><\/h2>\n\n\n\n
    dp[i][j] := edge of largest square with bottom right corner at (i, j)
    dp[i][j] = min(dp[i – 1][j], dp[i – 1][j – 1], dp[i][j – 1]) if m[i][j] == 1 else 0
    ans = sum(dp)<\/p>\n\n\n\n
    Time complexity: O(n*m)
    Space complexity: O(n*m)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int countSquares(vector>& matrix) {\n    const int n = matrix.size();\n    const int m = matrix[0].size();\n    \/\/ dp[i][j] := edge of largest square with right bottom corner at (i, j)\n    vector> dp(n, vector(m));\n    int ans = 0;\n    for (int i = 0; i < n; ++i)\n      for (int j = 0; j < m; ++j) {\n        dp[i][j] = matrix[i][j];\n        if (i && j && dp[i][j])\n          dp[i][j] = min({dp[i - 1][j - 1], dp[i][j - 1], dp[i - 1][j]}) + 1;\n        ans += dp[i][j];\n      }\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
    Given a m * n matrix of ones and zeros, return how many square submatrices have all ones. Example 1: Input: matrix = [   [0,1,1,1],   [1,1,1,1],  …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[18,278,177,519,285],"class_list":["post-5912","post","type-post","status-publish","format-standard","hentry","category-dynamic-programming","tag-dp","tag-grid","tag-medium","tag-ones","tag-square","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5912","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=5912"}],"version-history":[{"count":2,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5912\/revisions"}],"predecessor-version":[{"id":5914,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5912\/revisions\/5914"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=5912"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=5912"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=5912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}