{"id":7360,"date":"2020-09-12T22:22:59","date_gmt":"2020-09-13T05:22:59","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=7360"},"modified":"2020-09-12T22:23:51","modified_gmt":"2020-09-13T05:23:51","slug":"leetcode-1582-special-positions-in-a-binary-matrix","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/algorithms\/array\/leetcode-1582-special-positions-in-a-binary-matrix\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1582. Special Positions in a Binary Matrix"},"content":{"rendered":"\n

Given a rows x cols<\/code> matrix mat<\/code>, where mat[i][j]<\/code> is either 0<\/code> or 1<\/code>, return the number of special positions in mat<\/code>.<\/em><\/p>\n\n\n\n

A position (i,j)<\/code> is called special<\/strong> if mat[i][j] == 1<\/code> and all other elements in row i<\/code> and column j<\/code> are 0<\/code> (rows and columns are 0-indexed<\/strong>).<\/p>\n\n\n\n

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

Input:<\/strong> mat = [[1,0,0],\n              [0,0,1<\/strong>],\n              [1,0,0]]\nOutput:<\/strong> 1\nExplanation:<\/strong> (1,2) is a special position because mat[1][2] == 1 and all other elements in row 1 and column 2 are 0.\n<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> mat = [[1<\/strong>,0,0],\n              [0,1<\/strong>,0],\n              [0,0,1<\/strong>]]\nOutput:<\/strong> 3\nExplanation:<\/strong> (0,0), (1,1) and (2,2) are special positions. \n<\/pre>\n\n\n\n
Example 3:<\/strong><\/p>\n\n\n\n
Input:<\/strong> mat = [[0,0,0,1<\/strong>],\n              [1<\/strong>,0,0,0],\n              [0,1,1,0],\n              [0,0,0,0]]\nOutput:<\/strong> 2\n<\/pre>\n\n\n\n
Example 4:<\/strong><\/p>\n\n\n\n
Input:<\/strong> mat = [[0,0,0,0,0],\n              [1<\/strong>,0,0,0,0],\n              [0,1<\/strong>,0,0,0],\n              [0,0,1<\/strong>,0,0],\n              [0,0,0,1,1]]\nOutput:<\/strong> 3\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • rows == mat.length<\/code><\/li>
  • cols == mat[i].length<\/code><\/li>
  • 1 <= rows, cols <= 100<\/code><\/li>
  • mat[i][j]<\/code> is 0<\/code> or 1<\/code>.<\/li><\/ul>\n\n\n\n
    Solution: Sum for each row and column<\/strong><\/h2>\n\n\n\n
    Brute force:
    Time complexity: O(R*C*(R+C))
    Space complexity: O(1)<\/p>\n\n\n\n
    We can pre-compute the sums for each row and each column, ans = sum(mat[r][c] == 1 and rsum[r] == 1 and csum[c] == 1)<\/p>\n\n\n\n
    Time complexity: O(R*C)
    Space complexity: O(R+C)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \nclass Solution {\npublic:\n  int numSpecial(vector>& mat) {\n    const int rows = mat.size();\n    const int cols = mat[0].size();\n    vector rs(rows);\n    vector cs(cols);\n    for (int r = 0; r < rows; ++r)\n      for (int c = 0; c < cols; ++c) {\n        rs[r] += mat[r][c];\n        cs[c] += mat[r][c];\n      }\n    int ans = 0;\n    for (int r = 0; r < rows; ++r)\n      for (int c = 0; c < cols; ++c)\n        ans += mat[r][c] && rs[r] == 1 && cs[c] == 1;      \n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
    Given a rows x cols matrix mat, where mat[i][j] is either 0 or 1, return the number of special positions in mat. A position (i,j) is called special if mat[i][j] == 1 and all other elements in row i and column j are 0 (rows and columns are 0-indexed). Example…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[184],"tags":[222,216,649],"class_list":["post-7360","post","type-post","status-publish","format-standard","hentry","category-array","tag-easy","tag-matrix","tag-pre-compute","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/7360","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=7360"}],"version-history":[{"count":2,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/7360\/revisions"}],"predecessor-version":[{"id":7362,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/7360\/revisions\/7362"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=7360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=7360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=7360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}