{"id":5963,"date":"2019-12-14T14:04:07","date_gmt":"2019-12-14T22:04:07","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=5963"},"modified":"2019-12-14T14:04:19","modified_gmt":"2019-12-14T22:04:19","slug":"leetcode-1289-minimum-falling-path-sum-ii","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/dynamic-programming\/leetcode-1289-minimum-falling-path-sum-ii\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1289. Minimum Falling Path Sum II"},"content":{"rendered":"\n

Given a square grid of integers arr<\/code>, a falling path with non-zero shifts<\/em> is a choice of exactly one element from each row of arr<\/code>, such that no two elements chosen in adjacent rows are in the same column.<\/p>\n\n\n\n

Return the minimum sum of a falling path with non-zero shifts.<\/p>\n\n\n\n

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

Input:<\/strong> arr = [[1,2,3],[4,5,6],[7,8,9]]\nOutput:<\/strong> 13\nExplanation: <\/strong>\nThe possible falling paths are:\n[1,5,9], [1,5,7], [1,6,7], [1,6,8],\n[2,4,8], [2,4,9], [2,6,7], [2,6,8],\n[3,4,8], [3,4,9], [3,5,7], [3,5,9]\nThe falling path with the smallest sum is [1,5,7], so the answer is 13.\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • 1 <= arr.length == arr[i].length <= 200<\/code><\/li>
  • -99 <= arr[i][j] <= 99<\/code><\/li><\/ul>\n\n\n\n
    Solution: DP<\/strong><\/h2>\n\n\n\n
    dp[i][j] = min(dp[i-1][k]), 1 <= k <= m, k != j<\/p>\n\n\n\n
    Time complexity: O(n^3)
    Space complexity: O(n^2)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int minFallingPathSum(vector>& arr) {\n    constexpr int kInf = 1e6;\n    for (int i = 1; i < arr.size(); ++i)\n      for (int j = 0; j < arr[0].size(); ++j) {\n        int m = kInf;\n        for (int k = 0; k < arr[0].size(); ++k) {\n          if (k == j) continue;\n          m = min(m, arr[i - 1][k]);\n        }\n        arr[i][j] += m;\n    }\n    return *min_element(begin(arr.back()), end(arr.back()));\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
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