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  • 931. Minimum Falling Path Sum


    Given a square array of integers A, we want the minimum sum of a falling path through A.

    A falling path starts at any element in the first row, and chooses one element from each row.  The next row's choice must be in a column that is different from the previous row's column by at most one.

    Example 1:

    Input: [[1,2,3],[4,5,6],[7,8,9]]
    Output: 12
    Explanation: 
    The possible falling paths are:
    
    • [1,4,7], [1,4,8], [1,5,7], [1,5,8], [1,5,9]
    • [2,4,7], [2,4,8], [2,5,7], [2,5,8], [2,5,9], [2,6,8], [2,6,9]
    • [3,5,7], [3,5,8], [3,5,9], [3,6,8], [3,6,9]

    The falling path with the smallest sum is [1,4,7], so the answer is 12.

    Note:

    1. 1 <= A.length == A[0].length <= 100
    2. -100 <= A[i][j] <= 100

    Approath #1: Bottom to Top. [C++]

    class Solution {
        public int minFallingPathSum(int[][] A) {
            int l = A.length;
            int[][] dp = new int[l+1][l+1];
            for (int i = 0; i < l; ++i)
                for (int j = 0; j < l; ++j)
                    dp[i][j] = A[i][j];
            for (int i = l-2; i >= 0; --i) {
                for (int j = 0; j < l; ++j) {
                    int left = j > 0 ? dp[i+1][j-1] : Integer.MAX_VALUE;
                    int right = j < l-1 ? dp[i+1][j+1] : Integer.MAX_VALUE;
                    int down = dp[i+1][j];
                    dp[i][j] += Math.min(left, Math.min(down, right));
                    // System.out.print("dp[" + i + "][" + j + "]= " + dp[i][j] + " ");
                }
                // System.out.println();
            }
            
            int ans = Integer.MAX_VALUE;
            for (int i = 0; i < l; ++i)
                ans = Math.min(ans, dp[0][i]);
            
            return ans;
        }
    }
    

      

    Analysis:

    Solving this problem using the thought of 'bottom to top', we calculate the minimum sum using dp[i][j] = dp[i][j] + min(left, right, down).

    Finally,  we can find the answer at the first row.

    永远渴望,大智若愚(stay hungry, stay foolish)
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  • 原文地址:https://www.cnblogs.com/h-hkai/p/10602121.html
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