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:

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

 

Constraints:


Solution:

class Solution {
    public int minFallingPathSum(int[][] A) {
        int len = A.length;
        int[][] dp = new int[len][len];
        int min = Integer.MAX_VALUE;
        for (int j = 0; j < len; j ++) {
            dp[0][j] = A[0][j];
        }
        for (int i = 1; i < len; i ++) {
            for (int j = 0; j < len; j ++) {
                dp[i][j] = Integer.MAX_VALUE;
                if (j - 1 >= 0) {
                    dp[i][j] = Math.min(dp[i][j], dp[i - 1][j - 1] + A[i][j]);
                }
                dp[i][j] = Math.min(dp[i][j], dp[i - 1][j] + A[i][j]);
                if (j + 1 < len) {
                    dp[i][j] = Math.min(dp[i][j], dp[i - 1][j + 1] + A[i][j]);
                }
            }
        }
        for (int j = 0; j < len; j ++) {
            min = Math.min(min, dp[len - 1][j]);
        }
        return min;
    }
}