Minimum Falling Path Sum

给一个矩阵, 每个格子都能往下面的相邻的格子落, 问怎么落的相加后的和最小.

这题就是典型的矩阵dp.

class Solution {
    public int minFallingPathSum(int[][] matrix) {
        int n = matrix.length;
        int[][] dp = new int[n][n]; // dp[i][j] = the min falling path sum to the current cell [i][j]
        for(int i = 0; i < n; i++){
            dp[0][i] = matrix[0][i];
        }
        for(int i = 1; i < n; i++) {
            for(int j = 0; j < n; j++) {
                dp[i][j] = Math.min(Math.min(j > 0 ? dp[i - 1][j - 1] : Integer.MAX_VALUE, dp[i - 1][j]), j < n - 1 ? dp[i - 1][j + 1] : Integer.MAX_VALUE) + matrix[i][j];  
            }
        }
        int res = Integer.MAX_VALUE;
        for(int i = 0; i < n; i++){
            res = Math.min(dp[n - 1][i],res);
        }        
        return res;
    }
}