931. Minimum Falling Path Sum

Problem Statement

Medium

Given an n x n array of integers matrix, return the minimum sum of any falling path through matrix.

A falling path starts at any element in the first row and chooses the element in the next row that is either directly below or diagonally left/right. Specifically, the next element from position (row, col) will be (row + 1, col - 1), (row + 1, col), or (row + 1, col + 1).

Example 1:

Input: matrix = [[2,1,3],[6,5,4],[7,8,9]]
Output: 13
Explanation: There are two falling paths with a minimum sum as shown.

Example 2:

Input: matrix = [[-19,57],[-40,-5]]
Output: -59
Explanation: The falling path with a minimum sum is shown.

Constraints:

n == matrix.length == matrix[i].length
1 <= n <= 100
-100 <= matrix[i][j] <= 100

Java

Source file

class Solution {
    public int minFallingPathSum(int[][] matrix) {
        int m = matrix.length, n = matrix[0].length, ans = Integer.MAX_VALUE;
        for (int i = 1; i < m; i++) {
            matrix[i][0] += Math.min(matrix[i - 1][0], matrix[i - 1][1]);
            for (int j = 1; j < n - 1; j++)
                matrix[i][j] += Math.min(matrix[i - 1][j], Math.min(matrix[i - 1][j - 1], matrix[i - 1][j + 1]));
            matrix[i][n - 1] += Math.min(matrix[i - 1][n - 1], matrix[i - 1][n - 2]);
        }
        for (int j = 0; j < n; j++)
            ans = Math.min(ans, matrix[m - 1][j]);
        return ans;
    }
}