931. Minimum Falling Path Sum 

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class Solution {
    private static final int[][] DIRECTIONS = new int[][]{{-1, -1}, {-1, 0}, {-1, 1}};

    public int minFallingPathSum(int[][] matrix) {
        int n = matrix.length;

        for (int i = 1; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int min = Integer.MAX_VALUE;
                for (int[] direction : DIRECTIONS) {
                    int prevI = i + direction[0], prevJ = j + direction[1];
                    if (prevI >= 0 && prevI < n && prevJ >= 0 && prevJ < n) {
                        min = Math.min(min, matrix[prevI][prevJ]);
                    }
                }
                matrix[i][j] += min;
            }
        }

        int minPathSum = Integer.MAX_VALUE;
        for (int j = 0; j < n; j++) {
            minPathSum = Math.min(minPathSum, matrix[n - 1][j]);
        }
        return minPathSum;
    }
}

References

931. Minimum Falling Path Sum