931. Minimum Falling Path Sum

Problem

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

Solution

/**
 * @param {number[][]} matrix
 * @return {number}
 */
var minFallingPathSum = function(matrix) {
    for (var i = 1; i < matrix.length; i++) {
        for (var j = 0; j < matrix[i].length; j++) {
            matrix[i][j] += Math.min(
                j === 0 ? Number.MAX_SAFE_INTEGER : matrix[i - 1][j - 1],
                matrix[i - 1][j],
                j === matrix[i - 1].length - 1 ? Number.MAX_SAFE_INTEGER : matrix[i - 1][j + 1],
            );
        }
    }
    return Math.min(...matrix[matrix.length - 1]);
};

Explain:

nope.

Complexity:

• Time complexity : O(n * m).
• Space complexity : O(n).