Minimum Falling Path Sum

Problem statement

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: 13Explanation: There are two falling paths with a minimum sum as shown.

Example 2:

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

Constraints:

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

My solution

/**
 * @param {number[][]} matrix
 * @return {number}
 */
var minFallingPathSum = function(matrix) {
    let width = matrix.length;
    let height = matrix[0].length;
    
    for (let i = height - 2; i >= 0; i--) {
        for (let j = 0; j < width; j++) {
            if (j === 0) {
                matrix[i][j] += Math.min(matrix[i + 1][j], matrix[i + 1][j + 1]);
            } else if (j === width - 1) {
                matrix[i][j] += Math.min(matrix[i + 1][j], matrix[i + 1][j - 1]);
            } else {
                matrix[i][j] += Math.min(matrix[i + 1][j], matrix[i + 1][j - 1], matrix[i + 1][j + 1]);
            }
        }
    }
    
    return Math.min(...matrix[0])
};