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931. Minimum Falling Path Sum

Difficulty Topics

Description

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

minimum-falling-path-sum.py
class Solution:
    def minFallingPathSum(self, matrix: List[List[int]]) -> int:
        rows, cols = len(matrix), len(matrix[0])

        for i in range(1, rows):
            for j in range(cols):
                left = matrix[i - 1][j - 1] if j - 1 >= 0 else inf
                mid = matrix[i - 1][j]
                right = matrix[i - 1][j + 1] if j + 1 < cols else inf

                matrix[i][j] += min(left, mid, right)

        return min(matrix[-1])