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967. Minimum Falling Path Sum

Array Dynamic Programming Matrix

Problem - Minimum Falling Path Sum

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

Solutions

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class Solution:
    def minFallingPathSum(self, matrix: List[List[int]]) -> int:
        n = len(matrix)
        dp = [0] * n

        for row in matrix:
            current_dp = [0] * n
            for j, val in enumerate(row):
                left, right = max(0, j - 1), min(n, j + 2)
                current_dp[j] = min(dp[left:right]) + val
            dp = current_dp

        return min(dp)

Submission Stats:

  • Runtime: 19 ms (71.29%)
  • Memory: 18.4 MB (99.62%)