Minimum Falling Path Sum

Given an n x n matrix of integers, return the minimum sum of a falling path, where each step may move straight down, down-left, or down-right. Pattern focus: Direction variants. The allowed transitions define the dynamic programming recurrence.

Input Format

matrix is an n x n matrix

Output Format

minimum falling path sum

Constraints

  • 1 <= n <= 200

Examples

Example 1:

Input:

matrix = [[2,1,3],[6,5,4],[7,8,9]]

Output:

13

Explanation:

The best falling path has sum 13.

Example 2:

Input:

matrix = [[-19,57],[-40,-5]]

Output:

-59

Explanation:

The minimum sum is -59.

Example 3:

Input:

matrix = [[1]]

Output:

1

Explanation:

A single-cell matrix returns 1.

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Minimum Falling Path Sum - Dp Grid DSA Problem