Given an n x n matrix, return the minimum sum of a falling path where you may move to any column in the next row except the same column. Pattern focus: Direction variants. Track the smallest and second smallest values in each row to optimize the transition.
matrix is an n x n matrix
minimum falling path sum with column restriction
Example 1:
Input:
matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output:
13
Explanation:
The best path avoids reusing the same column and totals 13.
Example 2:
Input:
matrix = [[2,1,3],[6,5,4],[7,8,9]]
Output:
12
Explanation:
The best valid path totals 12.
Example 3:
Input:
matrix = [[7]]
Output:
7
Explanation:
A one-cell matrix returns 7.