1289. Minimum Falling Path Sum II

[F4NT0]

Given an n x n integer matrix grid, return the minimum sum of a falling path with non-zero shifts.

A falling path with non-zero shifts is a choice of exactly one element from each row of grid such that no two elements chosen in adjacent rows are in the same column.

Example 1:

• Input: grid = [[1,2,3],[4,5,6],[7,8,9]]
• Output: 13
• Explanation:
  • The possible falling paths are:
    [1,5,9], [1,5,7], [1,6,7], [1,6,8],
    [2,4,8], [2,4,9], [2,6,7], [2,6,8],
    [3,4,8], [3,4,9], [3,5,7], [3,5,9]
• The falling path with the smallest sum is [1,5,7], so the answer is 13.

Example 2:

• Input: grid = [[7]]
• Output: 7

Constraints:

• n == grid.length == grid[i].length
• 1 <= n <= 200
• -99 <= grid[i][j] <= 99