minimum-falling-path-sum-ii

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1289. Minimum Falling Path Sum II (Hard)

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: arr = [[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

Related Topics

[Array] [Dynamic Programming] [Matrix]

Similar Questions

1. Minimum Falling Path Sum (Medium)

Hints

Hint 1

Use dynamic programming.

Hint 2

Let dp[i][j] be the answer for the first i rows such that column j is chosen from row i.

Hint 3

Use the concept of cumulative array to optimize the complexity of the solution.