1289. Minimum Falling Path Sum II

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https://leetcode.com/problems/minimum-falling-path-sum-ii/

Given a square grid of integers arr, a falling path with non-zero shifts is a choice of exactly one element from each row of arr, such that no two elements chosen in adjacent rows are in the same column.
Return the minimum sum of a falling path with non-zero shifts.

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.

Constraints:
  • 1 <= arr.length == arr[i].length <= 200
  • -99 <= arr[i][j] <= 99
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Time - O( n * n)
Space - O(1)
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