minimum-falling-path-sum-ii

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Algorithms

Given an <code>n x n</code> integer matrix <code>grid</code>, 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 <code>grid</code> such that no two elements chosen in adjacent rows are in the same column.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/falling-grid.jpg" style="width: 244px; height: 245px;" />
<pre>
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&nbsp;[1,5,7], so the answer is&nbsp;13.
</pre>

Example 2:

<pre>
Input: grid = [[7]]
Output: 7
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 200</code></li>
	<li><code>-99 &lt;= grid[i][j] &lt;= 99</code></li>
</ul>