Given a square array of integers A, we want the minimum sum of a falling path through A.
A falling path starts at any element in the first row, and chooses one element from each row. The next row's choice must be in a column that is different from the previous row's column by at most one.
Example 1:
Input: [[1,2,3],[4,5,6],[7,8,9]] Output: 12 Explanation: The possible falling paths are:
<li><code>[1,4,7], [1,4,8], [1,5,7], [1,5,8], [1,5,9]</code></li>
<li><code>[2,4,7], [2,4,8], [2,5,7], [2,5,8], [2,5,9], [2,6,8], [2,6,9]</code></li>
<li><code>[3,5,7], [3,5,8], [3,5,9], [3,6,8], [3,6,9]</code></li>
The falling path with the smallest sum is [1,4,7], so the answer is 12.
Note:
<li><code>1 <= A.length == A[0].length <= 100</code></li>
<li><code>-100 <= A[i][j] <= 100</code></li>