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:
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`
**Solution:**
```
class Solution {
/**
* @param Integer[][] $grid
* @return Integer
*/
function minFallingPathSum($grid) {
$n = count($grid);
$minFirstPathSum = 0;
$minSecondPathSum = 0;
$prevMinPathCol = -1;
$kInfinity = PHP_INT_MAX;
foreach ($grid as $row) {
$newMinFirstPathSum = $kInfinity;
$newMinSecondPathSum = $kInfinity;
$newMinPathCol = -1;
for ($j = 0; $j < $n; ++$j) {
$currentSum = ($prevMinPathCol != $j ? $minFirstPathSum : $minSecondPathSum) + $row[$j];
if ($currentSum < $newMinFirstPathSum) {
$newMinSecondPathSum = $newMinFirstPathSum;
$newMinFirstPathSum = $currentSum;
$newMinPathCol = $j;
} else if ($currentSum < $newMinSecondPathSum) {
$newMinSecondPathSum = $currentSum;
}
}
$minFirstPathSum = $newMinFirstPathSum;
$minSecondPathSum = $newMinSecondPathSum;
$prevMinPathCol = $newMinPathCol;
}
return $minFirstPathSum;
}
}
```
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