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
class Solution {
public int minFallingPathSum(int[][] arr) {
// Bottom up approach
int minSum = Integer.MAX_VALUE, secondMinSum = Integer.MAX_VALUE;
int index = -1;
// Find 2 smallest sum path sum in each level
for (int i = arr.length - 1; i >= 0; i--) {
int tempSmall = Integer.MAX_VALUE, tempSecondSmall = Integer.MAX_VALUE;
int t = -1;
for (int j = 0; j < arr[i].length; j++) {
int currentSum = arr[i][j];
if (i != arr.length - 1) {
if (j != index)
currentSum += minSum;
else
currentSum += secondMinSum;
}
if (currentSum < tempSmall) {
tempSecondSmall = tempSmall;
tempSmall = currentSum;
t = j;
} else if (currentSum < tempSecondSmall)
tempSecondSmall = currentSum;
}
minSum = tempSmall;
secondMinSum = tempSecondSmall;
index = t;
}
return minSum;
}
}