931. Minimum Falling Path Sum
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:
[1,4,7], [1,4,8], [1,5,7], [1,5,8], [1,5,9]
[2,4,7], [2,4,8], [2,5,7], [2,5,8], [2,5,9], [2,6,8], [2,6,9]
[3,5,7], [3,5,8], [3,5,9], [3,6,8], [3,6,9]
The falling path with the smallest sum is [1,4,7]
, so the answer is 12
.
Note:
1 <= A.length == A[0].length <= 100
-100 <= A[i][j] <= 100
class Solution {
public int minFallingPathSum(int[][] A) {
if(A == null || A.length == 0 || A[0].length == 0) return 0;
int min = Integer.MAX_VALUE;
for(int i = 1; i < A.length; i++){
for(int j = 0; j < A[0].length;j++){
int left = j-1, mid = j, right = j+1;
//track i - 1;
if(inBound(left,A) && inBound(right,A)){
A[i][j] = A[i][j] + Math.min(A[i-1][left],Math.min(A[i-1][mid],A[i-1][right]));
}
else if(!inBound(left,A)){
A[i][j] = A[i][j] + Math.min(A[i-1][mid],A[i-1][right]);
}else{
A[i][j] = A[i][j] + Math.min(A[i-1][mid],A[i-1][left]);
}
}
}
for(int i = 0; i < A[0].length;i++){
if(A[A.length-1][i] < min){
min = A[A.length-1][i];
}
}
return min;
}
public boolean inBound(int x, int[][] A){
if(x < 0 || x >= A[0].length) return false;
else return true;
}
}
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