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) {
// dp[i][j] shows min fall path from this element
int[][] dp = new int[A.length][A.length];
// bottum up approach
for (int i = A.length - 1; i >= 0; i--) {
for (int j = 0; j < A.length; j++) {
dp[i][j] = A[i][j];
if(i==A.length-1)
continue; // base case
if (j == 0)
dp[i][j] += Math.min(dp[i + 1][j], dp[i + 1][j + 1]);
else if (j == A.length - 1)
dp[i][j] += Math.min(dp[i + 1][j - 1], dp[i + 1][j]);
else
dp[i][j] += Math.min(dp[i + 1][j], Math.min(dp[i + 1][j - 1], dp[i + 1][j + 1]));
}
}
// finding min from first row
int min = Integer.MAX_VALUE;
for (int x : dp[0])
min = Math.min(x, min);
return min;
}
}
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