【leetcode】931. Minimum Falling Path Sum

题目如下：

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

解题思路：动态规划的入门级题目。状态转移方程： dp[i][j] = min(dp[i-1][j],dp[i-1][j-1],dp[i-1][j+1]) + A[i][j]。

代码如下：

class Solution(object):def minFallingPathSum(self, A):""":type A: List[List[int]]:rtype: int"""for i in range(len(A)):for j in range(len(A[i])):if i - 1 < 0:continueminv = A[i-1][j]if j - 1 >= 0:minv = min(minv,A[i-1][j-1])if j + 1 < len(A[i]):minv = min(minv,A[i-1][j+1])A[i][j] = minv + A[i][j]#print Areturn min(A[-1])

转载于:https://www.cnblogs.com/seyjs/p/9869071.html

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