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]

Note:

1. 1 <= A.length == A[0].length <= 100
2. -100 <= A[i][j] <= 100

給定一個方形整數數組 A，我們想要得到通過 A 的下降路徑的最小和。

下降路徑可以從第一行中的任何元素開始，並從每一行中選擇一個元素。在下一行選擇的元素和當前行所選元素最多相隔一列。

示例：

輸入：[[1,2,3],[4,5,6],[7,8,9]]
輸出：12
解釋：
可能的下降路徑有：

• [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]

和最小的下降路徑是 [1,4,7]，所以答案是 12。

提示：

1. 1 <= A.length == A[0].length <= 100
2. -100 <= A[i][j] <= 100

196ms

 1 class Solution {
 2     func minFallingPathSum(_ A: [[Int]]) -> Int {
 3         let m:Int = A[0].count
 4         var dp:[Int] = A[0]
 5         for j in 0..<(A.count - 1)
 6         {
 7             var row:[Int] = A[j]
 8             var ndp:[Int] = [Int](repeating: Int.max / 2,count: m)
 9             for i in 0..<m
10             {
11                 for k in -1...1
12                 {
13                     if i+k >= 0 && i+k < m
14                     {
15                         ndp[i + k] = min(ndp[i + k], dp[i] + A[j + 1][i + k])
16                     }
17                 }
18             }
19             dp = ndp
20         }
21         var ret:Int = Int.max
22         for v in dp
23         {
24             ret = min(ret, v)
25         }
26         return ret
27     }
28 }

[Swift Weekly Contest 108]LeetCode931. 下降路徑最小和 | Minimum Falling Path Sum