LeetCode 64. Minimum Path Sum（最小和的路径）

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

题目标签：Array

　　这道题目和前面两题差不多，基本思想都是一样的。这题要求我们找到最小和的路径。同样用Dynamic programming，我们可以分析一下，path 只能走右边和下面，那么对于每一个点，它的path 只可能从左边和上面来，我们只要在两者中取一个小的加上自己就可以了。因此，遍历gird，对于每一个点，有四种情况：

　　case 1：它有left 和top，取小的加上自己；

　　case 2：它只有left，left + 自己；

　　case 3：它只有top， top + 自己；

　　case 4：它没有left 和top，什么都不需要做。

　　最后返回终点的值就可以了。这里可以in-place，也可以自己新建立一个matrix。

Java Solution:

Runtime beats 35.80%

完成日期：07/22/2017

关键词：Array

关键点：Dynamic Programming，逆向思考

 1 public class Solution
 2 {
 3     public int minPathSum(int[][] grid)
 4     {
 5         int rowSize = grid.length;
 6         int colSize = grid[0].length;
 7
 8
 9         for(int i=0; i<rowSize; i++) // row
10         {
11             for(int j=0; j<colSize; j++) // column
12             {
13                 // if this point has both left and top
14                 if(j-1 >=0 && i-1 >=0)
15                     grid[i][j] += Math.min(grid[i][j-1], grid[i-1][j]);
16                 else if(j-1 >=0) // if this point only has left
17                     grid[i][j] += grid[i][j-1];
18                 else if(i-1 >=0) // if this point only has top
19                     grid[i][j] += grid[i-1][j];
20                 // else, this point has no left and no top
21
22             }
23         }
24
25         return grid[rowSize-1][colSize-1];
26     }
27 }

参考资料：N/A

LeetCode 算法题目列表 - LeetCode Algorithms Questions List

转载于:https://www.cnblogs.com/jimmycheng/p/7223470.html

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