Leetcode 64. Minmum Path Sum

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.

思路：一个很典型的DP问题。由于只能向下或者右走，所以通过 [i,j] 这个点的最短路径，要么是从[i-1,j]过来，要么从[i,j-1]过来。注意当i=0和j=0时这两个边界特例。

 1 class Solution(object):
 2     def minPathSum(self, grid):
 3         """
 4         :type grid: List[List[int]]
 5         :rtype: int
 6         """
 7         m = len(grid)
 8         n = len(grid[0])
 9         minSum = [[0]*n for x in range(m)]
10
11         for i in range(m):
12             for j in range(n):
13                 if i == 0 and j == 0:
14                     minSum[0][0] = grid[0][0]
15                 elif i == 0:
16                     minSum[i][j] = minSum[i][j-1] + grid[i][j]
17                 elif j == 0:
18                     minSum[i][j] = minSum[i-1][j] + grid[i][j]
19                 else:
20                     minSum[i][j] = min(minSum[i-1][j], minSum[i][j-1]) + grid[i][j]
21
22         return minSum[-1][-1]