[leetcode DP]64. Minimum Path Sum

一个m*n的表格，每个格子有一个非负数，求从左上到右下最短的路径值

和62，63两个值是同一个思路，建立dp表，记录每个位置到右下角的最短路径的值

 1 class Solution(object):
 2     def minPathSum(self, grid):
 3         m,n = len(grid),len(grid[0])
 4         flag = [[0 for i in range(n)] for j in range(m)]
 5         flag[m-1][n-1] = grid[m-1][n-1]
 6         for i in range(m-1,-1,-1):
 7             for j in range(n-1,-1,-1):
 8                 if i==m-1:
 9                     if j!=n-1:
10                         flag[i][j] = grid[i][j] + flag[i][j+1]
11                 elif j==n-1:
12                     if i!=m-1:
13                         flag[i][j] = grid[i][j] + flag[i+1][j]
14                 else:
15                     flag[i][j] = min(flag[i+1][j],flag[i][j+1])+grid[i][j]
16         return flag[0][0]

占用线性空间的解法：

 1 class Solution(object):
 2     def minPathSum(self, grid):
 3         m,n = len(grid),len(grid[0])
 4         flag = [0]+[sys.maxint]*(n-1)
 5         for i in range(m):
 6             flag[0] += grid[i][0]
 7             for j in range(1,n):
 8                 flag[j] = min(flag[j],flag[j-1]) +  grid[i][j]
 9         return flag[-1]
10