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.
Example:
Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.
思路
动态规划，设置dp数组，dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j]
首先先计算第一行和第一列的dp值，因为只有唯一路径，再计算其他位置。
class Solution:
def minPathSum(self, grid) -> int:
m,n = len(grid), len(grid[0])
dp = [[0] * n for _ in range(m)]
dp[0][0] = grid[0][0]
for i in range(1, n):
dp[0][i] = dp[0][i-1] + grid[0][i]
for i in range(1, m):
dp[i][0] = dp[i-1][0] + grid[i][0]
for i in range(1, m):
for j in range(1, n):
dp[i][j] = min(dp[i][j-1], dp[i-1][j]) + grid[i][j]
print(dp)
return dp[m-1][n-1]
