给定一个包含非负整数的 m x n 网格,请找出一条从左上角到右下角的路径,使得路径上的数字总和为最小。
说明:每次只能向下或者向右移动一步。
示例:
输入:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
输出: 7
解释: 因为路径 1→3→1→1→1 的总和最小。
思路:使用动态规划
方法1:
class Solution:
def minPathSum(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
m = len(grid)
n = len(grid[0])
dp=[[0]*n for _ in range(m)]
for i in range(m):
for j in range(n):
if i == 0:
if j== 0:
dp[i][j]= grid[0][0]
else:
dp[i][j]=dp[i][j-1]+grid[i][j]
elif j == 0:
dp[i][j]=dp[i-1][j]+grid[i][j]
else:
dp[i][j] = min(dp[i][j-1],dp[i-1][j]) + grid[i][j]
return dp[m-1][n-1]
方法二:空间优化
m = len(grid)
n = len(grid[0])
dp=[[0] for _ in range(n)]
for i in range(m):
for j in range(n):
if i == 0:
if j== 0:
dp[j]= grid[0][0]
else:
dp[j]=dp[j-1]+grid[i][j]
elif j == 0:
dp[j]=dp[j]+grid[i][j]
else:
dp[j] = min(dp[j-1],dp[j]) + grid[i][j]
return dp[n-1]