64. 最小路径和
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。
来源:力扣(LeetCode)
链接:https://leetcode-cn.com/problems/minimum-path-sum/
Link:https://leetcode.com/problems/minimum-path-sum/
动态规划
O(MN)
思考步骤
遇上一题类似,最后一个只能从左边 or 上边到达
dp[x][y] = MIN(dp[x][y - 1], dp[x - 1][y]) + grid[x][y]
计算方向
从左上到右下
边界条件
dp[0][0] = grid[0][0]
top第一排:
dp[0][y] = dp[0][y-1] + grid[0][y]
left第一列
dp[x][0] = dp[x-1][0] + grid[x][0]
代码如下:
class Solution:
def minPathSum(self, grid: List[List[int]]) -> int:
if len(grid) == 0 or len(grid[0]) == 0:
return 0
m = len(grid)
n = len(grid[0])
dp = [[float('inf') for j in range(n)] for i in range(m)]
for i in range(m):
for j in range(n):
if i == 0 and j == 0:
dp[i][j] = grid[i][j]
elif i == 0:
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[-1][-1]
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