Leetcode 64.最小路径和

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方法

方法1：动态规划 O(mn)

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class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """

        if not grid:
            return

        r,c=len(grid),len(grid[0])
        dp=[[0]*c for _ in range(r)]
        dp[0][0]=grid[0][0]

        for i in range(1,r):
            dp[i][0]=dp[i-1][0]+grid[i][0]
        for i in range(1,c):
            dp[0][i]=dp[0][i-1]+grid[0][i]
        for i in range(1,r):
            for j in range(1,c):
                dp[i][j]=min(dp[i][j-1],dp[i-1][j])+grid[i][j]
        return dp[-1][-1]

仅仅改变grid自身

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class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """

        if not grid:
            return

        r,c=len(grid),len(grid[0])

        for i in range(1,r):
            grid[i][0]=grid[i-1][0]+grid[i][0]
        for i in range(1,c):
            grid[0][i]=grid[0][i-1]+grid[0][i]
        for i in range(1,r):
            for j in range(1,c):
                grid[i][j]=min(grid[i][j-1],grid[i-1][j])+grid[i][j]
        return grid[-1][-1]

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class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        if not grid:
            return

        r,c=len(grid),len(grid[0])
        dp=[[float('inf')]*(c+1) for i in range(r+1)]
        dp[0][1],dp[1][0]=0,0

        for i in range(1,r+1):
            for j in range(1,c+1):
                dp[i][j]=min(dp[i-1][j],dp[i][j-1])+grid[i-1][j-1]
        return dp[-1][-1]

参考资料