64.Minimum Path Sum

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.

class Solution:
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m,n = len(grid),len(grid[0])
        dp = [[0 for i in range(n)] for j 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]
                    continue
                if i==0:
                    dp[i][j] = dp[i][j-1] + grid[i][j]
                    continue
                if j==0:
                    dp[i][j] = dp[i-1][j] + grid[i][j]
                    continue
                dp[i][j] = min(dp[i-1][j],dp[i][j-1])+grid[i][j]
        return dp[-1][-1]