64.py

class Solution:
    # @param {integer[][]} grid
    # @return {integer}
    def minPathSum(self, grid):
        m = len(grid)
        n = len(grid[0])
        
        temp = grid[0][0]
        for i in range(1,m):
            grid[i][0] += temp
            temp = grid[i][0]
            
        temp = grid[0][0]
        for j in range(1,n):
            grid[0][j] += temp
            temp = grid[0][j]
        
        for i in range(1,m):
            for j in range(1,n):
                grid[i][j] += min(grid[i-1][j], grid[i][j-1])
                
        return grid[m-1][n-1]
        
    
    # new solution
    def minPathSum(self, grid):
        m = len(grid)
        n = len(grid[0])
        
        result = [float('inf')] * (n+1)
        result[1] = 0
        for i in range(0,m):
            for j in range(0,n):
                result[j+1] = min(result[j+1],result[j]) + grid[i][j]
                
        return result[-1]