LeetCode---64. Minimum Path Sum

题目

给出一个m * n的网格，网格里面的数字是非负数。找出一条从[0, 0]到[m -1, n - 1]的路径，使得路径上元素的和最小。注意：你每次只能向右和向下走一步。如：

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.

Python题解

class Solution:
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m, n = len(grid), len(grid[0])
        dp_grid = [[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_grid[i][j] = grid[i][j]
                elif i == 0:
                    dp_grid[i][j] = grid[i][j] + dp_grid[i][j - 1]
                elif j == 0:
                    dp_grid[i][j] = grid[i][j] + dp_grid[i - 1][j]
                else:
                    dp_grid[i][j] = min(dp_grid[i - 1][j], dp_grid[i][j - 1]) + grid[i][j]

        return dp_grid[-1][-1]