LeetCode 64. Minimum Path Sum

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题目

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:

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Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

思路

DP.
新的一个点的最短路径一定等于其上方、左方最短路径+当前的值，
即有:grid[i][j] = min(grid[i-1][j], grid[i][j-1]) + grid[i][j]
同时注意i=0和j=0时的边界。

代码

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class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        if not grid or not grid[0]:
            return 0
        m, n = len(grid), len(grid[0])
        for i in range(m):
            for j in range(n):
                if i == 0 and j == 0:
                    tmp = 0
                if i == 0 and j != 0:
                    tmp = grid[i][j-1]
                if i != 0 and j == 0:
                    tmp = grid[i-1][j]
                if i != 0 and j != 0:
                    tmp = min(grid[i-1][j], grid[i][j-1])
                grid[i][j] = tmp + grid[i][j]
        return grid[m-1][n-1]