[Leetcode]@python 64. Minimum Path Sum

题目链接：https://leetcode.com/problems/minimum-path-sum/

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 题目大意：在矩阵mxn中找到一条从（0,0）到（m,n）的路径，使得这条路径经过的点的总和最小，并返回这个值

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 解题思路：同样可以使用DP进行求解，用a[i][j]表示从(0,0)到(m,n)的所有路径中总和最小的值，动态转移方程为：a[i][j] = min(a[i - 1][j], a[i][j - 1]) + grid[i][j]，同样需要注意在矩阵边界时的特殊处理

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代码（python）：

class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m = len(grid)
        n = len(grid[0])

        ans = [[0 for i in range(n)] for j in range(m)]
        ans[0][0] = grid[0][0]

        for i in range(m):
            for j in range(n):
                if i != 0 and j == 0:
                    ans[i][j] = ans[i - 1][j] + grid[i][j]
                elif i == 0 and j != 0:
                    ans[i][j] = ans[i][j - 1] + grid[i][j]
                elif i != 0 and j != 0:
                    ans[i][j] = min(ans[i - 1][j], ans[i][j - 1]) + grid[i][j]
        return ans[m - 1][n - 1]

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