Lintcode 110. Minimum Path Sum (Easy) (Python)

最新推荐文章于 2020-06-03 05:27:45 发布

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最新推荐文章于 2020-06-03 05:27:45 发布

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文章标签： Lintcode Python

本文链接：https://blog.youkuaiyun.com/weixin_41677877/article/details/81301503

本文介绍了一种寻找矩阵中从左上角到右下角路径的算法，该路径上的数值之和最小。通过动态规划的方法更新矩阵中的每个元素，使其包含到达该位置的最小路径和。最终返回矩阵右下角的值即为最小路径和。

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Minimum Path Sum

Description:

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.

Code:

class Solution:
    """
    @param grid: a list of lists of integers
    @return: An integer, minimizes the sum of all numbers along its path
    """
    def minPathSum(self, grid):
        # write your code here
        m = len(grid)
        if m==1:
            return sum(grid[0])
        if m==0:
            return 0
        n = len(grid[0])

        for i in range(1,m):
            grid[i][0] += grid[i-1][0]
        for j in range(1,n):
            grid[0][j] += grid[0][j-1]

        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]