64. DP Minimum Path Sum

最新推荐文章于 2020-05-19 10:31:11 发布

原创最新推荐文章于 2020-05-19 10:31:11 发布 · 184 阅读

0 ·

CC 4.0 BY-SA版权

LeetCode 专栏收录该内容

13 篇文章

订阅专栏

本文介绍了一个算法问题，即在一个由非负数填充的mxn网格中，从左上角到右下角找到一条路径，使得路径上的所有数字之和最小。路径只能向下或向右移动。文章提供了一个解决方案，使用动态规划计算每个单元格到达右下角的最小路径和。

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:

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

class Solution:
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        #dp[i][j] = min(dp[i-1][j],dp[i][j-1]) + grid[i][j]
        m = len(grid)
        n = len(grid[0])
        for i in range(1, m):
            grid[i][0] += grid[i-1][0]
        for i in range(1, n):
            grid[0][i] += grid[0][i-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[-1][-1]