【LeetCode】64. Minimum Path Sum

Minimum Path Sum

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.

解题思路：

典型的动态规划。开辟m*n的矩阵path，path[i][j]存放从首元素(grid[0][0])到当前元素(grid[i][j])的最短路径长度。

对于每个元素来说，路径是从上或者从左边来的。

也就是说path[i][j] = min(path[i-1][j]+path[i][j-1]) + grid[i][j]。

注意：初始化第一行第一列。

class Solution {

public:

    int minPathSum(vector<vector<int> > &grid) {

        if(grid.empty() || grid[].empty())

            return ;

        int m = grid.size();

        int n = grid[].size();

        vector<vector<int> > path(m, vector<int>(n, ));

        path[][] = grid[][];

        for(int i = ; i < m; i ++)

            path[i][] = path[i-][] + grid[i][];

        for(int i = ; i < n; i ++)

            path[][i] = path[][i-] + grid[][i];

        for(int i = ; i < m; i ++)

        {

            for(int j = ; j < n; j ++)

            {

                path[i][j] = min(path[i-][j], path[i][j-]) + grid[i][j];

            }

        }

        return path[m-][n-];

    }

};

巴特西

【LeetCode】64. Minimum Path Sum

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