题目描述：

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.

思路：采用动态规划的方法，用数组存储起点到当前点距离的最小值。首先算出第一行和第一列的最小值，然后用公式grid[i][j]=grid[i][j] + min(grid[i-1][j],grid[i][j-1])算出其余点的最小值，即可得结果。

代码：

int Solution::minPathSum(vector<vector<int> > &grid)
{
    int m = grid.size();
    int n = grid[0].size();
    int i,j;
    for(i = 1;i < m;i++)
        grid[i][0] = grid[i-1][0] + grid[i][0];
    for(j = 1;j < n;j++)
        grid[0][j] = grid[0][j-1] + grid[0][j];
    for(i = 1;i < m;i++)
        for(j = 1;j < n;j++)
            grid[i][j] = grid[i][j] + min(grid[i-1][j],grid[i][j-1]);
    return grid[m-1][n-1];
}

LeetCode:Minimum Path Sum