Minimum Path Sum

Q:

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.

A: DP

    int minPathSum(vector<vector<int> > &grid) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int>> dp(m,vector<int>(n,0));
        int i,j;
        dp[0][0] = grid[0][0];
        for(j=1;j<n;j++)
            dp[0][j] = grid[0][j] + dp[0][j-1];
        for(i=1;i<m;i++)
            dp[i][0] = grid[i][0] + dp[i-1][0];
            
        for(i=1;i<m;i++)
            for(j=1;j<n;j++)
                dp[i][j] = min(dp[i-1][j],dp[i][j-1])+grid[i][j];
        return dp[m-1][n-1];
    }