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. http://leetcode.com/onlinejudge#question_64

leetcode_minimum_path_sum.cpp

#define MAXN 1000
#define MAX_INT 0x7fffffff
int ans[MAXN][MAXN];

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