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 {

public:

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

    int m=grid.size\(\);

    int n=grid\[0\].size\(\);

    int cost\[m+1\]\[n+1\];



    cost\[1\]\[1\]=grid\[0\]\[0\];

    for \(int i=2;i<=m;i++\){

        cost\[i\]\[1\]=cost\[i-1\]\[1\]+grid\[i-1\]\[0\];

    }

    for \(int j=2;j<=n;j++\){

        cost\[1\]\[j\]=cost\[1\]\[j-1\]+grid\[0\]\[j-1\];

    }

    for \(int i=2;i<=m;i++\){

        for\(int j=2;j<=n;j++\){

            cost\[i\]\[j\]=grid\[i-1\]\[j-1\]+min\(cost\[i-1\]\[j\],cost\[i\]\[j-1\]\);

            //cout<<cost\[i\]\[j\]<<endl;

        }

    }

    return cost\[m\]\[n\];

}

};