<p>Given a <code>m x n</code> <code>grid</code> filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.</p>

<p><strong>Note:</strong> You can only move either down or right at any point in time.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/05/minpath.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[1,3,1],[1,5,1],[4,2,1]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Because the path 1 &rarr; 3 &rarr; 1 &rarr; 1 &rarr; 1 minimizes the sum.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,2,3],[4,5,6]]
<strong>Output:</strong> 12
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 200</code></li>
</ul>

class Solution {
public:
vector<pair<int,int>> movements = {{0,1},{1,0}};
    bool isvalid(int i, int j, int m, int n){
        if(i>=m || j>=n || i<0 || j<0)return false;
        return true;
    }
    long long int func(vector<vector<int> > &grid, int m , int n,vector<vector<int> > &dp){
        long long int t=INT_MAX;
        if(m==grid.size()-1 && n==grid[0].size()-1){
            return grid[m][n];
        }
        if(dp[m][n]!=-1)return dp[m][n];
        for(auto &x: movements){
            int a = m+x.first;
            int b = n+x.second;
            if(isvalid(a,b,grid.size(),grid[0].size())){
                t=min(t,grid[m][n]+func(grid,a,b,dp));
            }
        }
        return  dp[m][n]= t;
    }
    int minPathSum(vector<vector<int>>& grid) {
        // int m=grid.size();
        // int n=grid[0].size();
        vector<vector<int> > dp(grid.size()+10,vector<int> (grid[0].size()+10,-1));
        return func(grid,0,0,dp);
    }
};
13200