<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:
    int dp[200][200];
    int solve(vector<vector<int>>& grid, int x , int y, int m ,int n){
        if(x <0 || x > m || y>n || y<0){
            return 0;
        }
        if(dp[x][y] >0){
            return dp[x][y];
        }
        cout<< x << " "<< y ;
        if(x == m-1 && y == n-1){
            return dp[x][y]=grid[x][y]; 
        }
        if(x == m-1){
            return dp[x][y]=grid[x][y] + solve(grid, x , y+1,m , n );
        }
        if( y == n-1){
             return dp[x][y]=grid[x][y] +solve(grid, x+1 , y,m , n );
        }
        int a = solve(grid, x+1, y , m ,n);
        int b= solve(grid, x, y+1 , m ,n);
        return dp[x][y]=grid[x][y] + min(a, b);
    }
    int minPathSum(vector<vector<int>>& grid) {
        memset(dp, -1, sizeof(dp));
        // vector<vector<bool>> vis(grid.size(), vector<int>(grid[0].size(), 0)); 
        return solve(grid, 0, 0 , grid.size(), grid[0].size()); 
    }
};
12600