<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:
    void miniPath(vector<vector<int>>& grid,int x,int y,vector<vector<int>>& ans){
        if(x>=grid.size() || y>=grid[0].size()){
            return;
        }
        if(x==grid.size()-1 && y==grid[0].size()-1){
            ans[x][y]=grid[x][y];
            return;
        }
        if(x==grid.size()-1){
                miniPath(grid,x,y+1,ans);
            ans[x][y]=grid[x][y]+ans[x][y+1];
            return;
        }
        if(y==grid[x].size()-1){
             miniPath(grid,x+1,y,ans);
            ans[x][y]=grid[x][y]+ans[x+1][y];
            return;
        }
        if(ans[x+1][y]!=-1 && ans[x][y+1]!=-1 ){
        ans[x][y]=grid[x][y]+min(ans[x+1][y],ans[x][y+1]);
        return;
        }
        if(ans[x+1][y]!=-1 && ans[x][y+1]==-1 ){
            miniPath(grid,x,y+1,ans);
        ans[x][y]=grid[x][y]+min(ans[x+1][y],ans[x][y+1]);
        return;

        }
        if(ans[x+1][y]==-1 && ans[x][y+1]!=-1 ){
            miniPath(grid,x+1,y,ans);
        ans[x][y]=grid[x][y]+min(ans[x+1][y],ans[x][y+1]);
        return;
        }
         miniPath(grid,x,y+1,ans);
          miniPath(grid,x+1,y,ans);
        ans[x][y]=grid[x][y]+min(ans[x+1][y],ans[x][y+1]);
    }
    int minPathSum(vector<vector<int>>& grid) {
        vector<vector<int>> ans(grid.size(),vector<int>(grid[0].size(),-1));
        miniPath(grid,0,0,ans);
        return ans[0][0];
    }
};
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