<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 minPathSum(vector<vector<int>>& grid) {
        int m=grid.size();
        int n=grid[0].size();
        int dp[m+1][n+1];
        for(int i=0;i<=n;i++)
        {
            dp[0][i]=0;
        }
        for(int i=0;i<=m;i++)
        {
            dp[i][0]=0;
        }
        for(int i=1;i<=n;i++){
          dp[1][i]=grid[0][i-1]+dp[1][i-1];
      }
      for(int j=1;j<=m;j++){
          dp[j][1]=grid[j-1][0]+dp[j-1][1];
      }
        for(int i=2;i<=m;i++)
        {
            for(int j=2;j<=n;j++)
            {
                dp[i][j]=grid[i-1][j-1]+min(dp[i][j-1],dp[i-1][j]); 
            }
        }
        return dp[m][n];
    }
};

       
    

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