<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();
        vector<vector<int>>dp(grid.size(),vector<int>(grid[0].size()));
        dp[0][0]=grid[0][0];
        for(int i=0;i<m;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(i==0 && j==0)
                continue;
                int val1=INT_MAX;
                int val2=INT_MAX;
                if(j-1>=0)
                val1=dp[i][j-1];
                if(i-1>=0)
                val2=dp[i-1][j];
                int c=min(val1,val2);
                dp[i][j]=grid[i][j]+c;
            }
        }
        return dp[m-1][n-1];
    }
};
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