<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 ispossible(int i,int j,int m, int n){
        if(i>=0&&i<m&&j>=0&&j<n) return 1;
        return 0;
    }
    
    int minPathSum(vector<vector<int>>& grid) {

        int m=grid.size();
        int n=grid[0].size();

        int dp[m][n];

        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                dp[i][j]=0;
            }
        }
        dp[0][0]=grid[0][0];
        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                if(ispossible(i-1,j,m,n)&&ispossible(i,j-1,m,n))dp[i][j]=min(dp[i-1][j]+grid[i][j],dp[i][j-1]+grid[i][j]);
                else if(ispossible(i-1,j,m,n)) dp[i][j]=dp[i-1][j]+grid[i][j];
                else if(ispossible(i,j-1,m,n)) dp[i][j]=dp[i][j-1]+grid[i][j];
            }
        }
        return dp[m-1][n-1];
    }
};
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