<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 row = grid.size();
        int col = grid[0].size();

        vector<int>dp(col,0);

        for(int i=0 ; i<row ; i++)
        {
            int temp=0;

            for(int j=0 ; j<col ; j++)
            {
                if(i==0 && j==0)
                    dp[0] = grid[0][0];

                else
                {
                    int up=INT_MAX;
                    int left=INT_MAX;

                    if(i>0) up = grid[i][j] + dp[j];

                    if(j>0) left = grid[i][j] + temp;

                    dp[j] = min(up,left);
                }

                temp = dp[j];
            }
        }

        return dp[col-1];

    }
};
12500