<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 n = grid.size(), m = grid[0].size();
        int dp[n + 1][m + 1];
        for (int i = 0; i < n + 1; i++){
            for (int j = 0; j <= m; j++){
                dp[i][j] = 900000;
            }
        }
        dp[1][1] = grid[0][0];
        dp[1][0] = 0;
        dp[0][1] = 0;
        for (int i = 1; i < n + 1; i++){
            for (int j = 1;j < m + 1; j++){
                    dp[i][j] = min(dp[i-1][j] + grid[i-1][j-1], dp[i][j-1]+grid[i-1][j-1]);
            }
        }
        return dp[n][m];
    }
};
14200