Minimum Path Sum
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0000-0099/0064.Minimum%20Path%20Sum/images/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>
Array; Dynamic Programming; Matrix
func minPathSum(grid [][]int) int {
	m, n := len(grid), len(grid[0])
	f := make([][]int, m)
	for i := range f {
		f[i] = make([]int, n)
	}
	f[0][0] = grid[0][0]
	for i := 1; i < m; i++ {
		f[i][0] = f[i-1][0] + grid[i][0]
	}
	for j := 1; j < n; j++ {
		f[0][j] = f[0][j-1] + grid[0][j]
	}
	for i := 1; i < m; i++ {
		for j := 1; j < n; j++ {
			f[i][j] = min(f[i-1][j], f[i][j-1]) + grid[i][j]
		}
	}
	return f[m-1][n-1]
}