Unique Paths
<p>There is a robot on an <code>m x n</code> grid. The robot is initially located at the <strong>top-left corner</strong> (i.e., <code>grid[0][0]</code>). The robot tries to move to the <strong>bottom-right corner</strong> (i.e., <code>grid[m - 1][n - 1]</code>). The robot can only move either down or right at any point in time.</p>

<p>Given the two integers <code>m</code> and <code>n</code>, return <em>the number of possible unique paths that the robot can take to reach the bottom-right corner</em>.</p>

<p>The test cases are generated so that the answer will be less than or equal to <code>2 * 10<sup>9</sup></code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0000-0099/0062.Unique%20Paths/images/robot_maze.png" style="width: 400px; height: 183px;" />
<pre>
<strong>Input:</strong> m = 3, n = 7
<strong>Output:</strong> 28
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> m = 3, n = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -&gt; Down -&gt; Down
2. Down -&gt; Down -&gt; Right
3. Down -&gt; Right -&gt; Down
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
</ul>
Math; Dynamic Programming; Combinatorics
func uniquePaths(m int, n int) int {
	f := make([][]int, m)
	for i := range f {
		f[i] = make([]int, n)
	}
	f[0][0] = 1
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			if i > 0 {
				f[i][j] += f[i-1][j]
			}
			if j > 0 {
				f[i][j] += f[i][j-1]
			}
		}
	}
	return f[m-1][n-1]
}