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
function uniquePaths(m: number, n: number): number {
    const f: number[][] = Array(m)
        .fill(0)
        .map(() => Array(n).fill(0));
    f[0][0] = 1;
    for (let i = 0; i < m; ++i) {
        for (let 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];
}
