Regions Cut By Slashes
<p>An <code>n x n</code> grid is composed of <code>1 x 1</code> squares where each <code>1 x 1</code> square consists of a <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or blank space <code>&#39; &#39;</code>. These characters divide the square into contiguous regions.</p>

<p>Given the grid <code>grid</code> represented as a string array, return <em>the number of regions</em>.</p>

<p>Note that backslash characters are escaped, so a <code>&#39;\&#39;</code> is represented as <code>&#39;\\&#39;</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0959.Regions%20Cut%20By%20Slashes/images/1.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;/ &quot;]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0959.Regions%20Cut%20By%20Slashes/images/2.png" style="width: 200px; height: 198px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;  &quot;]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0959.Regions%20Cut%20By%20Slashes/images/4.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot;/\\&quot;,&quot;\\/&quot;]
<strong>Output:</strong> 5
<strong>Explanation: </strong>Recall that because \ characters are escaped, &quot;\\/&quot; refers to \/, and &quot;/\\&quot; refers to /\.
</pre>

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

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or <code>&#39; &#39;</code>.</li>
</ul>
Depth-First Search; Breadth-First Search; Union Find; Array; Hash Table; Matrix
function regionsBySlashes(grid: string[]): number {
    const find = (x: number) => {
        if (p[x] !== x) {
            p[x] = find(p[x]);
        }
        return p[x];
    };

    const union = (a: number, b: number) => {
        const pa = find(a);
        const pb = find(b);
        if (pa !== pb) {
            p[pa] = pb;
            size--;
        }
    };

    const n = grid.length;
    let size = n * n * 4;
    const p = Array.from({ length: size }, (_, i) => i);

    for (let i = 0; i < n; i++) {
        for (let j = 0; j < n; j++) {
            const k = i * n + j;
            if (i < n - 1) {
                union(4 * k + 2, (k + n) * 4);
            }
            if (j < n - 1) {
                union(4 * k + 1, (k + 1) * 4 + 3);
            }
            if (grid[i][j] === '/') {
                union(4 * k, 4 * k + 3);
                union(4 * k + 1, 4 * k + 2);
            } else if (grid[i][j] === '\\') {
                union(4 * k, 4 * k + 1);
                union(4 * k + 2, 4 * k + 3);
            } else {
                union(4 * k, 4 * k + 1);
                union(4 * k + 1, 4 * k + 2);
                union(4 * k + 2, 4 * k + 3);
            }
        }
    }

    return size;
}
