Number Of Ways To Reconstruct A Tree
<p>You are given an array <code>pairs</code>, where <code>pairs[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>, and:</p>

<ul>
	<li>There are no duplicates.</li>
	<li><code>x<sub>i</sub> &lt; y<sub>i</sub></code></li>
</ul>

<p>Let <code>ways</code> be the number of rooted trees that satisfy the following conditions:</p>

<ul>
	<li>The tree consists of nodes whose values appeared in <code>pairs</code>.</li>
	<li>A pair <code>[x<sub>i</sub>, y<sub>i</sub>]</code> exists in <code>pairs</code> <strong>if and only if</strong> <code>x<sub>i</sub></code> is an ancestor of <code>y<sub>i</sub></code> or <code>y<sub>i</sub></code> is an ancestor of <code>x<sub>i</sub></code>.</li>
	<li><strong>Note:</strong> the tree does not have to be a binary tree.</li>
</ul>

<p>Two ways are considered to be different if there is at least one node that has different parents in both ways.</p>

<p>Return:</p>

<ul>
	<li><code>0</code> if <code>ways == 0</code></li>
	<li><code>1</code> if <code>ways == 1</code></li>
	<li><code>2</code> if <code>ways &gt; 1</code></li>
</ul>

<p>A <strong>rooted tree</strong> is a tree that has a single root node, and all edges are oriented to be outgoing from the root.</p>

<p>An <strong>ancestor</strong> of a node is any node on the path from the root to that node (excluding the node itself). The root has no ancestors.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1700-1799/1719.Number%20Of%20Ways%20To%20Reconstruct%20A%20Tree/images/trees2.png" style="width: 208px; height: 221px;" />
<pre>
<strong>Input:</strong> pairs = [[1,2],[2,3]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> There is exactly one valid rooted tree, which is shown in the above figure.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1700-1799/1719.Number%20Of%20Ways%20To%20Reconstruct%20A%20Tree/images/tree.png" style="width: 234px; height: 241px;" />
<pre>
<strong>Input:</strong> pairs = [[1,2],[2,3],[1,3]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are multiple valid rooted trees. Three of them are shown in the above figures.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> pairs = [[1,2],[2,3],[2,4],[1,5]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no valid rooted trees.</pre>

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

<ul>
	<li><code>1 &lt;= pairs.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= x<sub>i </sub>&lt; y<sub>i</sub> &lt;= 500</code></li>
	<li>The elements in <code>pairs</code> are unique.</li>
</ul>
Tree; Graph
func checkWays(pairs [][]int) int {
	g := make([][]bool, 510)
	v := make([][]int, 510)
	for i := range g {
		g[i] = make([]bool, 510)
	}
	for _, p := range pairs {
		x, y := p[0], p[1]
		g[x][y] = true
		g[y][x] = true
		v[x] = append(v[x], y)
		v[y] = append(v[y], x)
	}
	var nodes []int
	for i := 1; i <= 500; i++ {
		if len(v[i]) > 0 {
			nodes = append(nodes, i)
			g[i][i] = true
		}
	}
	sort.Slice(nodes, func(i, j int) bool {
		return len(v[nodes[i]]) < len(v[nodes[j]])
	})
	equal := false
	root := 0
	for i, x := range nodes {
		j := i + 1
		for ; j < len(nodes) && !g[x][nodes[j]]; j++ {
		}
		if j < len(nodes) {
			y := nodes[j]
			if len(v[x]) == len(v[y]) {
				equal = true
			}
			for _, z := range v[x] {
				if !g[y][z] {
					return 0
				}
			}
		} else {
			root++
		}
	}
	if root > 1 {
		return 0
	}
	if equal {
		return 2
	}
	return 1
}