# 1719. Number Of Ways To Reconstruct A Tree

https://leetcode.com/problems/number-of-ways-to-reconstruct-a-tree

## Description

You are given an array `pairs`, where `pairs[i] = [xi, yi]`, and:

* There are no duplicates.
* `xi < yi`

Let `ways` be the number of rooted trees that satisfy the following conditions:

* The tree consists of nodes whose values appeared in `pairs`.
* A pair `[xi, yi]` exists in `pairs` **if and only if** `xi` is an ancestor of `yi` or `yi` is an ancestor of `xi`.
* **Note:** the tree does not have to be a binary tree.

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

Return:

* `0` if `ways == 0`
* `1` if `ways == 1`
* `2` if `ways > 1`

A **rooted tree** is a tree that has a single root node, and all edges are oriented to be outgoing from the root.

An **ancestor** of a node is any node on the path from the root to that node (excluding the node itself). The root has no ancestors.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/12/03/trees2.png)

```
**Input:** pairs = [[1,2],[2,3]]
**Output:** 1
**Explanation:** There is exactly one valid rooted tree, which is shown in the above figure.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/12/03/tree.png)

```
**Input:** pairs = [[1,2],[2,3],[1,3]]
**Output:** 2
**Explanation:** There are multiple valid rooted trees. Three of them are shown in the above figures.
```

**Example 3:**

```
**Input:** pairs = [[1,2],[2,3],[2,4],[1,5]]
**Output:** 0
**Explanation:** There are no valid rooted trees.
```

**Constraints:**

* `1 <= pairs.length <= 105`
* `1 <= xi < yi <= 500`
* The elements in `pairs` are unique.

## ac

```java
```
