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:

**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:

**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.

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