1719 - Number Of Ways To Reconstruct A Tree.

Hard

You are given an array pairs, where <code>pairsi = x_i, y_i</code>, and:

• There are no duplicates.

• <code>x_i< y_i</code>

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 <code>x_i, y_i</code> exists in pairs if and only if <code>x_i</code> is an ancestor of <code>y_i</code> or <code>y_i</code> is an ancestor of <code>x_i</code>.

• 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:

• <code>1 <= pairs.length <= 10⁵</code>

• <code>1 <= x_i< y_i<= 500</code>

• The elements in pairs are unique.