Question

Write an algorithm that finds the number of descendants of each node v in an n node binary tree

Answer 1

An algorithm to find the number of descendants of each node in a binary tree can be implemented using a depth-first search approach.

Step-by-step explanation:

An algorithm to find the number of descendants of each node in a binary tree can be implemented using a depth-first search approach.

1. Start with the root node and initialize a counter for each node's descendants.
2. Recursively traverse the left and right subtrees. For each node encountered, increment its counter by adding the descendants of its left and right children.
3. Repeat this process until all nodes have been visited.
4. At the end, the counters will hold the number of descendants for each node in the binary tree.

For example, consider the binary tree:

1
/
2 3
/ \
4 5 6

The algorithm would yield the following counts:

Node 1: 5 descendants
Node 2: 2 descendants
Node 3: 1 descendant
Node 4: 0 descendants
Node 5: 0 descendants
Node 6: 0 descendants