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Chapter 9: Problem 14

Give an algorithm for constructing a full binary tree with \(n>1\) terminal vertices.

Short Answer

Expert verified
The algorithm for constructing a full binary tree with \(n>1\) terminal vertices involves initializing a new full binary tree with a single root node, and then adding \(n-1\) pairs of children nodes, each pair being attached to an existing node, starting from the root. At the end, the tree is verified to be a full binary tree with \(n\) terminal vertices.

Step by step solution

01

Initialize the tree

The algorithm begins by initializing a new full binary tree. This is done by creating a single root node.
02

Create terminal vertices

Then, create \(n-1\) pairs of children nodes. Each pair will be created as the children of one of the existing nodes in the tree, starting from the root.
03

Verify

Finally, verify the outcome. At this point, the tree should be a full binary tree with \(n\) terminal vertices.

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