Prove that a binary tree that is not full cannot correspond to an optimal prefix free code. Note: a full binary tree is a tree in which any non-leaf node has 2 children (see page 430). Your proof (which is very simple) should have the following structure: Consider a prefix-free code C, whose corresponding binary tree T has some node with only one child; show that you can transform T into another binary tree T', whose corresponding code C' has smaller average length and so is better than C (which means that C is not optimal). In your proof you need to indicate the transformation from T into T' and explain why the code C' is better than C.
Prove that a binary tree that is not full cannot correspond to an optimal prefix free code. Note: a full binary tree is a tree in which any non-leaf node has 2 children (see page 430). Your proof (which is very simple) should have the following structure: Consider a prefix-free code C, whose corresponding binary tree T has some node with only one child; show that you can transform T into another binary tree T', whose corresponding code C' has smaller average length and so is better than C (which means that C is not optimal). In your proof you need to indicate the transformation from T into T' and explain why the code C' is better than C.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Prove that a binary tree that is not full cannot correspond to an optimal prefix free code. Note: a full
binary tree is a tree in which any non-leaf node has 2 children (see page 430). Your proof (which is very
simple) should have the following structure: Consider a prefix-free code C, whose corresponding binary
tree T has some node with only one child; show that you can transform T into another binary tree T',
whose corresponding code C' has smaller average length and so is better than C (which means that C
is not optimal). In your proof you need to indicate the transformation from T into T' and explain why the
code C' is better than C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4bc34d5-9865-4edc-9563-489615bf75b2%2F3cebf31a-5696-4e83-b702-7f1647aeb20e%2Fw8xqz8n_processed.png&w=3840&q=75)
Transcribed Image Text:Prove that a binary tree that is not full cannot correspond to an optimal prefix free code. Note: a full
binary tree is a tree in which any non-leaf node has 2 children (see page 430). Your proof (which is very
simple) should have the following structure: Consider a prefix-free code C, whose corresponding binary
tree T has some node with only one child; show that you can transform T into another binary tree T',
whose corresponding code C' has smaller average length and so is better than C (which means that C
is not optimal). In your proof you need to indicate the transformation from T into T' and explain why the
code C' is better than C.
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