Question

Must a Huffman tree be a two-tree? Explain

Answer 1

HUFFMAN TREE:

Huffman coding assigns codes to characters such as the length of the code depends on the ratio or weight of the corresponding character. Huffman codes area unit of variable-length, and prefix-free (no code may be a prefix of any other). Any prefix-free computer code is often unreal as a binary tree with the encoded characters keep at the leaves.

Huffman cryptography tree or Huffman tree is a full binary tree within which every leaf of the tree corresponds to a letter within the given alphabet.

The Huffman tree is that the binary tree with minimum external path weight, i.e., the one with the minimum add of weighted path lengths for the given set of leaves. that the goal is to create a tree with the minimum external path weight.

There are primarily 2 major parts in Huffman coding:
1) Build a Huffman Tree from input characters.
2) Traverse the assign code of characters.

Three problems:
1.encoding
2.decoding
3.Huffman tree building

1.Encoding:
Encoding a string are often done by replacement every letter within the string with its computer code (the Huffman code).
Examples:
DEED 10100101 (8 bits)
MUCK 111111001110111101 (18 bits)

2.Decoding:

Decoding AN encoded string is often done by viewing the bits within the coded string from left to right till a letter decoded.
10100101 -> DEED

3.Huffman tree building:

A simple algorithm:
1. Prepare a set of n initial Huffman trees, every of that may be a single leaf node. place the n trees onto a priority queue organized by weight (frequency).
2. Remove the primary 2 trees (the ones with the bottom weight). be a part of these 2 trees to make a brand new tree whose root has the 2 trees as youngsters, and whose weight is that the addition of the weights of the 2 youngsters trees.
3. Put this new tree into the priority queue.
4. Repeat steps 2-3 till all of the partial Huffman trees are combined into one.

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