How to solve the problem that Huffman trees are not unique 5

Certainly not the only :

A string Huffman tree can be drawn in a variety of ways.

For example:"a fast runner need never be afraid of the dark"

There are 46 characters in total: Arranged by frequency of occurrence of characters from largest to smallest:

It can be drawn like this:

Take A's ** is: 1101

The second way to draw:

a= 10110

There are other ways to draw a=010

I've looked through all the information and really haven't found a unique way to draw a Huffman tree, since there are many ways to draw, the height is definitely different, and the height is definitely not the same. Please click Enter a description.

Huffman trees are not unique because there is no limit to the left and right subtrees, and when the weight values are repeated, the height of the tree may not be unique, but the only thing is that the sum of the weighted path lengths is the smallest.

Huffman tree, also known as optimal binary tree, refers to a group of leaf nodes with definite weights to construct a group of leaf nodes with definite weights. The branches from one node to another in the tree constitute the path between the two nodes, and the number of branches on the path is called the path length. The path length of a binary tree is the sum of the path lengths from the root node to all leaf nodes.

If the leaf nodes in the binary tree all have a certain weight, then this concept can be used.

If the binary tree has n leaf nodes with weights, then the sum of the product of the path length from the root node to each leaf node and the weight of the leaf node is called the path length of the binary tree, which is denoted as: WPL=W1L1+W2L2+WNLN, etc.; Wherein: n is the number of leaf nodes in the binary tree; wk is the weight of the k-th leaf; LK is the path length of the k-th leaf node.

Haverman trees can not be unique, but they have the same weighted path length.

In addition, the Haverman code is unique. Please distinguish between the two (Haverman tree and Haverman code)!

Absolutely unique.

1. Understand the meaning of the concept.

2. Don't make mistakes during operation.

Only uniqueness can guarantee the success of Huffman encoding and decoding.

Absolute.

Neither the Huffman tree nor the coding are unique! Only WPL is the only one!

Haverman trees can be non-unique, but they have the same weighted path length, and the Haverman code is unique.

Huffman Tree. Not unique, because there is no limit to the left and right subtrees, and when the weighted values are repeated, the height of the tree may not be unique, but the only thing is the sum of the weighted path lengths is the smallest.

Set up a binary tree. Leaf nodes with n weights.

The sum of the length of the path from the root node to each leaf node and the weight of the leaf node is called the binary tree path length, which is denoted as: WPL = W1L1 + W2L2 + WNLN and so on. Wherein: n is the number of leaf nodes in the binary tree; wk is the weight of the k-th leaf; LK is the path length of the k-th leaf node.

Huffman tree construction.

Huffman tree generated by a structured Huffman algorithm.

Ziling orders the wax trees are all ordered, so the nodes are generally sorted when generating huffman trees, and even then the results are not unique.

Huffman static encoding: it scans the data to be encoded twice: the first pass simply refers to counting the frequency of each character in the original data, using the obtained frequency value to create a Huffman tree, and must save the information of the tree, that is, the frequency value of the character 0-255 (2 8=256) is stored in the order of 2-4bytes in length, so that the ruler slides to create the same Huffman tree for decompression; The second pass is encoded according to the Huffman tree obtained by the first scan, and the codewords obtained after encoding are stored.

(2+3+4)*2+(1+3)*3=27, the italics part is the weight, and the tree I built is like this.