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Huffman Coding

Huffman Coding. An implementation using C++ STL (part of the material is due to the work of Mark Nelson, Dr. Dobb’s Journal, January 1996). Why C++. No special reason, also C, Java and many more The main advantage of using C++ is the presence of the STL (Standard Template Library).

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Huffman Coding

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  1. Huffman Coding An implementation using C++ STL (part of the material is due to the work of Mark Nelson, Dr. Dobb’s Journal, January 1996)

  2. Why C++ • No special reason, also C, Java and many more • The main advantage of using C++ is the presence of the STL (Standard Template Library) Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  3. What is the STL • It is a library of templates • A template is a class which has a data type that is a parameter (by the way, this data type can be primitive, or itself a class) vector<int>, queue<string> Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  4. What is a queue? • FIFO • Operations: push(), pop() • Very simple to implement, but sometimes we need a more sophisticated form of queue Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  5. What is a priority queue? • In a priority queue each elements has a priority • New elements are added through the function push() • pop() function gets an element from the queue. In a priority queue this element is not the oldest, but the element with the maximum priority • This could be useful in certain types of tasks, for example the scheduler of an operating system Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  6. What is a priority queue? Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  7. Implementation with a heap • One efficient implementation of a priority queue uses a heap • A heap is a data structure that keeps queue elements in a partially-sorted order. Insertion and extraction can be accomplished in log(N) time, where N is the number of elements Also memory overhead is almost null Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  8. Heap characteristics • The elements of a heap are stored in a contiguous array (let’s say, for convenience, from position 1 to position N) • The elements in the array are part of an implicit binary tree. Every element (except the root node) has a parent at location • Each node has a priority that is greater then or equal to both of each children Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  9. Heap

  10. Heap: push() swap Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  11. Heap: pop() • Something similar also happens when we call the pop() functions... • Details don’t matter... Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  12. STL priority_queue • It implements a priority queue using a heap • We don’t need to remember all the details about heap and resorting because ... all is automatic Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  13. Huffman implementation - I • Class node { public: int weight; unsigned char value; const node *child0; const node *child1; Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  14. Huffman implementation - II node(unsigned char c=0, int i=-1) { value=c; weight=i; child0=0; child1=0; } • Constructors • node(const node *c0, const node *c1) { • value=0; • weight=c0->weight + c1->weight; • child0=c0; • child1=c1; } Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  15. Huffman implementation - III • Comparison operator bool operator>(const node &a) const { return weight > a.weight; } Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

  16. The key loop while (q.size()>1) { node *child0 = new node(q.top()); q.pop(); node *child1 = new node(q.top()); q.pop(); q.push(node(child0, child1)); } • and now, let’s have a look at the results... Gabriele Monfardini - Corso di Basi di Dati Multimediali a.a. 2005-2006

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