Huffman Coding

Huffman coding is a lossless data compression algorithm named after its inventor, David A. Huffman. It is a variable-length prefix coding algorithm, which means that it assigns shorter codes to the more frequently occurring symbols in a dataset and longer codes to the less frequently occurring symbols. This results in a smaller overall size of the compressed data.

How it Works

The Huffman coding algorithm starts by building a frequency table of all the symbols in the dataset, which shows the number of occurrences of each symbol. Then, it creates a binary tree with each symbol represented by a leaf node. The parent node of two children represents the sum of their frequencies. The process continues until there is only one node left, which is the root of the tree.

Each leaf node in the tree is assigned a unique binary code, where a 0 is assigned to the left child and a 1 is assigned to the right child. The code for each symbol is the path from the root of the tree to the corresponding leaf node, where each edge is either a 0 or a 1. The symbols with the higher frequency are assigned shorter codes, which results in a smaller compressed size.

Example

Suppose we have a dataset that contains the following symbols: "A", "B", "C", "D", and "E", and the frequency of each symbol is as follows: "A" (45), "B" (13), "C" (12), "D" (16), and "E" (9). The frequency table would look like this:

Symbol	Frequency
A	45
B	13
C	12
D	16
E	9

The algorithm would start by building the binary tree, which would look like this:


       *
      / \\
     /   \\
    /     \\
   *       *
  / \\     / \\
 /   \\   /   \\
A     B C     D
       |
       E

Finally, the algorithm would assign binary codes to each symbol, which would look like this:

Symbol	Binary Code
A	0
B	100
C	101
D	11
E	1100

Applications and Real-World Examples

Huffman coding is widely used in various fields, including data compression, image and video compression, and communication networks. For example, the GIF image format uses Huffman coding to compress its data. The MP3 audio format also uses Huffman coding to reduce the size of the audio data.

Alternatives and New Developments

There are several alternatives to Huffman coding, including Arithmetic coding, Shannon-Fano coding, and Run Length Encoding. In recent years, there have been many new developments in the field of data compression, including the use of neural networks for compression and the development of lossy compression algorithms that use machine learning to remove less significant data from the dataset.

Conclusion

Huffman coding is a powerful and widely used data compression algorithm that assigns shorter codes to more frequently occurring symbols in a dataset. It is used in a variety of applications, including image and video compression, communication networks, and data compression. The algorithm is relatively simple to implement and can result in significant reductions in the size of the compressed data.

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Krishna ki chetawani -- कृष्ण की चेतावनी

कृष्ण की चेतावनी -- रामधारी सिंह दिनकर वर्षों तक वन में घूम घूम बाधा विघ्नों को चूम चूम सह धूप घाम पानी पत्थर पांडव आये कुछ और निखर सौभाग्य न सब दिन सोता है देखें आगे क्या होता है मैत्री की राह दिखाने को सब को सुमार्ग पर लाने को दुर्योधन को समझाने को भीषण विध्वंस बचाने को भगवान हस्तिनापुर आए पांडव का संदेशा लाये दो न्याय अगर तो आधा दो पर इसमें भी यदि बाधा हो तो दे दो केवल पाँच ग्राम रखो अपनी धरती तमाम हम वहीँ खुशी से खायेंगे परिजन पे असी ना उठाएंगे दुर्योधन वह भी दे ना सका आशीष समाज की ले न सका उलटे हरि को बाँधने चला जो था असाध्य साधने चला जब नाश मनुज पर छाता है पहले विवेक मर जाता है हरि ने भीषण हुँकार किया अपना स्वरूप विस्तार किया डगमग डगमग दिग्गज डोले भगवान कुपित हो कर बोले जंजीर बढ़ा कर साध मुझे हां हां दुर्योधन बाँध मुझे ये देख गगन मुझमे लय है ये देख पवन मुझमे लय है मुझमे विलीन झंकार सकल मुझमे लय है संसार सकल अमरत्व फूलता है मुझमे संहार झूलता है मुझमे उदयाचल मेरा दीप्त भाल, भूमंडल वक्षस्थल विशाल, भुज परिधि-बन्ध को घेरे हैं, मैनाक-मेरु पग मेरे हैं। दिपते जो ग्रह नक्षत्र निकर, सब हैं

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देखने वाले देखते हैं, सब कुछ देखते हैं ये लोग देख देख कुछ करते नहीं, जाने कहाँ से लगा ये रोग । गरीब देखा, पीड़ित देखा, देखे उनके खेत बंजर फर्क उनको कुछ पड़ा नहीं, देख किसानों का ये मंजर झूठ वादा, झूठे काम, किसानों के प्रति झूठा सम्मान सब देख मंद मुस्काते हैं, चाहे फांद गला लटके किसान हिन्दू देखा, मुस्लिम देखा, देखी जाने कितनी जाती पर जिससे इंसान दिखें, ऐसी कला कहाँ उनको आती देखने वाले देखते हैं, सब कुछ देखते हैं ये लोग देख देख कुछ करते नहीं, जाने कहाँ से लगा ये रोग । घर में देखा, ऑफिस में देखा, देखा ओलंपिक्स में परचम लहराते चाहे जितने हुनर उनके देखे, पर कसी फब्तियां आते जाते कल के दुश्मन आज हैं भाई, गले पड़े भुला के सब लफड़े लेकर ठेका आदर्शवाद का, नाप रहे दूजों के कपडे अधरों पे बेशर्मी का पर्दा, जो पीड़ित है उसी की गलती देख देख इन बड़बोलों को, दानवों की कमी कहाँ है खलती देखने वाले देखते हैं, सब कुछ देखते हैं ये लोग देख देख कुछ करते नहीं, जाने कहाँ से लगा ये रोग । सड़क नहीं, बिजली नहीं, जनता का पैसा, उनकी जेब जहाँ देखो वहीँ मिलेंगे, भरे प

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