Huffman Encoding Algorithm - Concepts and Example

Huffman Encoding Algorithm - Concepts and Example

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  Huffman Encoding Dr.Mary Jacob Department ofComputer Science Kristu Jayanti College(Autonomous),Bengaluru
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  What is HuffmanEncoding? Ø Huffman Encoding is a lossless data compression algorithm. Ø It assigns shorter codes to more frequent characters and longer codes to less frequent ones. Ø It was developed by David A. Huffman in 1952.
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  Ø Prefix Code:No code is a prefix of another (e.g., 10 and 101 are invalid). Ø Binary Tree: The algorithm builds a binary tree where each character is a leaf node. Ø Variable-Length Encoding: Frequently used characters get shorter binary representations. Key Concepts
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  � ️ Steps to PerformHuffman Encoding Ø Count the frequency of each character. Ø Build a priority queue (min-heap) with all characters and their frequencies. Ø While there is more than one node in the queue: Ø Remove the two nodes with the lowest frequency.Create a new internal node with frequency = sum of the two nodes.Add this new node back to the queue.The remaining node is the root of the Huffman Tree. Ø Assign codes: ØTraverse left: assign 0 ØTraverse right: assign 1 ØEncode the data by replacing each character with its Huffman code.
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  �Example String : AA B C C C D D D D Step 1: Frequency Count Character Frequency A 2 B 1 C 3 D 4
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  �Example Step 2: CreateNodes and Build Huffman Tree 1. Insert nodes: A(2), B(1), C(3), D(4) 2. Combine smallest two: B(1) + A(2) = BA(3) 3. New queue: BA(3), C(3), D(4) 4. Combine two smallest: BA(3) + C(3) = BAC(6) 5. New queue: BAC(6), D(4) 6.Combine final two: D(4) + BAC(6) = Root(10) [10] / D(4) [6] / BA(3) C(3) / B(1) A(2)
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  �Example [10] / D(4) [6] / BA(3) C(3) / B(1) A(2) Step 3: Assign Codes from Tree Let’s assign binary codes (left = 0, right = 1): From root traverse to the leaf: ü D = 0 ü C = 11 ü B = 100 ü A = 101 1 1 1 0 0 0
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  Step 4: Encodethe String Original string: A A B C C C D D D D Huffman codes: A = 101, B = 100, C = 11, D = 0 Encoded binary string:101 101 100 11 11 11 0 0 0 0 Key Concepts
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  ✅ Advantages ofHuffman Encoding Lossless compression. Reduces file size. Efficient when character frequency varies. ❗ Limitations: Needs the frequency table to decode. Not ideal if all characters have similar frequency.
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  Thank You