For example, suppose we are given the same encoding tree above, and we are asked to decode a file containing the following bits: Leaf nodes represent characters, so once you reach a leaf, you output that character. If the bit is a 0, you move left in the tree. The decoding algorithm is to read each bit from the file, one at a time, and use this bit to traverse the Huffman tree. You can use a Huffman tree to decode text that was previously encoded with its binary patterns. But this will not cause problems in decoding the file, because Huffman encodings by definition have a useful prefix property where no character's encoding can ever occur as the start of another's encoding. It might worry you that the characters are stored without any delimiters between them, since their encodings can be different lengths and characters can cross byte boundaries, as with 'a' at the end of the second byte. You do not need to worry about this it is part of the underlying file system. Files are stored as sequences of whole bytes, so in cases like this the remaining digits of the last bit are filled with 0s. Since the character encodings have different lengths, often the length of a Huffman-encoded file does not come out to an exact multiple of 8 bits. Require 22 bits, or almost 3 bytes, compared to the original file of 10 bytes. The following table details the char-to-binary mapping in more detail. Using the preceding encoding map, the text "ab ab cab" would be encoded as: Using the encoding map, we can encode the file's text into a shorterīinary representation. This structure can be used to create an efficient encoding in the next step. Notice that the nodes with low frequencies end up far down in the tree, and nodes with high frequencies end up near The following diagram shows this process. This will be the root of our finished Huffman tree. This process is repeated until the queue contains only one binary tree node with all the othersĪs its children. The new node the first removed becomes the left child, and the second the right. Now the algorithm repeatedly removes the two nodes from the front of the queue (the two with the smallestįrequencies) and joins them into a new node whose frequency is their sum. (The priority queue is somewhat arbitrary in how it breaks ties, such as 'c' being before EOF and 'a' being before 'b'). The nodes are then put into a priority queue, which keeps them in prioritized order with smaller counts having higher priority, so that characters with lower counts will come out of the queue sooner. Step 2 of Huffman's algorithm places our counts into binary tree nodes, with each node storing a character and a count of its occurrences. Your program's output format should exactly match the abridged log of execution above. Version of that character to the destination file. encode data: Re-examine the source file's contents, and for each character, output the encoded binary.build encoding map: Traverse the binary tree to discover the binary encodings of each character.A priority queue is used to help build the tree along the way. build encoding tree: Build a binary tree with a particular structure, where each node represents a characterĪnd its count of occurrences in the file.count frequencies: Examine a source file's contents and count the number of occurrences of each.The steps involved in Huffman encoding a given text source file into a destination compressed file are:
The table below compares ASCII values of various characters to possible Huffman encodings for some English text.įrequent characters such as space and 'e' have short encodings, while rarer ones like 'z' have longer ones. Infrequently, so the extra cost is worth it. Than 8 bits, but this is reserved for characters that occur Some characters may need to use encodings that are longer
The common letter 'e', it could be given a shorter encoding This is that if a character occurs frequently in the file, such as Requirement and use different-length binaryĮncodings for different characters. Huffman encoding is to abandon the rigid 8-bits-percharacter Normally text data is stored in a standard format of 8 bits perĬharacter using an encoding called ASCII that maps everyĬharacter to a binary integer value from 0-255. It are still used today in computer networks, fax machines, This relatively simpleĬompression algorithm is powerful enough that variations of Huffman of MIT in 1952 for compressing text data to make aįile occupy a smaller number of bytes. Huffman encoding is an algorithm devised by David A. 24 Breadth First Search and Depth First Search.
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