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Huffman Coding

Explore the fascinating world of Huffman Coding in Computer Science in this comprehensive guide. Discover what Huffman Coding is, its vital role in data representation, and delve deep into understanding the complexities of the Huffman Coding algorithm. Furthermore, get insight into real-world applications of Huffman Coding through practical examples and Python implementations. Finally, gain an in-depth understanding of Huffman Coding's role in data compression, all in a simple, easy-to-follow manner. This guide promises to be an excellent resource for both budding and experienced computer scientists.

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Jetzt kostenlos anmeldenExplore the fascinating world of Huffman Coding in Computer Science in this comprehensive guide. Discover what Huffman Coding is, its vital role in data representation, and delve deep into understanding the complexities of the Huffman Coding algorithm. Furthermore, get insight into real-world applications of Huffman Coding through practical examples and Python implementations. Finally, gain an in-depth understanding of Huffman Coding's role in data compression, all in a simple, easy-to-follow manner. This guide promises to be an excellent resource for both budding and experienced computer scientists.

Huffman Coding: An efficient data compression algorithm, it creates variable-length codes to represent characters such that most common characters have the shortest codes and the less common characters have the longest codes.

- Character Frequency Calculation
- Heap Tree Creation
- Huffman Tree Creation

Character | Frequency |

A | 15 |

B | 7 |

C | 6 |

D | 6 |

E | 5 |

The Heap Tree is constructed based on the frequency of the characters. The characters with higher frequencies are placed near the root of the tree, and the characters with lesser frequencies are placed deeper.

Procedure HuffmanCoding is Input: A set of symbols together with their weights (usually proportional to probabilities). Output: An optimal prefix-free binary code with the minimum expected codeword length. 1. If there is only one symbol, its code is [ 0 ], otherwise: 2. Let a and b be the two symbols in Prim with the smallest weights. 3. Replace a and b in Prim by a single symbol a+b, whose weight is the sum of the weights of a and b. 4. Assign binary codes to each symbol, giving the merged symbol the compound code and the others, codes with the same prefix and an additional bit 0 or 1. Repeat steps 1 to 4 until Prim contains only one symbol.

Enhance Storage Efficiency: Huffman coding represents frequently used characters with shorter bit codes, effectively compressing the data. This leads to more efficient utilization of storage resources.

Facilitate Faster Data Transmission: With smaller, more efficient representations of data, Huffman coding can help speed up data transmission across networks.

Consider transmitting a video file over the internet. If the file is uncompressed, it might take a significant amount of time and bandwidth to send. However, if the file is compressed using Huffman coding or another data compression technique, it can be transmitted more quickly and consume less network resources.

- Character Frequency Calculation: Count the frequency of occurrence of each character in the data set.
- Heap Creation: Create a heap or priority queue and insert all characters into the heap, with their frequencies as the keys.
- Huffman Tree Creation: Construct a Huffman tree by repeatedly removing the two nodes with the least frequencies, combining them, and putting the combined node back into the heap. Continue until only one node is left in the heap, which will be the root of the Huffman Tree.
- Code Generation: Traverse the Huffman Tree to generate the Huffman codes, by assigning a '0' for every left child and a '1' for every right child.
- Code Storage: Store the generated Huffman codes in a dictionary or map for easy lookup when doing data compression or decompression.

Character | Frequency |

H | 1 |

U | 1 |

F | 2 |

M | 1 |

A | 1 |

N | 1 |

Begin compute the frequency of each character in the data set. make each character a node and create a minimum heap. while heap contains more than one node remove node1 and node2 from heap create a new node with frequency = frequency(node1)+frequency(node2) insert node into heap end while traverse heap to generate Huffman codes End.In providing an effective compression of character data, Huffman Coding uses these specially derived codes and leverages the character frequency metrics to provide efficient representation.

(H,1), (U,1), (M,1), (A,1), (N,1), (F,2)Now, we begin constructing the Huffman Tree. We remove the two nodes with the smallest frequencies from the heap. Here, we have five nodes with the same frequency. The selection can be arbitrary, so let's take the nodes for 'H' and 'U'. We create a new node with the combined frequency of 'H' and 'U', which is \(1 + 1 = 2\). This new node becomes the parent of 'H' and 'U' in the tree, with 'H' as the left child and 'U' as the right child. We give a '0' to the left edge and a '1' to the right edge. We put this new node back into the heap. Our heap now looks like this:

(M,1), (A,1), (N,1), (F,2), (HU,2)We repeat this process. We can arbitrarily select 'M' and 'A' and merge them into a new node with a combined frequency of \(1 + 1 = 2\). It makes 'M' the left child and 'A' the right child. After reinserting it, the heap is:

(N,1), (F,2), (HU,2), (MA,2)Next, we take out 'N' and 'F' with the lowest frequencies. Their combined frequency is \(1 + 2 = 3\). We insert the new node back into the heap:

(HU,2), (MA,2), (NF,3)We continue this until we only have one node left, which becomes the root of our Huffman tree. The final Huffman Tree would look like this:

(HU,2) - 0 (H,1) - 1 (U,1) (MA,2) - 0 (M,1) - 1 (A,1) (NF,3) - 0 (N,1) - 1 (F,2)By navigating from the root to each character, we generate the Huffman codes. For example, the Huffman code for 'H' is '00', for 'U' is '01', and so on. The nodes close to the root have shorter codes, and nodes deeper in the tree have longer codes, reflecting their frequencies in the original data. This is how a Huffman Coding Tree is constructed, leading to the generation of Huffman codes, which are then used to compress data. The process, though complex, is systematic and deterministic, producing efficient and replicable results every time.

class Node: def __init__(self, char, frequency, left_child=None, right_child=None): self.char = char self.frequency = frequency self.left_child = left_child self.right_child = right_childOnce you have established your Node class, the initial step is to calculate the frequency count for each character in the data set. Python's built-in dictionary, where each character from the data set is associated with its frequency count, is perfect for this task.

def character_frequency(data): frequency_dict = {} for char in data: if char not in frequency_dict: frequency_dict[char] = 0 frequency_dict[char] += 1 return frequency_dictThe calculation of character frequencies is followed by the creation of a priority queue, managed as a binary heap. Python has a built-in module named 'heapq' providing heap queue algorithms that are ideal for this task. Each item in your heap queue should be a node object that encapsulates the character and its frequency of occurrence. Upon constructing your heap queue, you can proceed to create the Huffman Tree:

import heapq def build_huffman_tree(frequency_dict): heap = [[weight, Node(char, weight)] for char, weight in frequency_dict.items()] heapq.heapify(heap) while len(heap) > 1: lo = heapq.heappop(heap) hi = heapq.heappop(heap) combined_node = Node(None, lo[0] + hi[0], lo[1], hi[1]) heapq.heappush(heap, [combined_node.frequency, combined_node]) return heap[0]In this section of the code, you create a heap from the frequency dictionary items. The while loop then iterates until only one element, the root node of the Huffman tree, remains in the heap. In each iteration, you pop the two nodes with the smallest frequencies, create a new combined node, and push it back into the heap. Finally, you traverse the Huffman Tree to generate the Huffman codes. Again, a dictionary provides an excellent way to store these codes for easy lookup.

def generate_huffman_codes(root): huff_code_dict = {} def get_codes_helper(node, code_prefix=""): if node is not None: if node.char is not None: huff_code_dict[node.char] = code_prefix get_codes_helper(node.left_child, code_prefix + "0") get_codes_helper(node.right_child, code_prefix + "1") get_codes_helper(root[1]) return huff_code_dictHere, you use a helper function, `get_codes_helper()`, to navigate the Huffman Tree in a recursive manner, generating the Huffman codes by adding '0' for the left child and '1' for the right child at each node. Running these functions in sequence on your dataset will generate a dictionary with Huffman codes for each character, which can then be utilised for data compression tasks.

- Creation of the Node class acting as the ground for the Huffman Tree structure.
- Frequency count of each character, yielding a dictionary of frequencies.
- Formation of a priority queue (heap) from the frequency dictionary.
- Construction of the Huffman Tree by combining two nodes from the heap in each cycle until only one node (the root) remains in the heap.
- Traversal of the Huffman tree and generation of the Huffman codes, resulting in a dictionary of codes.

A **Huffman coder** is a particular type of entropy encoder used in lossless data compression. The process of finding or using such a code is called Huffman coding and forms part of the broader area of codeword optimisation.

Huffman Coding is so impactful in the field of data compression that it's widely utilised in various applications, including file compression utilities like PKZIP and GZIP, languages like Java and scripting languages like Perl. In addition, genres like image and video compression, e.g., JPEG and MPEG, use Huffman Coding.

original_text = "Huffman Coding in Python"Passing this string through a Huffman encoding would involve the following steps:

- Computing the frequency of each character in the string. For example, "a" appears once, whereas "n" appears three times.
- Creating individual Huffman Tree nodes for each character-frequency pair and adding these nodes to a priority queue. For instance, a node would be created for ("a", 1).
- Constructing the Huffman Tree by iteratively combining the two nodes with the lowest frequency from the priority queue into a new node and inserting this new node back into the priority queue. This process continues until the priority queue contains only one node, which becomes the root of the Huffman Tree.
- Generating the Huffman codes by traversing the Huffman Tree in a depth-first manner and appending a "0" for every left turn and a "1" for every right turn.

To provide an instance, character 'n' from the sentence "Huffman coding in Python" might be represented by '101' while 'a' could be '00'. After replacing all characters with their corresponding Huffman codes, the string "na" would become '10100'. That's the compressed form of 'na' using Huffman codes.

- Huffman Coding is an algorithm that uses character frequency to create an efficient, variable-length coding scheme for data compression.
- Data compression algorithms like Huffman Coding enhance storage efficiency and data transmission speeds by representing frequently appearing characters with shorter codes.
- The Huffman Coding algorithm involves the calculation of character frequencies, creation of a heap or priority queue, construction of a Huffman tree, generation of Huffman codes, and storing these codes for easy lookup.
- The Huffman Tree is constructed by creating a node for each character, then continually removing the two nodes with the smallest frequencies, merging them into a new node, and reinserting this new node into the heap, until only one node (the root) remains.
- Python can be used to implement the Huffman Coding algorithm using intrinsic data structures, namely nodes, dictionaries, and heaps.

What is Huffman coding in computer science?

Huffman coding is a widespread algorithm used in computer science for lossless data compression. The method is based on the frequency of occurrence of individual characters or symbols, assigning shorter bit codes to more frequently occurring ones and longer bit codes to less frequently occurring ones.

What are the fundamental steps in Huffman coding?

Huffman coding consists of three primary steps: Character Frequency Calculation, Heap Tree Creation, and Huffman Tree Creation. The algorithm assigns shorter bit codes to more frequently occurring characters and longer bit codes to less frequently occurring characters.

What roles does Huffman coding play in data representation?

Huffman coding enhances storage efficiency by compressing data and enabling efficient utilization of storage resources. It can also speed up data transmission across networks due to smaller, more efficient representations of data.

What are the steps involved in the Huffman Coding Algorithm?

The steps are: 1) Character frequency calculation, 2) Heap creation, 3) Huffman Tree creation, 4) Code generation and 5) Code storage.

What role does Huffman Coding play in data compression?

Huffman Coding plays a significant role in data compression by producing shorter codes for characters that occur more frequently, reducing the overall data size and promoting efficient storage and faster data transmission.

How does the Huffman Coding Algorithm assign binary codes to characters?

It starts at the root of the Huffman Tree and moves towards each leaf node, assigning a '0' every time it moves to the left child, and a '1' every time it moves to the right child.

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