input.txt

The Huffman algorithm, devised by David A. Huffman in 1952, is a fundamental technique in the field of data compression. Its primary objective is to efficiently encode data by assigning shorter codes to more frequent symbols and longer codes to less frequent symbols. The algorithm starts by analyzing the frequency of each symbol in the input data and constructs a binary tree, known as the Huffman tree or Huffman coding tree, where symbols with higher frequencies are placed closer to the root. This binary tree is constructed in a way that ensures that no code is a prefix of another, hence the term "prefix-free" or "prefix code". Once the tree is constructed, the Huffman codes are determined by traversing the tree from the root to each leaf node, with left branches representing binary '0' and right branches representing binary '1'. These paths from the root to each leaf node represent the unique binary codes assigned to each symbol. The resulting Huffman code provides an efficient representation of the input data, enabling significant compression ratios, particularly for data with skewed frequency distributions. Moreover, since the Huffman code is constructed based solely on the input data's statistics, it can be uniquely decoded back into the original data without loss, making it suitable for lossless compression applications in various domains such as telecommunications, data storage, and multimedia compression.

Time complexity analysis is a crucial aspect of algorithm design, focusing on evaluating the performance of an algorithm in terms of the time it takes to execute as a function of the input size. Different algorithms exhibit varying time complexities, often classified using Big O notation, which describes the upper bound on the algorithm's runtime. For example, algorithms with linear time complexity (O(n)) have runtime proportional to the input size, while those with quadratic time complexity (O(n^2)) experience a quadratic increase in runtime as the input size grows. Time complexity analysis aids in understanding and comparing algorithms' efficiency, guiding the selection of the most suitable algorithm for a given problem based on input size constraints and performance requirements. Moreover, it provides insights into scalability and helps identify potential bottlenecks in algorithmic solutions, facilitating algorithm optimization and improving overall system performance.