Created by Artem Kysliakov
Recursion, in the context of algorithms, refers to a function that calls itself as part of its execution. This technique allows for elegant and efficient solutions to problems that can be broken down into smaller, self-similar subproblems. One way to conceptualize recursion is to envision a pyramid, where each level builds upon the one below it. A pyramid of a certain height can be defined as a pyramid of one less height with an additional row. This breakdown continues until the simplest case, a single brick, is reached. This recursive definition mirrors how recursive algorithms function. They solve a problem by breaking it down into smaller, similar subproblems until a simple base case is encountered, at which point the recursion stops. [1]
A classic example of recursion in algorithms is the binary search algorithm. In essence, binary search determines the position of a target value within a sorted array. The algorithm achieves this by repeatedly halving the search interval. Initially, it compares the target value to the middle element of the array. If they match, the search is complete. If the target value is less than the middle element, the search continues in the left half, and vice versa. The process of dividing the search interval in half persists until the target value is located or the search interval is empty. The recursive nature of binary search is evident in its repeated application to smaller subarrays. [2]
It is important to note that for a recursive function to be effective, it needs a well-defined base case to prevent infinite recursion. A base case is a condition that, when met, stops the recursive calls and returns a value. Without a base case, the function would continuously call itself, ultimately leading to a program crash due to a stack overflow. This situation is similar to searching for a name in a phone book. If there are no pages left in the phone book, the search is complete. This concept can be represented in pseudocode as "if John Harvard not in phone book or if no lockers or doors left, then just exit or return". [3]
Sources highlight the value of recursion as a problem-solving method in programming. It allows for concise and clear code, often enhancing readability and maintainability compared to iterative approaches. Additionally, recursion aligns well with certain data structures and problem domains, making it a potent tool for programmers.
Assembly Code: A low-level representation of a program that is specific to a particular computer processor architecture. It uses mnemonic codes to represent instructions that the processor can understand and execute. Assembly code is more human-readable than machine code (which is purely numerical).
Preprocessing: The initial stage of compilation, where lines starting with '#', like #include, are replaced with their actual code equivalents. Preprocessing prepares the source code for the next stage, compilation
Compiling: The process of converting source code (written in a programming language like C) into assembly code (a low-level representation of a program that can be understood by a specific type of computer processor). This process typically involves multiple stages, including preprocessing, compiling, assembling, and linking.
Pseudocode: A way of describing algorithms without using a formal programming language. It uses a combination of natural language and simplified code-like structures to convey the logic of an algorithm in a human-readable form. Pseudocode is not meant to be executed by a computer but serves as a blueprint or plan for writing actual code.
Алгоритми - покрокові інструкції для розв'язання проблеми.
Алгоритми можуть бути виражені будь-якою людською мовою, але в комп'ютерних науках ми перекладаємо їх у код - мову, яку розуміють комп'ютери.
Ці алгоритми реалізуються за допомогою коду на різних мовах програмування, таких як C або Python.
Комп'ютерна наука - це наукова та практична дисципліна.
Вона вивчає, як комп'ютери працюють, як вони "думають" та як вони можуть допомогти нам робити речі швидше та краще. Це також про те, як ми можемо навчити комп'ютери робити нові речі, наприклад, створювати музику, малюнки або ігри.
Arrays: Offer a straightforward way to store element sequences but have a fixed size limitation [18].
Linked Lists: Address the fixed size of arrays by enabling dynamic resizing and non-contiguous storage
Tries: A specialized tree structure optimized for efficient prefix searches, often used in applications like autocomplete
Hash Tables: Facilitate rapid data retrieval by employing a hash function to map keys to corresponding values
Trees: Establish hierarchy and relationships within data. Different tree types suit specific tasks
Linear Search: Linear search is a simple search algorithm that checks each element in a list or array sequentially until the desired element is found or the entire list has been searched. [1, 2] This approach is analogous to checking gym lockers one by one to find a specific number. [3, 4] Linear search is relatively easy to implement but can be inefficient for large datasets.
Binary Search: Binary search is a more efficient search algorithm that operates on sorted data. [6] It works by repeatedly dividing the search interval in half. [6] The algorithm begins by comparing the target value to the middle element of the data. If the target value matches the middle element, its position is returned. [6] If the target value is less than the middle element, the search continues in the left half of the data. [7] Conversely, if the target value is greater than the middle element, the search continues in the right half. [7] This process of halving the search interval continues until the target value is found or the search interval becomes empty. [7] Binary search is significantly faster than linear search for large datasets because it eliminates half of the remaining data with each comparison. [8, 9]