PROGRAMMING AND OPTIMIZATION OF RECURSIVE ALGORITHMS: THEORY, ANALYSIS AND PRACTICAL APPLICATIONS

Ibragimov Ulugbek Muradilloyevich

Authors

Ibragimov Ulugbek Muradilloyevich Associate Professor, Asia International University

Keywords:

Recursion, recursive algorithm, base case, call stack, divide and conquer, memoization, dynamic programming, tail recursion, tail call optimization, backtracking, time complexity, space complexity, stack overflow, Fibonacci sequence, merge sort, algorithm analysis.

Abstract

Recursion is one of the most powerful and elegant paradigms in computer science, enabling the decomposition of complex problems into simpler, self-similar subproblems. This article provides a comprehensive examination of recursive algorithms, covering their theoretical foundations, execution mechanics, time and space complexity analysis, and systematic optimization techniques. The core concepts — base cases, recursive cases, call stack behavior, and stack frame allocation — are analyzed both theoretically and through algorithmic pseudocode. The article demonstrates how recursion serves as the underlying mechanism for divide-and-conquer algorithms, tree and graph traversals, dynamic programming, and backtracking search. A detailed comparative analysis between recursive and iterative approaches clarifies when each paradigm is optimal. Advanced optimization topics including memoization, tail call optimization, bottom-up tabulation, and stack overflow prevention are presented with full solutions to illustrate the practical depth of recursive algorithm mastery.

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