Ch 5. Recurrence Relations
Learning Objectives
By the end of this chapter, students should be able to:
- Understand and apply recurrence relations to model iterative and recursive processes
- Solve simple recurrences (iterative and closed-form methods)
- Analyze recursive algorithms and their time complexity
- Apply recurrence relations to computing contexts (algorithms, dynamic programming, data structures)
In computing and information technology, many problems are defined in terms of smaller subproblems. Whether you're analyzing the performance of a recursive algorithm, modelling the growth of a data structure, or designing a dynamic programming solution, recurrence relations provide a powerful mathematical tool for expressing and solving these problems.
An equation that defines a sequence recursively is a recurrence relation, with each term being defined in terms of previous terms. For example, the Fibonacci sequence is defined by the recurrence relation:
[latex]f_{n} = f_{n-1} + f_{n-2}[/latex], with [latex]f_{0} = 0, f_{1} = 1[/latex]
In this chapter, you will be introduced to the notation and techniques for solving recurrence relations, explore how they are used to analyze recursive algorithms, and be provided with practical examples from computing.
