On the number of recursive calls of recursive functions

Authors:
Yannis Manolopoulos
Affiliations:
Aristotle University, Thessaloniki, Greece
Venue:
ACM SIGCSE Bulletin
Year:
2005

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Data structures and algorithm analysis in C++

Data structures and algorithm analysis in C++
Fundamentals of algorithmics

Fundamentals of algorithmics
How many recursive calls does a recursive function make?

ACM SIGCSE Bulletin

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Abstract

The advantages and disadvantages of recursion are early introduced to students. Simplicity in coding but time and space inefficiency during execution are the main characteristics. In many occasions, recursive formulae lead to recursive functions/procedures that are highly inefficient as calls with the same parameters are executed several times. Here, we elaborate on a previous report [2], where a generalized analysis is carried out to derive the number of recursive calls of a recursive formula, the calculation of the Fibonacci numbers in particular. Here we re-examine the problem using a different and simpler approach, which generalizes as well.