Recursive algorithms in computer science courses: Fibonacci numbers and binomial coefficients

We observe that the computational inefficiency of branched recursive functions was not appropriately covered in almost all textbooks for computer science courses in the first three years of the curriculum. Fibonacci numbers and binomial coefficients were frequently used as examples of branched recur...

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Vydáno v:IEEE transactions on education Ročník 43; číslo 3; s. 273 - 276
Hlavní autor: Stojmenovic, I.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.08.2000
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Binomial coefficients
Branched
Complexity
Computer science education
Education
Fibonacci numbers
Proving
Recursive functions
Textbooks
ISSN:0018-9359, 1557-9638
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Shrnutí:We observe that the computational inefficiency of branched recursive functions was not appropriately covered in almost all textbooks for computer science courses in the first three years of the curriculum. Fibonacci numbers and binomial coefficients were frequently used as examples of branched recursive functions. However, their exponential time complexity was rarely claimed and never completely proved in the textbooks. Alternative linear time iterative solutions were rarely mentioned. We give very simple proofs that these recursive functions have exponential time complexity. The proofs are appropriate for coverage in the first computer science course.
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ISSN:0018-9359
1557-9638
DOI:10.1109/13.865200