Main Article Content


Abstract. Solving strategies in the computation the time complexity of an algorithm is very essentials. Some existing methods have inoptimal in the explanations of solutions, because it takes a long step and for the final result is not exact, or only limited utilize in solving by the approach. Actually there have been several studies that develop the final model equation Fibonacci time complexity of recursive algorithms, but the steps are still needed a complex operation. In this research has been done several major studies related to recursive algorithms Fibonacci analysis, which involves the general formula series, begin with determining the next term directly with the equation and find the sum of series also with an equation too. The method used in this study utilizing decomposition technique with backward substitution based on a single side outlining. The final results show of the single side outlining was found that this technique is able to produce exact solutions, efficient, easy to operate and more understand steps.
Keywords: Time Complexity, Non-Recursive, Recursive, Fibonacci Algorithm

Article Details

How to Cite
Cholissodin, I., & Riyandani, E. (2016). Review: A State-of-the-Art of Time Complexity (Non-Recursive and Recursive Fibonacci Algorithm). Journal of Information Technology and Computer Science, 1(1), 14–27.


  1. Charles Burnett. (2016, September). Leonard of Pisa (Fibonacci) and Arabic Arithmetic, [Online], Available:
  2. Clive N. Menhinick. The Fibonacci Resonance and other new Golden Ratio discoveries. OnPerson International Limited, Poynton, Cheshire (2015). 618 pp.+xiv, ISBN: 978-0- 9932166-0-2
  3. Sandeep. (2016, September). Fibonacci numbers in Plants: Design of Leaf, Petals, Branches and Flowers, [Online]. Available:
  4. Md. Akhtaruzzaman, Amir A. Shafie, Geometrical Substantiation of Phi, the Golden Ratio and the Baroque of Nature, Architecture, Design and Engineering, International Journal of Arts (2011); 1(1): 1-22.
  5. Manuel Rubio, Bozena Pajak, Fibonacci numbers using mutual recursion, (2005).
  6. Anany Levitin, Introduction To The Design & Analysis of Algorithms, Addison Wesley, (2003).
  7. Watt D.A., Brown D.F. Java Collections. An Introduction to Abstract Data Types, Data Structures, and Algorithms (2001).
  8. JOC/EFR © (2016, September). François Édouard Anatole Lucas, School of Mathematics and Statistics University of St Andrews, Scotland. (1996). Available:
  9. R. Odendahl, (2016, September). Analysis of Algorithms. Available:
  10. Alexey Stakhov, The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science. World Scientific Publishing Co. Pte. Ltd. (2009).
  11. Alexey Stakhov, Samuil Aranson. The “Golden†Non-Euclidean Geometry: Hilbert's Fourth Problem, “Golden†Dynamical System, and the Fine-Structure Constant. (2016).
  12. J. L. Holloway. Algorithms for Computing Fibonacci Numbers Quickly. (1988).
  13. Thomas Koshy. Fibonacci, Lucas, and Pell Numbers, and Pascal’s Triangle. (2011).
  14. Jeffrey J. McConnell. Analysis of Algorithms: An Active Learning Approach, by Jones and Bartlett Publishers, Inc., (2001).