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Unlocking Recursion: Understanding and Mastering Recursive Algorithms

Delve into the world of recursion with Dr. Jeyakesavan Veerasamy to explore its concepts, applications, and complexities. Learn how to analyze, optimize, and appreciate the beauty of recursive algorithms in this comprehensive guide. Gain insights into common problems like the Tower of Hanoi, the N-Queens puzzle, and more. This resource covers inductive proofs, non-recursive solutions, tail recursion, and efficient parameter handling. Enhance your logical thinking skills and embark on a journey to unravel the mysteries of recursion!

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Unlocking Recursion: Understanding and Mastering Recursive Algorithms

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  1. Good morning!

  2. Recursive Algorithms Dr. Jeyakesavan Veerasamy jeyv@utdallas.edu

  3. Example: Gift box!

  4. Example: Gift box!

  5. Example: Gift box!

  6. Value of gift box : Equation?

  7. Example: Treasure hunt!

  8. What is recursion? • Popular in math definitions • Inductive proof

  9. Example: factorial(n)

  10. Example: factorial(n) • Non-recursive solution

  11. How does recursion work? • Stack memory • How much stack memory is needed?

  12. How to understand recursion? • Method invocations & returns diagram • Example: factorial(5)

  13. How to understand recursion? • Method invocations & returns diagram • Example: fibonacci(n)

  14. How to understand recursion? • Tree diagram • Example: fibonacci(n)

  15. fibonacci(n) : non-recursive solution?

  16. How to analyze recursion? • Recurrence relation & Time complexity

  17. Example: Hanoi tower

  18. Example: Fractals

  19. Petrol cost minimization problem

  20. Similar solution: Quick-sort

  21. Quick-sort: non-recursive solution?

  22. Similar solution: Merge-sort

  23. Example: Knapsack problem • Item weights: 40, 10, 46, 23, 22, 16, 27, 6 • Instance #1: Target : 50 • Instance #2: Target: 60 • Instance #3: Target: 70

  24. How to make recursion efficient? • Parameters • Tail recursion

  25. Example: N-Queens puzzle

  26. Example: Knight’s tour

  27. Example: Sudoku’s puzzle

  28. Example: Maximizing total conviviality

  29. Conclusions • Recursion is one of the difficult concepts to understand, perhaps it is not that intuitive. • As per a few mathematicians & CS folks, it is one of the most beautiful concepts! • While it is not used much in commercial applications, it certainly puts your logical thinking skills to work! • It is easy to remove tail recursion, but all others are lot harder to remove.

  30. Questions & Answers?

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