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Good morning!

Good morning!. Recursive Algorithms. Example: Gift box!. Example: Gift box!. Example: Gift box!. Value of gift box : Equation?. Example: Treasure hunt!. What is recursion?. Popular in math definitions Inductive proof. Example: factorial(n). Example: factorial(n).

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Good morning!

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  1. Good morning!

  2. Recursive Algorithms

  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

  24. Example: Change for $ 100 • Available denominations: 1c, 5c, 10c, 25c, $1, $2, $5, $10, $20, $50, $100 • How many combinations are there?

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

  26. Example: N-Queens puzzle

  27. Example: Knight’s tour

  28. Example: Sudoku’s puzzle

  29. Example: Maximizing total conviviality

  30. 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.

  31. Questions & Answers?

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