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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

Good morning!








What is recursion
What is recursion?

  • Popular in math definitions

  • Inductive proof



Example factorial n1
Example: factorial(n)

  • Non-recursive solution


How does recursion work
How does recursion work?

  • Stack memory

  • How much stack memory is needed?


How to understand recursion
How to understand recursion?

  • Method invocations & returns diagram

  • Example: factorial(5)


How to understand recursion1
How to understand recursion?

  • Method invocations & returns diagram

  • Example: fibonacci(n)


How to understand recursion2
How to understand recursion?

  • Tree diagram

  • Example: fibonacci(n)


Fibonacci n non recursive solution
fibonacci(n) : non-recursive solution?


How to analyze recursion
How to analyze recursion?

  • Recurrence relation & Time complexity









Example change for 100
Example: Change for $ 100

  • Available denominations: 1c, 5c, 10c, 25c, $1, $2, $5, $10, $20, $50, $100

  • How many combinations are there?


How to make recursion efficient
How to make recursion efficient?

  • Parameters

  • Tail recursion






Conclusions
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.



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