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Good morning!. Recursive Algorithms. Dr. Jeyakesavan Veerasamy jeyv@utdallas.edu. 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).

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recursive algorithms

Recursive Algorithms

Dr. Jeyakesavan Veerasamy

jeyv@utdallas.edu

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)
how to analyze recursion
How to analyze recursion?
  • Recurrence relation & Time complexity
example knapsack problem
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
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.