Good afternoon!. Recursive Algorithms Dr. Jeyakesavan Veerasamy

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Advanced Analysis of Algorithms

Presentation transcript:

Good afternoon!

Recursive Algorithms Dr. Jeyakesavan Veerasamy

Example: Gift box!

Value of gift box : Equation?

Example: Treasure hunt!

What is recursion? Popular in math definitions Inductive proof

Example: factorial(n)

Non-recursive solution

How does recursion work? Stack memory How much stack memory is needed?

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

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

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

fibonacci(n) : non-recursive solution?

How to analyze recursion? Recurrence relation & Time complexity

Example: Hanoi tower

Example: Fractals

Petrol cost minimization problem

Similar solution: Quick-sort

Quick-sort: non-recursive solution?

Similar solution: Merge-sort

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? Parameters Tail recursion

Example: N-Queens puzzle

Example: Knight’s tour

Example: Sudoku’s puzzle

Example: Maximizing total conviviality

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.

Questions & Answers?