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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!

Recursive algorithms

Recursive Algorithms

Example gift box

Example: Gift box!

Example gift box1

Example: Gift box!

Example gift box2

Example: Gift box!

Value of gift box equation

Value of gift box : Equation?

Example treasure hunt

Example: Treasure hunt!

What is recursion

What is recursion?

  • Popular in math definitions

  • Inductive proof

Example factorial n

Example: factorial(n)

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 hanoi tower

Example: Hanoi tower

Example fractals

Example: Fractals

Petrol cost minimization problem

Petrol cost minimization problem

Similar solution quick sort

Similar solution: Quick-sort

Quick sort non recursive solution

Quick-sort: non-recursive solution?

Similar solution merge sort

Similar solution: Merge-sort

Example knapsack problem

Example: Knapsack problem

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

Example n queens puzzle

Example: N-Queens puzzle

Example knight s tour

Example: Knight’s tour

Example sudoku s puzzle

Example: Sudoku’s puzzle

Example maximizing total conviviality

Example: Maximizing total conviviality



  • 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

Questions & Answers?

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