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Recursion Suppose You Are Waiting in L ine HI YOU! A Very Long Line You want to determine how many people are in front of you, but you cannot see and youre not allowed to move . You are only allowed to speak to the person in front of

  1. Recursion

  2. Suppose You Are Waiting in L ine… HI YOU!

  3. … A Very Long Line

  4. You want to determine how many people are in front of you, but you cannot see and you’re not allowed to move . You are only allowed to speak to the person in front of you and behind you . How do you do it?

  5. Recursion  A programming technique that breaks down a complex problem into smaller, manageable pieces  Recursive solutions solve a problem by applying the same algorithm to each piece and then combining the results.

  6. The General Formula #people in front of person in front of you + person in front of you = # people in front of you

  7. The Solution Tap the shoulder of the person in front of 1. you and ask how many people are in front of him/her Wait for his/her response and add 1 2. If someone asked, tell them how many 1. people are in front of you

  8. A Diagram  Ask and wait  Ask and wait  Ask and wait….  …. Reached first in line. Tell person behind it is 0.  Tell person behind it is 0+1  Tell person behind it is 1+1…  Tell Person behind it is x +1

  9. Recursive Algorithms  There are two main components to recursive algorithms  1) Base Case  2) The Recursive Case

  10. Recursive Algorithms  There are two main components to recursive algorithms  1) Base Case: The point where you stop applying the recursive case  2) Recursive Case: The set of instructions that will be used over and over

  11. In the Queue Problem…  Recursive case is  Tap person in front of you. Ask #people in front of him. Wait for his answer and add 1.  Base case is  person 0. You do not do execute the above.

  12. Recursion and Programming  A recursive function is a function that calls itself numberOfPeopleInFront(person){ If (there is no one to tap) return 0 Else tap person in front of you (F) #ppl in front of F = numberOfPeopleInFront(F) return #ppl in front of F + 1  }

  13. Pseudo-code diagram  Ask and wait  Ask and wait  Ask and wait….  …. Reached first in line. Return 0.  Return 0+1  Return 1+1…  Return x +1

  14. Towers of Hanoi  A prominent recursive problem  Starting Configuration:  Goal: Move tower from A to B

  15. Rules  Move one disk at a time  A larger disk cannot be placed on top of a smaller disk  We can use some needles as temporary storage

  16. Subgoals  Get top x-1 disks from A to C  Get bottom disk from A to B  Move top x-1 disks from C to B

  17. Recursion Behind Towers  Base Case: Moving the Largest Disk to Needle B  Recursive Case: Do same for the x – 1 disk above it  http://www.mazeworks.com/hanoi/  Fun Fact: It takes at least 2 n -1 moves to solve the puzzle

  18. Fractals  A rough or fragmented geometric shape that can be split into parts, each of which is (at least an approx. of) a reduced copy of the whole  Base case: Starting shape  Recursive case: Repeating shape in different sizes Koch Snowflake

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