Tutorial 1 C Programming

1
Tutorial 6Recursion
2
Beautiful Recursion Fractal

• Sierpinski Triangle
• Recursive Tree

• Koch Snowflake
• http//en.wikipedia.org/wiki/Fractal

3
More Examples

• Droste Effect
• http//en.wikipedia.org/wiki/Droste_effect
• Russian Doll
• http//en.wikipedia.org/wiki/Matryoshka_doll
• Recursive Acronyms
• PHP PHP Hypertext Preprocessor
• GNU GNUs Not Unix
• VISA VISA International Service Association
• http//en.wikipedia.org/wiki/Recursive_acronym
• A Definition in an English-English dictionary
• Recursion
• See Recursion.
• If you are tired, stop.

4
Recursion Basic Idea

• Template for ANY recursion
• Recursive_Function_Name(Parameter_List)
• // you will always see selection statement
  (if, switch, etc)
• if (Base Case)
• do something simple
• else // Recursive Case
• Recursive_Function_Name(Modified
  Parameter_List)
• Modified Parameter_List must bring the recursive
  function closer to the base case (simplified
  problem).

5
ExampleHow many ways to choose k items out of n
items?

• How many ways to choose when k out of (n3)?
• 0, actually this problem is undefined for k such case will never exist.
• How many ways to choose when k n, e.g. (k4)
  out of (n3)?
• 0, also undefined, impossible
• How many ways to choose when k n, e.g. (k3)
  out of (n3)?
• 1, take all
• How many ways to choose when k 0, e.g. (k0)
  out of (n3)?
• 1, do not take anything
• How many ways to choose in general case, e.g. k n, k 0 (k2) out of (n3)?
• Either I take one item X,
• My problem becomes choosing k-1 (k1) out of n-1
  (n2)
• Plus if I do not take that one item X
• My problem becomes choosing k (k2) out of n-1
  (n2)
• Code it
• int c(int n,int k) if (kn) // assume kundefined return 0 if (k n k 0)
  return 1 return c(n-1,k-1) c(n-1,k)

6
Recursion is Powerful

• Divide and Conquer
• Dynamic Programming
• Used in future lectures in CS1102
• Sorting Mergesort and Quicksort are recursive
• Tree/Heap/Graph these data structures and
  operations are naturally recursive
• Can also be used for past CS1102 materials
• Linked List data structure and operations are
  also naturally recursive

7
Student Presentation

• Gr3 Main Backup
• Cao Hoang Dang Cai Jingfang, Du Xin
• Chng Jiajie Ding Ying Shiaun
• Chen Tianni Rebecca Jashan Deep Kaur
• Huang Chuanxian Leow Wei Jie, Lim Wei Hong
• Gr4 Main Backup
• Tan Peck Luan Tan Shu Yu Cynthia
• Li Yawen Tan Miang Yeow
• Wang Kang Ahmed Shafeeq
• Wong Suet Teng, M Chong Tze Koi
• Overview of the questions
• Trace IsEven/IsOdd
• Recursive counting
• Recursive sort
• Reversing BasicLinkedList
• The rabbit question is your homework

• Gr5 Main Backup
• Wu Shujun Joyeeta Biswas
• Teo Sim Yee, Stephanie Tan Yan Hao
• Wang Ruohan Zheng Yang
• Liu Na Zhang Denan
• Gr6 Main Backup
• Rasheilla Bte Rajah Tan Ping Yang
• Lou Wei Chen Gerard J Koh Jye Yiing
• Zhang Chao Wong Shiang Ker
• Gan Zhi Wei James Kuganeswari D/O K

8
Q1 Trace

• boolean isEven(int number)
• if (number 0)
• return true
• else
• return isOdd(number-1)
• boolean isOdd(int number)
• if (number 0)
• return false
• else
• return isEven(number-1)

• Trace isEven(5)!
• Trace isOdd(1), isEven(2)!
• There are repeated sub-problems!
• You will learn how to optimize this situation in
  more advanced modules!
• Are these two functions recursive?
• http//en.wikipedia.org/wiki/Mutual_recursion
• In what situation(s) these two functions may
  fail?
• Negative numbers
• How to improve these codes to address the
  situation above?
• If input is negative, multiply it with -1 first.

9
Q2 Recursive Counting

• Adam can climb
• 1 stair per step, or
• 2 stairs per step
• Given n stairs,Count how many waysAdam can go
  upFrom stair 0 (ground) to stair n!
• n 4
• 1111
• 112
• 121
• 211
• 22

• Thinking steps
• Let steps(n) the number of ways
• Start from small cases
• steps(0), not defined, assume n0
• steps(1), 1 way (1 step)
• steps(2), 2 ways (11 or 2)
• steps(3), 3 ways(111, 21, or12)
• steps(4), 5 ways(1111, 211, 121,
  or112, 22)
• Feel that this problem is recursive!
• Go backwards!
• There are two ways to reach stair n
• From stair n-2, then Adam 2 stairs, or
• From stair n-1, then Adam 1 stair
• Naturally
• steps(n) steps(n-1)steps(n-2)

10
Q3 Recursive Sort

• Many options
• We will learn this again in details in Lecture 6
  (Sorting)

• Possible answers
• Recursive bubble sort
• Recursive selection sort
• Recursive merge sort
• Recursive quick sort
• Recursive selection sort
• sort(array, size)
• if (size 1)
• return // done (base case)
• pass through the array one time to get the
  maximum item M
• swap M with arraysize-1
• call sort(array, size-1) // recursive

11
Q4 Reversing BLL Recursively

• Original BLL
• A ? B ? C ? D
• Head is A
• Reversed BLL
• A ? B ? C ? D
• Head is D
• Given a BLL,reverse it, recursively!

• Possible answer
• node reverse(node n)
• node newhead
• if (n.next ! null)
• newhead reverse(n.next)
• n.next.next n // change arrow!
• n.next NULL
• else // base case, this is old tail!
• newhead n // now new head
• return newhead
• Call with
• head reverse(head)

12
Food For Thought

• If you are asked to design a recursive function
  to model your life while taking CS1102, what kind
  of function that you will design?
• void CS1102_Life(int week_ID)
  do_tutorial_and_lab(week_ID) if (next_week)
  CS1102_Life(week_ID1)
• Wrong, this is infinite
• void CS1102_Life(int week_ID)
  do_tutorial_and_lab(week_ID) if (week_ID !
  end of semester) CS1102_Life(week_ID1)
• It is going to be over ?

13
Midterm Test

• If you want to know the truth
• Visit my website
• I have scanned my answers and upload the PDF
  there.