1. CS 18000 Problem Solving and Object Oriented Programming Spring 2019
Section LE2
Week 14: Lecture 27, April
Slides updated: 9:21am, April 22, 2019
Aditya Mathur
Professor, Department of Computer Science
Purdue University
West Lafayette, IN, USA

2. ©Aditya Mathur. CS 180. Fall 2019.Week 15
This week
Recursion
Some mathematical recursive functions
Tower of Hanoi
Binary trees
Quicksort
04/22/2019
©Aditya Mathur. CS 180. Fall 2019.Week 15

3. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Recursion
Using a function or a method to evaluate itself!
Some problems have a easier to find recursive than an iterative solution.
In some cases a recursive solution may turn out to be more expensive than an iterative solution.
Thus, use recursion when the problem demands it!
04/22/2019
©Aditya Mathur. CS 180. Fall 2019.Week 15

4. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Sample recursive functions
Fibonnacci(n)= 1; if n=0 or 1;
=Fibonnaci(n-1)+Fibonnaci(n-2); if n>1;
Fibonnaci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34….
fact(n)= 1; if n=0
=n*fact(n-1) if n>0
GCD(x,y)= x; if x=y
=GCD(x-y,y); x>y
=GCD(x,y-x); x<y
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©Aditya Mathur. CS 180. Fall 2019.Week 15

5. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Tower of Hanoi A C B
N discs in tower A
Smaller disc must always be above a larger disc; arranged in order
Move all discs from A to C via B.
Only one disc can be moved at a time and must be placed on a tower and not anywhere else.
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©Aditya Mathur. CS 180. Fall 2019.Week 15

6. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Tower of Hanoi: Solution
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©Aditya Mathur. CS 180. Fall 2019.Week 15

7. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Live demo
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©Aditya Mathur. CS 180. Fall 2019.Week 15

8. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Binary tree T3 T1 T2
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©Aditya Mathur. CS 180. Fall 2019.Week 15

9. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Binary tree: Elements
Root
Nodes
Left
link
Right
link
Leaf nodes
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©Aditya Mathur. CS 180. Fall 2019.Week 15

10. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Binary tree: with data
Data: 12, 8, -2, 11, 17, 99, 3 12 8 17 11 99 -2 3
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©Aditya Mathur. CS 180. Fall 2019.Week 15

11. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Binary tree: traversal
Inorder: Left, Root, Right 12 8 -2 11 17 99 3
Preorder: Root, Left, Right
Postorder: Left, Right, Root
Level order: Level by level
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©Aditya Mathur. CS 180. Fall 2019.Week 15

12. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Quiz: 04/22/2019
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©Aditya Mathur. CS 180. Fall 2019.Week 15

13. Quicksort: The algorithm
Problem: Sort an array:
data=[d0 d1 d2 d3 dN ]
Quicksort(data, 0, N)
Select an element in the array; this is element is known as
the pivot.
Partition the array so that the left partition (Pleft) has elements less than pivot and the right partition (Pright) has elements equal to or greater than the pivot.
Apply Quicksort( ) to Pleft and Pright

14. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Quicksort: Illustration of partitioning
j=0
Pivot
i=-1
i=-1; j=0 Compare 15 with the pivot (8)
[ ]
15>8; array not changed
J=1; i=-1; compare 3 with 8.
[ ]
3<8; bring 3 to position 0
J=2; i=0; compare 19 with 8
[ ]
19>8; no change
J=3; i=0; compare 2 with 8
[ ]
2<8; move 2 to i+1
J=4; i=1;
[ ]
Exchange pivot with 19
J=4; i=2;
[ ]
Exchange pivot with 19
J=4; i=2;
[ ]
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©Aditya Mathur. CS 180. Fall 2019.Week 15

15. ©Aditya Mathur. CS 180. Fall 2019.Week 15
Quicksort: Apply quicksort on two subarrays
[ ]
[3 2 ]
Quicksort
[ ]
Quicksort
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©Aditya Mathur. CS 180. Fall 2019.Week 15