CS 18000 Problem Solving and Object Oriented Programming Spring 2019 Section LE2 Week 14: Lecture 27, April 22. 2019 Slides updated: 9:21am, April 22, 2019 Aditya Mathur Professor, Department of Computer Science Purdue University West Lafayette, IN, USA https://www.cs.purdue.edu/homes/apm/courses/CS180_Java/CS180Spring2019/

©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

©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

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

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

©Aditya Mathur. CS 180. Fall 2019.Week 15 Tower of Hanoi: Solution 04/22/2019 ©Aditya Mathur. CS 180. Fall 2019.Week 15

©Aditya Mathur. CS 180. Fall 2019.Week 15 Live demo 04/22/2019 ©Aditya Mathur. CS 180. Fall 2019.Week 15

©Aditya Mathur. CS 180. Fall 2019.Week 15 Binary tree T3 T1 T2 04/22/2019 ©Aditya Mathur. CS 180. Fall 2019.Week 15

©Aditya Mathur. CS 180. Fall 2019.Week 15 Binary tree: Elements Root Nodes Left link Right link Leaf nodes 04/22/2019 ©Aditya Mathur. CS 180. Fall 2019.Week 15

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

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

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

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

©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 3 19 2 8] 15>8; array not changed J=1; i=-1; compare 3 with 8. [15 3 19 2 8] 3<8; bring 3 to position 0 J=2; i=0; compare 19 with 8 [3 15 19 2 8] 19>8; no change J=3; i=0; compare 2 with 8 [3 15 19 2 8] 2<8; move 2 to i+1 J=4; i=1; [3 15 19 2 8] Exchange pivot with 19 J=4; i=2; [3 2 19 15 8] Exchange pivot with 19 J=4; i=2; [3 2 8 15 19] 04/22/2019 ©Aditya Mathur. CS 180. Fall 2019.Week 15

©Aditya Mathur. CS 180. Fall 2019.Week 15 Quicksort: Apply quicksort on two subarrays [3 2 8 15 19] [3 2 ] Quicksort [15 19] Quicksort 04/22/2019 ©Aditya Mathur. CS 180. Fall 2019.Week 15