SLIDE 1
CS171 Introduction to Computer Science II
2/28/2012 1
CS171 Introduction to Computer Science II Recursion Li Xiong - - PowerPoint PPT Presentation
CS171 Introduction to Computer Science II Recursion Li Xiong - - PowerPoint PPT Presentation
CS171 Introduction to Computer Science II Recursion Li Xiong 2/28/2012 1 What we have learned so far Basic data structure Arrays Linked list Abstract data types Abstract data types Stacks Queues Linked List A
SLIDE 2
SLIDE 3
Linked List
A Linked List is a sequence of nodes chained together. Each node, element, or link contains a data item, and a reference to next node
SLIDE 4
Stacks and Queues
Can be implemented by both (resizing) arrays and linked list
SLIDE 5
Today
Quiz on stacks, queues, linked list Recursion
SLIDE 6
Recursion
Recursion concept Examples
Factorial Fibonacci GCD GCD Recursive graph Htree
Next lecture
Divide and conquer Binary search Tower of Hanoi Cost analysis of recursive algorithms
SLIDE 7
2/28/2012 7
SLIDE 8
What is recursion?
SLIDE 9
SLIDE 10
Factorial
N! = N*(N-1)*(N-2)*…..* 2 * 1
SLIDE 11
Recursive Method
A method that calls itself (direct recursion)
SLIDE 12
Recursive Method
A method that calls itself (direct recursion) Every recursive method must have a base case that is not recursive
SLIDE 13
Better version of recursion definition
Recursion
- n. If you still don't get
it, see Recursion.
SLIDE 14
Recursion
A method calls itself
Calls a “clone” of itself to solve a smaller problem Buck Passing
Must have a base case Must have a base case
The buck stops here! (does not call the method)
SLIDE 15
Example: Fibonacci Numbers
Recursive formula:
= −+ − = =
0, 1, 1, 2, 3, 5, 8, 13, …..
SLIDE 16
Fibonacci Numbers: Java Code
SLIDE 17
SLIDE 18
SLIDE 19
SLIDE 20
SLIDE 21
Visual Recursion
SLIDE 22
Fractals
2/28/2012 22
SLIDE 23
SLIDE 24
SLIDE 25
SLIDE 26
SLIDE 27