1. Advanced Java Programming
Session #, Speaker Name
Advanced Java Programming
CSS446
Spring 2014
Nan Wang
08/24/11

2. Chapter Goals To learn to “think recursively”
To be able to use recursive helper methods
To understand the relationship between recursion and iteration
To understand when the use of recursion affects the efficiency of an algorithm
To analyze problems that are much easier to solve by recursion than by iteration
To process data with recursive structures using mutual recursion

3. Recursion
The recursion method is to break up complex computational problem into simpler, smaller ones.
Recursion refers to that face that the same computation recurs, or occurs repeatedly as the problem is solved.
E.g. Fibonacci sequence:

4. Triangle Numbers
To compute the area of a triangle of width n, assuming that each [] square has area 1. []
[][]
[][][]
[][][][]
Area(1) = 1
Area(4) = Area(3) + 1
=>Area(n) = Area(n-1) + n

6. Palindrome test
Test whether a sentence is a palindrome – a string that is equal to itself when you reverse all characters.
Madam, I’m Adam
A man, a plan, a canal – Panama!

9. Fibonacci Sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, 55

12. Loop version of Fib

13. Recursion Vs. Loop

14. Permutations The string ‘eat’ has six permutations:
eat eta aet ate tea tae
Index=0 e—at ta
Index=1 a—et te
Index=2 t—ea ae

16. Mutual Recursion
Recursive solution 1: a method call itself to solve a simpler problem.
In a mutual recursion, a set of cooperating methods calls each other repeatedly.

17. Evaluating an Expression
Compute the values of arithmetic expressions
3+4*5, (3+4)/5, 3-(4-5) etc

19. Backtracking
Backtracking is a problem solving technique that builds up partial solutions that get increasingly closer to the goal.
If a partial solution cannot be completed, one abandons it and returns to examining the other candidates.

20. Homework assignment 5 DO NOT implement
Submit a softcopy to