Java Lecture Recursion 29th feb 2005

1
Java LectureRecursion29th feb 2005

• AshishFA_at_cse.iitb.ac.in

2
Recursion

• solve(problem)
• If problem is simple
• Return the answer
• Else
• Break the problem as p1,p2,p3 pn
• For each problem P
• solve (P)

3
Properties

• Calls the same function with smaller i/p.
• Divide and conquer strategy

4
Example

• Little tricky

5
Application of recursion

• ?

6
Towers of Hanoi

• Lets try this
• Hanoi
• Rules
• Input
• Output
• Solution for 1, 2, 3, 4, n

7
Define the problem

• Graphical interface
• NO
• What is input ?
• -Number of discs!
• What is output?
• -Final state ?
• Y/N
• -Sequence of moves ?
• -How to represent ?

8
Analogy with recursion

• Solution for 4 discs
• Can the solution for 4 be broken?
• Broken problem must be small.
• It should be same as the main problem.
• When to stop ?
• Solution for x discs is very simple. Solve it
  directly

9
Steps

• Problem definition
• Input representation
• Output representation
• Algorithm
• Implementation

10
Design

• We know
• Recursive condition
• Terminating condition
• Lets try the algorithm for n

11
Input/Output

• Name the function solve_hanoi
• Input argument (integer n)
• Output
• Assume 3 towers three names..
• 3 variables t1 ,t2, t3
• t1 left
• t2 middle
• t3 right
• Are the t1, t2, t3 also arguments ?

12
Skeleton code

• Solve_hanoi(integer n, towers t1, t2, t3)
• Do something.
• Do something
• solve_hanoi(some small n, t1, t2, t3)
• Do something.
• Do something

13
Temination

• Solve_hanoi(integer n, towers t1, t2, t3)
• If (n 1) then
• move the discn from t1 to t3
• Do something
• solve_hanoi(some small n)
• Do something.
• Do something

14
Subdivsion
N-1 discs
Nth disc
Start(X)
End(Y)
Middle(Z)
15
Contd.

• Solve_hanoi(integer n, towers t1, t2, t3)
• 1. Move the n-1 discs from t1 to t2 using t3
• 2. Now move only remaining disc from t1 to t3
• 3. Move the n-1 discs from t2 to t3 using t1
• Which steps are recursive ?

16
Formulate recursive call

• Solve_hanoi(integer n, towers t1, t2, t3)
• If (n 1) then
• move the discn from t1 to t3.
• Else
• Solve_hanoi(n-1, t1, t3, t2).
• move the discn from t1 to t3.
• Solve_hanoi(n-1, t2, t1, t3).

17
Complete java function

• Public static void solve_hanoi(int n, String t1,
  t2, t3)
• if (n 1) then
• System.out.println(move the discn from
  t1 to t3)
• else
• solve_hanoi(n-1, t1, t3, t2)
• System.out.println(move the discn from
  t1 to t3) solve_hanoi(n-1, t2, t1, t3)

18
Reference

• Play the game or see the solutions here
• http//www.mazeworks.com/hanoi/
• Recursionhttp//www.cs.ucla.edu/klinger/dorene/m
  ath4.htm
• History of the game http//www.lawrencehallofsci
  ence.org/Java/Tower/towerhistory.html

19
Thank you
Thank you