1. Java Lecture Recursion 29th feb 2005

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); }
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3. Properties Calls the same function with smaller i/p.
Divide and conquer strategy
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4. Example
Little tricky
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5. Application of recursion?
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6. Towers of Hanoi Let’s try this Hanoi Rules Input Output
Solution for 1, 2, 3, 4, … n
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7. Define the problem Graphical interface What is input ?NO
What is input ?
-Number of discs!
What is output?
-Final state ?
Y/N
-Sequence of moves ?
-How to represent ?
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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
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9. Steps Problem definition Input representation Output representation
Algorithm
Implementation
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10. Design We know Let’s try the algorithm for n Recursive condition
Terminating condition
Let’s try the algorithm for n
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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 ?
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12. Skeleton code Solve_hanoi(integer n, towers t1, t2, t3) {
Do something….
Do something…
solve_hanoi(some small n, t1, t2, t3) }
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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…. }
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14. Subdivsion N-1 discs Nth disc Start(X) Middle(Z) End(Y)
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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 ?
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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).
Solve_hanoi(n-1, t2, t1, t3). }
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17. Complete java function
Public static void solve_hanoi(int n, String t1, t2, t3) {
if (n == 1) then
System.out.println(“move the disc”+n+” from “+t1+” to “+ t3);
else
solve_hanoi(n-1, t1, t3, t2)
System.out.println(“move the disc”+n+” from “+t1+” to “+ t3); solve_hanoi(n-1, t2, t1, t3) }
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18. Reference Play the game or see the solutions here
Recursion:
History of the game :
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19. Thank you
Thank you
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