Iteration and Recursion

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Iteration and Recursion

• Michael Prestia
• COT 4810
• February 7, 2008

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Iteration

• Straightforward
• Instructions are processed in order they are
  received
• Mutable state

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Recursion

• Breaks a problem down into self-similar
  sub-problems
• How it works
• Function calls itself
• Instance pushed onto stack
• Once base condition is reached, pop from stack
• Immutable state

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Towers of Hanoi

• 3 Towers
• Variable number of rings
• Move all rings to another tower
• Larger ring can never be placed on a smaller ring

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Recursive Solution
procedure hanoi(n, A, B) if n1 then move
disk from A to B else hanoi(n-1, A, C)
move disk from A to B hanoi(n-1, C, B)
A
B
C
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hanoi(3, A, B)
A
B
C
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hanoi(3, A, B) hanoi(2, A, C)
hanoi(1, A, B) move disk from A to
B
A
B
C
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hanoi(3, A, B) hanoi(2, A, C) Move
disk from A to C
A
B
C
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hanoi(3, A, B) hanoi(2, A, C)
hanoi(1, B, C) move disk from B to
C
A
B
C
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hanoi(3, A, B) move disk from A to B
A
B
C
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hanoi(3, A, B) hanoi(2, C, B)
hanoi(1, C, A) move disk from C to
A
A
B
C
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hanoi(3, A, B) hanoi(2, C, B) move
disk from C to B
A
B
C
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hanoi(3, A, B) hanoi(2, C, B)
hanoi(1, A, B) move disk from A to
B
A
B
C
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Buneman-Levy Solution
procedure tower repeat move
smallest disk clockwise move second
smallest disk to remaining tower until all
disks are on one peg
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Walsh Solution
1. Move smallest disk onto even disk 2. if all
disks are on the same peg then exit else move
second disk onto other disk go to 1
n 1
n 3
n 2
5
4
6
28
5
1
6
29
5
2
1
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2
3
1
31
1
3
6
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1
4
3
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2
1
3
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5
1
2
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5
4
1
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Summary

• Iteration
• Mutable state
• Order of execution
• Recursion
• Immutable state
• Time and space complexity

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References

• Dewdney, A.K. The New Turing Omnibus. New York
  Henry Hold and Company, 1993
• Knowlton, Todd. Introduction to Computer Science
  Using C. Cincinnati South-Western Educational
  Publishing, 1998.

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Homework

• What is one disadvantage of recursion?
• How does the Walsh algorithm represent the towers
  in Towers of Hanoi?