Recursion

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Recursion
For example in the series
we use the operator ! factorial.
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In the algorithm for the series we have used
Along this line
So factorial(5) calls factorial(4),
factorial(4) calls factorial(3),
factorial(3) calls factorial(2), etc.
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Fibonacci
1, 1, 2, 3, 5, 8, 13, 21, ...
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Applying recursion
fibonacci(n)
This algorithm expresses clearly that a term
equals the sum of the two preceding terms.
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Bisection
No tests for roots on the specified interval!
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• Layout of a recursive function
• no recursive calls needed (stopping case), see
  factorial(1)
• one or more cases where a recursive call is
  needed

Make sure the function stops!

• Advantage formulation is simple and clear
• Disadvantage inefficient
• calling a function takes time a.o. transport of
  arguments
• more calls are needed, see fibonacci

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Towers of Hanoi
Bring disks from pole A to pole C.
A
B
C
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• n1 A to C
• n 2 A to B. A to C. B to C
• n 3 Use step n 2 to move the first two disks
  to B while
• using C as temporary storage.
• A to B. Use step n 2 to move these
  two disks
• from B to C using A as temporary
  storage
• n-2 ..
• n-1 Use step n-2 to move n-2 disks from A to B
  (C temporary).
• Move A to C.
• Use step n-2 to move the n-2 disks from
  B to C (A temporary)
• n Use step n-1 to move n-1 disks from A to B
  (C temporary)
• Move A to C.
• Use step n-1 to move the n-1 disks from
  B to C (A temporary)

Demo
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• n1 Move A to C
• Use step n-1 to move n-1 disks from A to B (C
  temporary)
• Move A to C
• Use step n-1 to move the n-1 disks from
  B to C (A temporary)

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• Sometimes a variable with the values
• 0 (false or not true) or
• 1 (true)
• Assume you want adult to become 1 if age 18
• adult to become 0
  if age lt 18
• adult is a so-called boolean variable
• You can accomplish that in two ways

Or