Comp 245 Data Structures

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Comp 245Data Structures

• Recursion

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What is Recursion?

• A problem solving concept which can be used with
  languages that support the dynamic allocation of
  memory.
• In programming, it is the ability for a function
  to call itself!
• The concept has its foundation in mathematics.

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The Factorial Function

• 5! 5 4 3 2 1 120
• 5! 5 4! 5 4 3!
• Definition

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if n 0
n!
if n gt 0
n (n - 1)!
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Coding the Factorial FunctionITERATIVELY

• float Fact (int N)
• float product 1
• for (int i 1 i lt N i)
• product product i
• return product

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Coding the Factorial FunctionRECURSIVELY

• float Fact (int N)
• //Anchor Point
• if ((N 0) (N 1))
• return 1
• else
• //Recursive Call approaches anchor
• return N Fact(N 1)

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Two Requirements for Recursive Code

• There must be an anchor point. (Sometimes this
  is called the base case.)
• Each recursive call must approach the anchor
  point (or base case).

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A Walkthru of Recursive Code

• Run Time Stack
• Winding and Unwinding the stack
• Local variables, parameters, return values stored
  on the stack

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Advantage/Disadvantage of Recursion

• ADVANTAGE
• Usually a more concise coding solution, some
  solutions are more easily implemented using
  recursion
• DISADVANTAGE
• Less efficient due to overhead involved with
  function calls.

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The Fibonacci Number Sequence

• The Italian mathematician Leonardo Fibonacci
  discovered this sequence which is evident in
  nature. He discovered the sequence while
  researching the breeding of rabbits.
• The sequence is as follows
• 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, (and so
  on)
• We define the sequence as follows
• Fib(0) 0
• Fib(1) 1
• Fib(N) Fib(N-2) Fib(N-1)
• How would Fib(4) be defined?

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Fib(4) Part I
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Coding the Fibonacci FunctionRecursively

• int Fib (int N)
• if ((N0) (N1))
• return N
• else
• return Fib(N-1) Fib(N-2)