Recursion

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Recursion

• CS-240/CS341

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What is recursion?

• a function calls itself
• direct recursion
• a function calls its invoker
• indirect recursion

f1
f
f2
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Outline of a Recursive Function
function header if (answer is known)
return the answer else recursive
call to solve a "smaller" problem
base case
recursive case
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Factorial (n) - recursive
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How Recursion Works

• a recursive function call is like any other
  function call
• each function call has its own activation record
  (space for storing parameters and local
  variables)
• created when the function is called
• destroyed when the function returns to its caller
• activation records are stacked up as recursive
  calls are made
• when the base case is reached the recursion
  unwinds

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Recursive Call Tree
RecFact (4)
long factorial (int n) if (n 0)
return 1 else return n factorial
(n-1)
What happens with factorial (-2)?
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Factorial (n) - iterative
Factorial (n) n (n-1) (n-2) ... 1
for n gt 0 Factorial (0) 1
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Euclid'sAlgorithm

• Finds the greatest common divisor of two
  nonnegative integers that are not both 0
• Recursive definition of gcd algorithm
• gcd (a, b) a (if b is 0)
• gcd (a, b) gcd (b, a b) (if b ! 0)
• Write a recursive gcd function
• prototype?
• implementation?

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Tracing gcd (54, 30)
int gcd (int a, int b) if (b 0)
return a else return gcd (b, a
b)
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Iterative gcd?
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Another recursive definition
Fibonacci numbers are the sequence of integers
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, .
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Tracing fib(5)