Recursion

1
Recursion

• A function is said to be recursive if it calls
  itself, either directly or indirectly.
• void repeat( int n )
• cout ltlt n ltlt " "
• repeat( --n )

2
Recursion contd.

• Simple recursive routines follow a standard
  pattern. Typically there is a base case ( or
  cases ) that is tested for, upon entry to the
  function. Then there is a general recursive case
  in which one of the variables, often an integer,
  is passed as an argument in such a way as to
  ultimately lead to the base case.

3
Recursion contd.

• When writing a recursive function, there are two
  rules that need to be adhered to.
• Every recursive function must have a base case,
  where the result is known
• When a function invokes itself, the value is
  defined in terms of previously defined function
  values, and the value used for testing for the
  base case must change.

4
Recursion contd.

• void repeat( int n )
• if( nlt0 )
• cout ltlt "END" ltlt endl
• return
• else
• cout ltlt n ltlt " "
• repeat( --n )

5
Recursion Example

• int sum( int n )
• if (n lt 1 )
• return n // base case
• else
• return (n sum( n -1 )) // current value is
  defined in terms of
• // a different value of the parameter
• sum(1) 1
• sum(2) 2 sum(1) 2 1
• sum(3) 3 sum(2) 3 2 1

6
Factorial Example

• Lets find the factorial of n where n is a
  non-negative integer.
• Product of integers from 1 to n
• If n 0, then n! is 1
• 0! 1
• n! n(n-1) 3.2.1 for n gt 0
• int factorial( int n )
• if (n lt 1 )
• return 1
• else
• return ( n factorial(n-1 ) )

What is the Big-Oh?
7
Iterative Version of the Factorial Example

• int factorial( int n )
• int value 1
• for ( int i2, iltn, i )
• value i
• return value

What is the Big-Oh for this?
8
Pros and Cons of Recursion

• Disadvantages
• Slow time is taken for function call
• Uses more memory requires space for stack frame
• Advantages
• When it is a simple, elegant solution that is
  easy to understand
• When the number of recursive calls is a fraction
  of n

9
When to Use Recursion

• 1. Iterative functions are typically faster than
  their recursive counterparts. So, if speed is an
  issue, you would normally use iteration.
• 2. If the stack limit is too constraining then
  you will prefer iteration over recursion.
• 3. Some procedures are very naturally programmed
  recursively, and all but unmanageable
  iteratively. Here, then, the choice is clear.

10
Example of When to Use Recursion
Algorithm Power( x, n ) Input base x, exponent
n where n ³ 0 Output value of xn if n 0
then return 1 if n is odd then y
Power(x,(n-1)/2) return x y y else y
Power(x,n/2) return y y