Recursion in C

1
Recursion in C
2
Recursion

• Recursive tasks
• A task that is defined in terms of itself.
• A function that calls itself.
• With each invocation, the problem is reduced to a
  smaller task (reducing case) until the task
  arrives at some terminal case.

3
Recursive Functions

• A recursive function has two parts
• the terminal/base case.
• - a stopping condition
• the reducing case/recursive step
• an expression of the computation or definition in
  terms of itself

4
General algorithm for recursion

• if (!terminal_condition)
• reducing_case

• if (terminal_condition)
• terminal_case
• else
• reducing_case

5
The Factorial Function

• n! n (n-1) (n -2) 2 1
• 5! 5 4 3 2 1
• The same function can be defined recursively as
  fallows
• 0! 1 terminal case
• n! n (n - 1)! - the reducing case

6
The Factorial Function

• 5! 5 4!
• 4! 4 3!
• 3! 3 2!
• 2! 2 1!
• 1! 1! 0!
• 0! 1 - Terminal Case

Reducing Case
7
Recursive Factorial Function in C

• int fact(int n)
• if (n lt 2) // terminal case
  return 1 else //
  recursive step return (n fact(n - 1))

8

• include ltiostreamgt
• include ltcstdlibgt
• using namespace std
• int sum_of (int ary , int num)
• int main ()
• int ary 5 5, 10, 15, 20, 25
• int num 5
• int ans
• ans sum_of (ary, num)
• coutltlt"\nThe sum of the elements of the array is
  "ltltans
• system("pause")
• return EXIT_SUCCESS
• int sum_of (int ary , int num)

9
int ary 5 5, 10, 15, 20, 25

• Descending - num is 5
• Descending - num is 4
• Descending - num is 3
• Descending - num is 2
• Descending - num is 1 At the ladder bottom - num
  is 0
• Ascending - num is 1 sum is 5
• Ascending - num is 2 sum is 15
• Ascending - num is 3 sum is 30
• Ascending - num is 4 sum is 50
• Ascending - num is 5 sum is 75