This document discusses recursion, which is a technique for solving problems by breaking them down into smaller subproblems and solving those subproblems recursively until reaching a base case. It provides examples of recursive functions like calculating factorials and the Fibonacci sequence. Recursion involves functions that call themselves, breaking a problem into smaller calls until a base case is reached. While recursion and iteration both involve repetition, they differ in how termination is handled - recursion relies on reaching a base case while iteration uses an explicit loop condition. Both techniques can result in infinite loops if not implemented properly.

1. RECURSION Lecture 2.4
Prepared by: Mian Saeed Akbar

2. Recursion
Calculating the value of a function on larger input in terms of the value of the same function on
smaller input.
Recursive functions
o Functions that call themselves
o Can only solve a base case
If not base case
o Break problem into smaller problem(s)
o Launch new copy of function to work on the smaller problem (recursive call/recursive step)
• Slowly converges towards base case
• Function makes call to itself inside the return statement
o Eventually base case gets solved
• Answer works way back up, solves entire problem

3. Recursion
Factorial: n! = n * ( n – 1 ) * ( n – 2 ) * … * 1
 Recursive relationship ( n! = n * ( n – 1 )! )
5! = 5 * 4!
4! = 4 * 3!…
 Base case (1! = 0! = 1)
Fibonacci series: 0, 1, 1, 2, 3, 5, 8...
 Each number sum of two previous ones
 Example of a recursive formula:
 fib(n) = fib(n-1) + fib(n-2)
long fibonacci( long n ){
if ( n == 0 || n == 1 ) // base case
return n;
else
return fibonacci( n - 1 ) + fibonacci( n – 2 );
}
f( 3 )
f( 1 )
f( 2 )
f( 1 ) f( 0 ) return 1
return 1 return 0
return +
+
return

4. Recursion vs. Iteration
Repetition
 Iteration: explicit loop
 Recursion: repeated function calls
Termination
 Iteration: loop condition fails
 Recursion: base case recognized
Both can have infinite loops
Balance between performance (iteration) and good software engineering (recursion)

5. Thank you
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