1. Recursion

2.  A recursive function contains a call to itself Example: the factorial n!=n*(n-1)! for n>1 n!=1 for n=1 int factorial (int n) { if (n == 0) { return 1; } else { return (n * factorial (n-1)); }

3. Stacks and The Recursive Call  Computers use a structure called a stack to keep track of recursion  A stack is a memory structure analogous to a stack of paper: Last In First Out  Whenever a function is called, the computer uses a "clean sheet of paper“ called active frame  The function definition is copied to the paper  The arguments are plugged in for the parameters  The computer starts to execute the function body

4. Recursion  Key elements of a recursive function  The function calls itself  There must be some terminal condition that ends the recursion  Otherwise you will call yourself infinitely and the program will blow up  The recursion should be getting simpler on each call

5. Examples  power function: int power(int base, int exponent); power (2,4)=2*2*2*2 power(2,4)=2*power(2,3) power(x,n)=x*power(x,n-1) (for n>0) =1 (for n=0) int power (int base, int exponent) { fill in the space };

6. power function  int power(int base, int exponent) { If (exponet==0) return 1; else If (exponet>0) return (base*power(base, exponent-1)); else { cout<<“we only take care of positive exponent”<<endl ; exit(1) }

7. Fibonacci sequence  Fibonacci sequence

8. Fibonacci sequence function int fibonacci(int n) { if (n == 1) { return 1; } else if (n == 2) { return 1; } else { return fibonacci(n-1) + fibonacci(n-2); }

9. Recursion and iteration  Any task that can be accomplished using recursion can also be done without recursion  A nonrecursive version of a function typically contains a loop or loops  A non-recursive version of a function is usually called an iterative-version  A recursive version of a function  Usually runs slower  Uses more storage  May use code that is easier to write and understand