1. March 2005 1R. Smith - University of St Thomas - Minnesota QMCS 130: Today’s Class More about FunctionsMore about Functions RecursionRecursion

2. March 2005 2R. Smith - University of St Thomas - Minnesota A Simple Function int add (int a, int b) { return (a + b); } x = add (1, 1); => x = 1 + 1;

3. March 2005 3R. Smith - University of St Thomas - Minnesota Points about Functions “Substitutes” the parameters into the definition“Substitutes” the parameters into the definition Then we “run” the definitionThen we “run” the definition The result is substituted for the function callThe result is substituted for the function call Functions can call themsleves!Functions can call themsleves! You can use function calls as parameters:You can use function calls as parameters: –X = add(1, add(2, add(3, 4))) Which MeansWhich Means –X = add(1, add(2, 3 + 4))), or –X = add(1, 2 + 3 + 4), or X = 1+2+3+4

4. March 2005 4R. Smith - University of St Thomas - Minnesota Let’s calculate “Factorial” Definition:Definition: For X < 2, Factorial(X) = 1,For X < 2, Factorial(X) = 1, For X > 1, Factorial(X) = X * Factorial(X-1)For X > 1, Factorial(X) = X * Factorial(X-1) What is Factorial (4) ?What is Factorial (4) ? Factorial(4) =Factorial(4) = –= 4 * Factorial (3) –= 4 * 3 * Factorial(2) –= 4 * 3 * 2 * Factorial(1) –= 4 * 3 * 2 * 1

5. March 2005 5R. Smith - University of St Thomas - Minnesota Factorial as a Function For X < 2, Factorial(X) = 1,For X < 2, Factorial(X) = 1, For X > 1, Factorial(X) = X * Factorial(X-1)For X > 1, Factorial(X) = X * Factorial(X-1) Can we write this in C?Can we write this in C? What statements do we need?What statements do we need?

6. March 2005 6R. Smith - University of St Thomas - Minnesota Let’s try writing it out.

7. March 2005 7R. Smith - University of St Thomas - Minnesota Fibonacci Numbers Fib(x)Fib(x) –For X < 3, Fib(X) = 1 –For X > 2, Fib(X) = Fib(X-1)+Fib(X-2) Fib(6) =Fib(6) = –= Fib(5) + Fib(4) –= (Fib(4)+Fib(3))+(Fib(3)+Fib(2)) –… etc.

8. March 2005 8R. Smith - University of St Thomas - Minnesota Fibonacci in C … should be obvious!… should be obvious!

9. March 2005 9R. Smith - University of St Thomas - Minnesota Creative Commons License This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by- sa/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.