Comp 245 Data Structures

1. Comp 245Data Structures Recursion

2. What is Recursion? • A problem solving concept which can be used with languages that support the dynamic allocation of memory. • In programming, it is the ability for a function to call itself! • The concept has it’s foundation in mathematics.

3. The Factorial Function • 5! = 5 * 4 *3 * 2 * 1 = 120 • 5! = 5 * 4! = 5 * 4 * 3! = … • Definition 1 if n = 0 n! = if n > 0 n * (n - 1)!

4. Coding the Factorial FunctionITERATIVELY float Fact (int N) { float product = 1; for (int i = 1; i <= N; i++) product = product * i; return product; }

5. Coding the Factorial FunctionRECURSIVELY float Fact (int N) { //Anchor Point if ((N == 0) || (N == 1)) return 1; else //Recursive Call – approaches anchor return N * Fact(N – 1); }

6. Two Requirements for Recursive Code • There must be an anchor point. (Sometimes this is called the base case.) • Each recursive call must approach the anchor point (or base case).

7. A Walkthru of Recursive Code • Run Time Stack • Winding and Unwinding the stack • Local variables, parameters, return values stored on the stack

8. Advantage/Disadvantage of Recursion • ADVANTAGE Usually a more concise coding solution, some solutions are more easily implemented using recursion • DISADVANTAGE Less efficient due to overhead involved with function calls.

9. The Fibonacci Number Sequence • The Italian mathematician Leonardo Fibonacci discovered this sequence which is evident in nature. He discovered the sequence while researching the breeding of rabbits. • The sequence is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … (and so on) • We define the sequence as follows: Fib(0) = 0 Fib(1) = 1 Fib(N) = Fib(N-2) + Fib(N-1) • How would Fib(4) be defined?

10. Fib(4) – Part I

11. Coding the Fibonacci FunctionRecursively int Fib (int N) { if ((N==0) || (N==1)) return N; else return Fib(N-1) + Fib(N-2); }