1. Comp 245 Data 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

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

5. Coding the Factorial Function RECURSIVELY 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 Fib(4) Fib(3) Fib(2) Fib(1)Fib(0) Fib(1) Fib(2) Fib(1)Fib(0)

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