CSci 160 Lecture 18

1. CSci 160Lecture 18 Martin van Bommel

2. Fibonacci Sequence • Fibonacci investigated how fast rabbits could breed in ideal circumstances • Mate at one month, produce pair of rabbits every month from month two on • Link on web • Fibonacci sequence for number of pairs is 1 1 2 3 5 8 13 21 34 55 ...

3. Fibonacci Equation • Sequence 1 1 2 3 5 8 ... can be definedFib(1) = 1Fib(2) = 1Fib(n) = Fib(n-1) + Fib(n-2) if n > 2

4. Recursive Fibonacci long int Fib(int n) { if (n <= 2) return (1); return (Fib(n-1) + Fib(n-2)); } • fibr.c • Number of recursive calls to Fib = Fib(n+1)

5. Non-recursive Fibonacci long int Fib(int n) { int i, n1 = 1, n2 = 1, f = 1; for (i = 3 ; i <= n; i++) { f = n1 + n2; n1 = n2; n2 = f; } return f; }