METYCSSA (#6): Fibonacci

• Recursive Fibonacci:

int Fib(n)

if (n == 0 or n == 1) return 1

else return Fib(n - 1) + Fib(n - 2)

• Lower bound analysis

• T(0), T(1) >= b

T(n) <= T(n - 1) + T(n - 2) + c if n > 1

• Analysis

let ? be (1 + ?5)/2 which satisfies ?2 = ? + 1

show by induction on n that T(n) >= b?n - 1

Previous slide

Next slide

Back to first slide

View graphic version