Intro to Recursion

Fibonacci Numbers (1) f0 = 1 f1 = 1 f2 = 1 + 1 = 2 f3 = 2 + 1 = 3 In general: fn = fn-1 + fn-2 for n ≥ 2

Fibonacci Numbers (2) The Fibonacci number problem has the recursive property The problem fibonacci(n) (= fn) can be solved using the solution of two smaller problem: The base (simple) cases n = 0 and n = 1 of the Fibonacci problem can be solved readily:

Fibonacci Numbers (3) 1. Which smaller problem do we use to solve fibonacci(n):

Fibonacci Numbers (4) 2. How do we use the solution sol1 to solve fibonacci(n) 3. Because we used fibonacci(n−2), we will need the solution for 2 base cases:

Fibonacci Numbers (5)

The recursive binary search algorithm(1) You are given a sorted array (of numbers) Locate the array element that has the value x

The recursive binary search algorithm(2) Locate the array element that has the value 27

The recursive binary search algorithm(3) Locate the array element that has the value 28

The recursive binary search algorithm(4)

The recursive binary search algorithm(5)