Intro to Recursion
Fibonacci Numbers (1)
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f0 = 1
f1 = 1
f2 = 1 + 1 = 2
f3 = 2 + 1 = 3
f4 = 3 + 2 = 5
f5 = 5 + 3 = 8
f6 = 8 + 5 = 13
• In general: fn = fn-1 + fn-2
• for n ≥ 2
f0 = 1
f1 = 1
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)