Fibonacci Numbers & Recursion

Index

Fibonacci Numbers

with

Human Computers

Instructions

Each student receives algorithmic instructions:

 

 when you are asked for fib(n):
 if n is 1 or 2 return 1
 otherwise return fib(n-1) + fib(n-2)

 

To compute fib(n-1) or fib(n-2) find another student and give them this task. Wait for their response. When you get both responses, respond to whomever asked you for fib(n).

 

Instructor starts process by asking one student for, say, fib(7).

Text

function fibonacci(n) {
  if (n < 3) {
    return 1}
  else {
    return fibonacci(n-1) + fibonacci(n-2)}

    } 

Index

fib(22)

fib(19)

fib(20)

fib(21)

fib(18)

fib(19)

fib(20)

fib(18)

fib(17)

fib(18)

fib(19)

fib(17)

fib(18)

fib(17)

fib(18)

Index

Calculating the 22nd Fibonacci number recursively

What about fib(22)?

Index

F6 calls F5 and waits...​
F5 calls F4 and waits...​
F4 calls F3 and waits...​
F3 calls F2 and waits...​
F2 returns 1
F3 calls F1 and waits...​
F1 returns 1
F3 returns 2=1+1
F4 calls F2 and waits...​
F2 returns 1
F4 returns 3=2+1
F5 calls F3 and waits...​
F3 calls F2 and waits...​
F2 returns 1
F3 returns 2=1+1
F3 calls F1 and waits...​
F1 returns 1
F5 returns 5=3+2
F6 calls F4 and waits...​
F6 returns 8=5+3
1,1,2,3,5,8
F4 calls F3 and waits...​
F3 calls F2 and waits...​
F2 returns 1
F3 calls F1 and waits...​
F1 returns 1
F3 returns 2=1+1
F4 calls F2 and waits...​
F2 returns 1
F4 returns 3=2+1