Fibonacci Series

In [14]:

import time

Using Formula¶

Formula is the best way to reduce complexity of code.

In [1]:

def fibonacci(n):
    return int(((1 + 5**0.5)**n - (1 - 5**0.5)**n)/(2**n * 5**0.5))

In [2]:

print(fibonacci(10))

55

Using loops¶

Way 1¶

In [17]:

start = time.time()

f1, f2 = 1, 1

# to get the first 10 elements in fibonacci series
for _ in range(10):
    print(f1, end=' ')
    f1, f2 = f2, f1+f2
    
end = time.time()
print('\nCode execution time : ', end - start)

1 1 2 3 5 8 13 21 34 55 
Code execution time :  0.004085063934326172

Way 2¶

*** Use this method

In [4]:

# you may use list to store the values

fib, f1, f2 = [], 1, 1

# to get the first 10 elements in fibonacci series
for i in range(10):
    fib.append(f1)
    f1, f2 = f2, f1+f2
    
print(fib)

[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]

Way 3¶

In [5]:

def fibonacci(n):
    fib = [1, 1]
    
    for i in range(2, n):  
        fib.append(fib[-1] + fib[-2])
    return fib

In [6]:

print(fibonacci(10))

[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]

Using Recursive function¶

In [7]:

def fibonacci(n):
    if n<2:
        return 1
    else:
        return fibonacci(n-1) + fibonacci(n-2)

In [8]:

# fibonacci should return (n+1)th element from fibonacci series
print(fibonacci(10))

89

Using yield generator¶

In [9]:

def fibonacci():
    f1, f2 = 1, 1

    while True:
        yield f1
        f1, f2 = f2, f1+f2

In [10]:

# fibonacci() should print until element less than condition
for element in fibonacci():
    if element > 100:
        break
    print(element, end=' ')

1 1 2 3 5 8 13 21 34 55 89 

In [11]:

fib = []

for element in fibonacci():
    if element > 100:
        break
    fib.append(element)
print(fib)

[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]

In [12]:

for index, element in zip(range(10), fibonacci()):
     print('{}th element : {}'.format(index+1, element))

1th element : 1
2th element : 1
3th element : 2
4th element : 3
5th element : 5
6th element : 8
7th element : 13
8th element : 21
9th element : 34
10th element : 55