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Python | Program to calculate n-th term of a Fibonacci Series

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mahmoud2506
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2022-05-18
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Python program to calculate n-th term of Fibonacci series with the help to two approaches (there are many approaches to calculate n-th term).

Description:

    1. First Approach: Dynamic Programming
      In this approach, we calculate all the terms of Fibonacci series up to n and if we need to calculate any other term which is smaller than n, then we don’t have to calculate it again.
    2. Second Approach: By Formula
      In this approach we calculate the n-th term of Fibonacci series with the help of a formula.
    Formula:
    phi = ( 1 + sqrt(5) ) / 2
    An = phin/ sqrt(5)

Example:

    Input:
    for n = 5
    for n = 8

    Output:
    a5  = 5
    a8 = 21

 

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mahmoud2506
2022-05-18
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Python code to calculate n-th term of a Fibonacci series

def dynamic_fibonacci(n):
    '''
    This function will calculate fobonacci
    series with the help of dynamic
    programming.
    '''
    l = [0]*(n+1)
    l[0] = 0
    l[1] = 1
    for i in range(2, n+1):
        l[i] = l[i-1] + l[i-2]

    return l

    # Time complexity O(n)


def fibonacci_by_formula(n):
    '''
    This function will calculate n-th
    term of fibonacci series with the
    help of a formula.
    '''
    from math import sqrt
    
    phi = (1 + sqrt(5))/2

    fib = round(pow(phi, n)/sqrt(5))

    return fib

    # Time complexity O(1)

def main():
    n = 8
    lst = dynamic_fibonacci(n)
    x = fibonacci_by_formula(n)

    print('By Dynamic Programming:',lst[n])
    print()
    print('By Formula:',x)

main()

Output

By Dynamic Programming: 21

By Formula: 21

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