Fibonacci Numbers In Python

Lecture 53:-  Fibonacci Numbers In Python

Fibonacci numbers are a sequence of numbers where each number is the sum of the two preceding ones. The sequence starts with 0 and 1, and the subsequent numbers are obtained by adding the last two numbers in the sequence. Here's how you can generate Fibonacci numbers in Python:

1. Using Loop:

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def fibonacci_loop(n):    fib_seq = [0, 1]    while len(fib_seq) < n:        next_num = fib_seq[-1] + fib_seq[-2]        fib_seq.append(next_num)    return fib_seq # Example usage: num_terms = 10 fibonacci_sequence = fibonacci_loop(num_terms) print(f"Fibonacci Sequence ({num_terms} terms): {fibonacci_sequence}")

Output:

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Fibonacci Sequence (10 terms): [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

In this example, the fibonacci_loop() function generates the Fibonacci sequence using a while loop. The sequence starts with [0, 1], and it continues to append new numbers to the sequence until it reaches the specified number of terms n. The function returns the generated Fibonacci sequence as a list.

1. Using Recursion:

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def fibonacci_recursive(n):    if n <= 0:        return []    elif n == 1:        return [0]    elif n == 2:        return [0, 1]    else:        fib_seq = fibonacci_recursive(n - 1)        fib_seq.append(fib_seq[-1] + fib_seq[-2])        return fib_seq # Example usage: num_terms = 10 fibonacci_sequence = fibonacci_recursive(num_terms) print(f"Fibonacci Sequence ({num_terms} terms): {fibonacci_sequence}")

Output:

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Fibonacci Sequence (10 terms): [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

In this example, the fibonacci_recursive() function generates the Fibonacci sequence using recursion. The base cases handle scenarios where n is less than or equal to 0, 1, or 2. For n > 2, the function calls itself to generate the previous terms and then appends the sum of the last two terms to the sequence.

Both approaches will generate the same Fibonacci sequence with the specified number of terms. You can adjust the value of num_terms to generate a longer or shorter Fibonacci sequence. However, keep in mind that the recursive approach may be less efficient for large values of num_terms due to the overhead of function calls.