Fibonacci Sequence in Python

The task is to generate the first N numbers in the Fibonacci sequence. The Fibonacci sequence is a series of numbers where each is the sum of the two preceding ones, usually starting with 0 and 1.

We will implement three ways to find the Fibonacci Sequence in Python. Let’s explore:

Recursive Method

def fibonacci_recursive(n):
    if n <= 0:
        return []
    elif n == 1:
        return [0]
    elif n == 2:
        return [0, 1]
    else:
        fib_sequence = fibonacci_recursive(n - 1)
        fib_sequence.append(fib_sequence[-1] + fib_sequence[-2])
        return fib_sequence

# Example usage
N = 10
print("Fibonacci Sequence (Recursive):", fibonacci_recursive(N))

Iterative Method

def fibonacci_iterative(n):
    if n <= 0:
        return []
    fib_sequence = [0, 1]
    for i in range(2, n):
        fib_sequence.append(fib_sequence[-1] + fib_sequence[-2])
    return fib_sequence[:n]

# Example usage
N = 10
print("Fibonacci Sequence (Iterative):", fibonacci_iterative(N))

Memoization Method

def fibonacci_memoization(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 0:
        return []
    elif n == 1:
        return [0]
    elif n == 2:
        return [0, 1]
    else:
        memo[n] = fibonacci_memoization(n - 1, memo) + [fibonacci_memoization(n - 1, memo)[-1] + fibonacci_memoization(n - 2, memo)[-1]]
        return memo[n]

# Example usage
N = 10
print("Fibonacci Sequence (Memoization):", fibonacci_memoization(N))

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