. While elegant, a basic recursive function is highly inefficient for large numbers because it recalculates the same values multiple times, leading to an exponential time complexity of
Python's built-in decorator makes memoization incredibly easy: fibonacci python
F(n+1)F(n)the fraction with numerator cap F open paren n plus 1 close paren and denominator cap F open paren n close paren end-fraction approaches the Golden Ratio ( ≈1.618is approximately equal to 1.618 Using functools
To fix the performance issues of recursion, you can use . This technique stores the results of expensive function calls and returns the cached result when the same inputs occur again. Using functools.lru_cache Using functools.lru_cache def fibonacci_generator(): a
def fibonacci_generator(): a, b = 0, 1 while True: yield a a, b = b, a + b # Usage fib_gen = fibonacci_generator() for _ in range(10): print(next(fib_gen)) Use code with caution. Advanced Applications
In Python, there are several ways to generate this sequence, ranging from simple loops to advanced memory-saving techniques. The Basic Iterative Approach