diff --git a/maths/fibonacci.py b/maths/fibonacci.py index 9b193b74a..ca4f4a236 100644 --- a/maths/fibonacci.py +++ b/maths/fibonacci.py @@ -1,13 +1,19 @@ # fibonacci.py """ -Calculates the Fibonacci sequence using iteration, recursion, and a simplified -form of Binet's formula +Calculates the Fibonacci sequence using iteration, recursion, memoization, +and a simplified form of Binet's formula -NOTE 1: the iterative and recursive functions are more accurate than the Binet's -formula function because the iterative function doesn't use floats +NOTE 1: the iterative, recursive, memoization functions are more accurate than +the Binet's formula function because the Binet formula function uses floats NOTE 2: the Binet's formula function is much more limited in the size of inputs that it can handle due to the size limitations of Python floats + +RESULTS: (n = 20) +fib_iterative runtime: 0.0055 ms +fib_recursive runtime: 6.5627 ms +fib_memoization runtime: 0.0107 ms +fib_binet runtime: 0.0174 ms """ from math import sqrt @@ -86,6 +92,39 @@ def fib_recursive(n: int) -> list[int]: return [fib_recursive_term(i) for i in range(n + 1)] +def fib_memoization(n: int) -> list[int]: + """ + Calculates the first n (0-indexed) Fibonacci numbers using memoization + >>> fib_memoization(0) + [0] + >>> fib_memoization(1) + [0, 1] + >>> fib_memoization(5) + [0, 1, 1, 2, 3, 5] + >>> fib_memoization(10) + [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55] + >>> fib_iterative(-1) + Traceback (most recent call last): + ... + Exception: n is negative + """ + if n < 0: + raise Exception("n is negative") + # Cache must be outside recursuive function + # other it will reset every time it calls itself. + cache: dict[int, int] = {0: 0, 1: 1, 2: 1} # Prefilled cache + + def rec_fn_memoized(num: int) -> int: + if num in cache: + return cache[num] + + value = rec_fn_memoized(num - 1) + rec_fn_memoized(num - 2) + cache[num] = value + return value + + return [rec_fn_memoized(i) for i in range(n + 1)] + + def fib_binet(n: int) -> list[int]: """ Calculates the first n (0-indexed) Fibonacci numbers using a simplified form @@ -127,4 +166,5 @@ if __name__ == "__main__": num = 20 time_func(fib_iterative, num) time_func(fib_recursive, num) + time_func(fib_memoization, num) time_func(fib_binet, num)