Added memoization function in fibonacci

Author: JDeepD

maths/fibonacci.py

@@ -1,17 +1,18 @@
 # 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 iterative function doesn't use 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
 """
 
 from math import sqrt
 from time import time
+from typing import Callable
 
 
 def time_func(func, *args, **kwargs):
@@ -86,6 +87,35 @@ def fib_recursive_term(i: int) -> int:
     return [fib_recursive_term(i) for i in range(n + 1)]
 
 
+def fib_memoization() -> Callable[[int], int]:
+    """
+    Calculates the nth fibonacci number using Memoization
+    >>> fib_memoization()(5)
+    5
+    >>> fib_memoization()(100)
+    354224848179261915075
+    >>> fib_memoization()(25)
+    75025
+    >>> fib_memoization()(40)
+    102334155
+    """
+    # Cache must be outside recursuive function
+    # other it will reset every time it calls itself.
+    cache: dict[int, int] = {1: 1, 2: 1}  # Prefilled cache
+
+    def rec_fn_memoized(num: int) -> int:
+        if num < 1:
+            raise Exception("n is negative")
+        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
+
+
 def fib_binet(n: int) -> list[int]:
     """
     Calculates the first n (0-indexed) Fibonacci numbers using a simplified form
@@ -127,4 +157,5 @@ def fib_binet(n: int) -> list[int]:
     num = 20
     time_func(fib_iterative, num)
     time_func(fib_recursive, num)
+    time_func(fib_memoization(), num)
     time_func(fib_binet, num)