@@ -27,6 +27,20 @@ def fib(n: int) -> int:
2727
2828 return Fibonacci .fib (n - 2 ) + Fibonacci .fib (n - 1 )
2929
30+ @staticmethod
31+ def fast_fib (n : int , cache : {int : int }) -> int :
32+ """Fibonacci sequence algorithm utilizing dynamic programing and memoization"""
33+ if n == 0 :
34+ cache [n ] = 0
35+ return 0
36+ 37+ if n == 1 :
38+ cache [n ] = 1
39+ return 1
40+ 41+ cache [n ] = cache [n - 2 ] + cache [n - 1 ]
42+ return cache [n ]
43+ 3044
3145# ---------------------------------------------------------------------------------------------------------
3246
@@ -135,6 +149,8 @@ def main():
135149
136150 test_int_matrix = [[0 ] * 2 for _ in range (3 )]
137151
152+ cache = {}
153+ 138154 for i in range (3 ):
139155 for j in range (2 ):
140156 test_int_matrix [i ][j ] = generator .randint (0 , 9 )
@@ -163,6 +179,12 @@ def main():
163179 print ()
164180 print (f"floor of lg(128): { lg (128 ) } )
165181
182+ print ()
183+ print ("- Dynamic Programming and Memoization Fib" )
184+ 185+ for i in range (40 ):
186+ print (Fibonacci .fast_fib (i , cache ))
187+ 166188 print ()
167189 print ("- Recursive Fib" )
168190
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