diff --git a/fib_recursive_memo.py b/fib_recursive_memo.py new file mode 100644 index 00000000..9e1578c6 --- /dev/null +++ b/fib_recursive_memo.py @@ -0,0 +1,49 @@ +""" +The Fibonacci numbers, commonly denoted F(n) form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is, + +F(0) = 0, F(1) = 1 +F(n) = F(n - 1) + F(n - 2), for n > 1. +Given n, calculate F(n). + +Example 1: + +Input: n = 2 +Output: 1 +Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1. + +Example 2: + +Input: n = 3 +Output: 2 +Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2. + +Example 3: + +Input: n = 4 +Output: 3 +Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3. +""" + +# Fibonacci sequence exercise applied with dynamic programming (memoization): + + +def memoized(): + # cache that saves already calculated values + memo = {} + + def fib(n: int) -> int: + if n < 2: + return n + + if n in memo: + return memo[n] + else: + memo[n] = fib(n - 1) + fib(n - 2) + return memo[n] + return fib + + +fib_memo = memoized() +fib_of = 9 + +print(f"The fibonacci of {fib_of} = {fib_memo(fib_of)}")