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).
cazoo = {0: 0, 1: 1}
# The above line creates a buffer
# where we store the already solved fib(of a given value).
# We shall always reference it too see if a
# case we need is already stored in this cache
def fib(n: int) -> int:
if n in cazoo:
return cazoo[n]
# Here we are checking if a value whose
# fib we are calculating is already in the cache
cazoo[n] = fib(n-1) + fib(n-2)
# here we are adding fib of a given value to the cache
return cazoo[n]
# here we are returning fib of a value after
# we have added it to the cache. We are using memoization approach
print(fib(z) for z in range(5))
output => [0, 1, 1, 2, 3]
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.