Playground

Here's a Python function using memoization to efficiently compute the n-th Fibonacci number:

def fib(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 1:
        return n
    memo[n] = fib(n - 1) + fib(n - 2)
    return memo[n]

This runs in O(n) time and O(n) space. The dictionary persists across calls, so repeated invocations are even faster.