leetcode-509-fibonacci-number.swift

/**

Copyright (c) 2020 David Seek, LLC

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https://leetcode.com/problems/fibonacci-number/


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).

*/

/**
Big O Annotation
Time complexity O(n) where n is N.
Space complexity O(n) where n is N.

The bottom up approach takes more memory 
than the recursive approach.

But the recursive approach might fail
as a stackoverflow protection when the 
recursive function is called too many times
in a short amount of time.

Happens for example on the CodeRunner application.
*/
func fib(_ N: Int) -> Int {
        
    // Init a bottom up array
    var bottomUp: [Int] = []
    
    /**
    Add the 3 known starting cases of 
    the fibonacci sequence
    */
    bottomUp.append(0)
    bottomUp.append(1)
    bottomUp.append(1)
    
    // Check that N is larger than 2
    if N > 2 {
        
        // If so, iterate up through N + 1
        for index in 3...N + 1 {

            // And calculate the fib for that spot
            bottomUp.append(bottomUp[index - 1] + bottomUp[index - 2])
        }
    }
    
    // Return the Nth fib
    return bottomUp[N]
}