509. Fibonacci Number

1. Description

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).

2. Example

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.

3. Constraints

• 0 <= n <= 30

4. Solutions

My Accepted Solution

Time complexity: O(n)
Space complexity: O(1)

// DP
class Solution {
public:
    int fib(int n) {
        array<int, 2> fibs = {0, 1};
        for (int i = 2; i <= n; ++i) {
            int newFib = fibs[0] + fibs[1];

            fibs[0] = fibs[1];
            fibs[1] = newFib;
        }

        return n == 0 ? fibs[0] : fibs[1];
    }
};