509. 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 0and 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: 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.

Example 2:

Input: 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.

Example 3:

Input: 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.

Note:

0 ≤ N ≤ 30.

M1: recursion, time = O(2^n), space = O(n)

M2: dp, time = O(n), space = O(1)

class Solution {
    public int fib(int N) {
        if(N <= 1) {
            return N;
        }
        int f0 = 0, f1 = 1, f2 = f0 + f1;
        for(int i = 1; i < N; i++) {
            f2 = f0 + f1;
            f0 = f1;
            f1 = f2;
        }
        return f2;
    }
}