Fibonacci Number

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).

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.

Constraints:

• 0 <= n <= 30

Code

Time Complexity: $O(n)$, Space Complexity: $O(1)$

差別在於使用 while loop or for loop，以及是 return b 還是 c。

class Solution {
public:
    int fib(int n) {
        if (n <= 1) return n;
        int a = 0;
        int b = 1;
        int c = a + b;
        while(n-- >= 2){
            c = a + b;
            a = b;
            b = c;
        }
        return b;
    }
};

class Solution {
public:
    int fib(int n) {
        if (n <= 1) return n;
        int a = 0;
        int b = 1;
        int c;
        for(int i = 2; i <= n; i++){
            c = a + b;
            a = b;
            b = c;
        }
        return c;
    }
};

Link

• 509. Fibonacci Number