509. 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).

Constraints

• 0 <= n <= 30

Approach

Links

• GeeksforGeeks

• Leetcode

• ProgramCreek

• YouTube

Examples

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.

Solutions

Solution 1

/**
 * Time complexity : O(2^N), The amount of operations needed, for each level
 *     of recursion, grows exponentially as the depth approaches N.
 * Space complexity : O(N), We need space proportionate to N to account for 
 *    the max size of the stack, in memory.
 */

public class Solution {
    public int fib(int N) {
        if (N <= 1) {
            return N;
        }
        return fib(N-1) + fib(N-2);
    }
}

Solution 2

/**
 * Time complexity : O(N)
 * Space complexity : O(1)
 */

class Solution {
    public int fib(int n) {
        if(n < 2) {
            return n;
        }
        int prev = 0;
        int curr = 1;
        for(int i = 2; i <= n; i++) {
            int temp = prev + curr;
            prev = curr;
            curr = temp;
        }
        return curr;
    }
}

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