509_fibonacci-number.md

Problem

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: 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.

Question Source - Leetcode

Solution

Using Recursion

/**
 * @param {number} N
 * @return {number}
 */
var fib = function(N) {
  if (N == 0) return 0
  if (N == 1 || N == 2) return 1
  return fib(N - 1) + fib(N - 2)
}

• Time complexity: O(2^n)- since T(n) = T(n-1) + T(n-2)is an exponential time
• Space complexity: O(n) - space for recursive function call stack