• Problem
  • Example 1
  • Example 2
  • Example 3
  • Constraints
• Approach 1: Recursive
  • Algorithm
  • Implementation
  • Complexity Analysis

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).

• Input: n = 2
• Output: 1
• Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.

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

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

• 0 <= n <= 30

對於任意大於一的正整數而言, F(n) = F(n-1) + F(n-2), 可直接透過 recursive 的方式求解

func fibRecursive(n int) int {
	if n == 0 {
		return 0
	}
	if n == 1 {
		return 1
	}
	return fibRecursive(n-1) + fibRecursive(n-2)
}

• Time complexity: $O(2^n)$

  • Recursion tree which will have depth n and intuitively figure out that this function is asymptotically $O(2^n)$
  • Runtime: 13 ms, faster than 21.35% of Go online submissions for Fibonacci Number.

• Space complexity: O(n)

  • Recursion tree which will have depth n, for function call stack.
  • Memory Usage: 6.2 MB, less than 34.38% of Go online submissions for N-ary Tree Preorder Traversal.