Fibonacci Number
The Fibonacci numbers, commonly denoted as 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, and F(n) = F(n - 1) + F(n - 2) for n > 1. Given n, calculate F(n).
Constraints:
- 0 <= n <= 30
Examples:
Input: 2
Output: 1
Explanation: Because F(2) = F(1) + F(0) = 1 + 0 = 1
Solutions
Dynamic Programming
Time: O(n)Space: O(n)
We use dynamic programming to store the Fibonacci numbers as we calculate them. We start with the base cases F(0) = 0 and F(1) = 1, and then calculate each subsequent Fibonacci number as the sum of the two preceding ones.
def fib(n):
dp = [0, 1]; for i in range(2, n + 1):
dp.append(dp[i - 1] + dp[i - 2]); return dp[n]Follow-up:
Can you optimize the space complexity to O(1)?
