509-fibonacci-number

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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

Solution(Python)

class Solution:
    def fib(self, n: int) -> int:
        return self.Iterativelesspace(n)

    # Time Complexity: O(2^n)
    # Space Complexity: O(n)
    def Recursive(self, n):
        if n <= 1:
            return n
        else:
            return self.Recursive(n - 1) + self.Recursive(n - 2)

    # Time Complexity: O(n)
    # Space Complexity: O(n)
    def Iterative(self, n):
        if n <= 1:
            return n
        fib = [0] * (n + 1)

        fib[1] = 1

        for i in range(2, n + 1):
            fib[i] = fib[i - 1] + fib[i - 2]

        return fib[n]

    # Time Complexity: O(n)
    # Space Complexity: O(1)
    def Iterativelesspace(self, n):
        if n <= 1:
            return n

        prev2, prev1 = 0, 1

        for i in range(2, n + 1):
            cur = prev2 + prev1
            prev2 = prev1
            prev1 = cur

        return cur