509. Fibonacci Number

catepk·2021년 8월 28일
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509. Fibonacci Number

문제

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

풀이

-----recursion-----

class Solution:
    def fib(self, n: int) -> int:
        if  n <= 1:
            return n
        return self.fib(n - 1) + self.fib(n - 2)

-----memoization-----

class Solution:
    dp = collections.defaultdict(int)
    def fib(self, n: int) -> int:
        if n <= 1:
            return n
        if self.dp[n]:
            return self.dp[n]
        self.dp[n] = self.fib(n - 1) + self.fib(n - 2)
        return self.dp[n]

-----tabulation-----

class Solution:
    dp = collections.defaultdict(int)
    def fib(self, n: int) -> int:
        self.dp[0] = 0
        self.dp[1] = 1
        
        for i in range(2, n + 1):
            self.dp[i] = self.dp[i - 1] + self.dp[i - 2]
        return self.dp[n]

-----other way-----

class Solution:
    def fib(self, n: int) -> int:
        x, y = 0, 1
        for i in range(0, n):
            x, y = y, x + y
        return x
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