509. Fibonacci_Number_dp_solution.py

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.

############################## Memoization Solution #############################

class Solution:
    def fib(self, n: int) -> int:
        def memo(n, dp):
            if n <= 1:
                return n
            if n not in dp:
                dp[n] = memo(n - 1, dp) + memo(n - 2, dp)
            return dp[n]

        dp = {}
        return memo(n, dp)


############################## Tabulation Solution ##########################

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

        return dp[n]