Problem 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,

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F(0) = 0, F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n > 1.

Given n, calculate F(n).

Example 1:

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

Example 2:

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

Solution:

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class Solution:
    
    def fib(self, n: int) -> int:
        self.dic = {}
        
        def dfs(n):
            if n == 0:
                return 0
            if n == 1:
                return 1
            if n-1 not in self.dic:
                self.dic[n-1] = dfs(n-1)
            if n-2 not in self.dic:
                self.dic[n-2] = dfs(n-2)
            
            return self.dic[n-1] + self.dic[n-2]
        return dfs(n)

time complexity: $O()$
space complexity: $O()$
reference:
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