DP

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


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

dynamic programming

def fib(self, N: int) -> int:        
	dp = [0, 1]+[0]*(N-1)
	for i in range(2, N+1):
		dp[i] = dp[i-1]+dp[i-2]
	return dp[N]

O(1) space

def fib(self, N: int) -> int:
	if N < 2: return N
	a, b = 0, 1
	for _ in range(N-1):
		c = a+b
		a, b = b, c
	return c