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#include <iostream>
#include <vector>
#include <unordered_map>

int fib(int n)
{
	if (n <= 1)	
		return n;
	
	return fib(n - 1) + fib(n - 2);
}

int fib_topDown(int n, std::unordered_map<int, int>& memo)
{
	if (n <= 1) 
		return 1;
	
	auto result = memo.find(n);
	if (result != memo.end()) 
		return result->second;
	
	return memo[n] = fib_topDown(n - 1, memo) + fib_topDown(n - 2, memo);
}

int fib_buttonUp(int n)
{
	std::vector<int> results(n + 1);
	results[0] = 0;
	results[1] = 1;
	for (int i = 2; i <= n; i++) 
		results[i] = results[i - 1] + results[i - 2];
	
	return results.back();
}

int main(int argc, char *argv[]) {

	std::cout << fib(40) << std::endl;

	std::unordered_map<int, int> memo;
	memo[1] = 0;
	memo[2] = 1;
	std::cout << fib_topDown(40, memo) << std::endl;

	std::cout << fib_buttonUp(40) << std::endl;

	getchar();
	return 0;
}