斐波纳契数列

Fibonacci三种不同的方法

/*
	Fibonacci
	Version 1: Recursion
	Version 2: Dynamic Programming (Top-Down Memoization)
	Version 3: Dynamic Programming (Bottom-Up tabulation)
*/

#include <iostream>
using namespace std;

#define MAX 100
#define LABEL -1
int lookup_table[MAX];
int fib_recursion(int n);
int fib_memoization(int n);
void initialize();
int fib_tabulation(int n);

int main()
{
	int n = 40;

	cout<<"Recursion Method: "<<endl;
	cout<<fib_recursion(n)<<endl;

	cout<<"Dynamic Programming Top-Down (Memoization): "<<endl;
	initialize();
	cout<<fib_memoization(n)<<endl;

	cout<<"Dynamic Programming Bottom-Up (Tabulation): "<<endl;
	cout<<fib_tabulation(n)<<endl;

	system("pause");
	return 0;
}

int fib_recursion(int n)
{
	if (n <= 1)
	{
		return 1;
	}

	return (fib_recursion(n-1) + fib_recursion(n-2));
}

void initialize()
{
	for (int i=0; i<MAX; i++)
	{
		lookup_table[i] = LABEL;
	}
}

int fib_memoization(int n)
{
	if (lookup_table[n] == LABEL)
	{
		if (n <= 1)
		{
			lookup_table[n] = 1;
		}
		else
		{
			lookup_table[n] = fib_memoization(n-1) + fib_memoization(n-2);
		}
	}

	return lookup_table[n];
}

int fib_tabulation(int n)
{
	int *table = new int[n+1];

	table[0] = 1;
	table[1] = 1;

	for (int i=2; i<=n; i++)
	{
		table[i] = table[i-1] + table[i-2];
	}

	return table[n];
}