Fibonacci

• 真言

no games，no movies, but music. 

• 引言

no more words, just so these. I find a website from there.

• 介绍

Fibonacci was so wonderful, and made a great progress with development in algorithm.

There are three ways to get Fibonacci number.

first one

// function Fibonacci recursion
int Fibonacci_re(int n)
{
	if(n<0) return -1;
	else if(n==0) return 0;
	else if(n==1) return 1;
	return Fibonacci_re(n-1)+Fibonacci_re(n-2);
}

Running time is so bad. I have no words about it.

Running space O(n),store function

second two

// function Fibonacci array
int Fibonacci_ar(int n)
{
	if( n<0 ) return -1;
	else if( n==0 ) return 0;
	else if( n==1 ) return 1;
	int * data = new int[n+1];
	data[0] = 0;
	data[1] = 1;
	for(int i = 2;i <= n;i++)
	{
		data[i] = data[i-1]+data[i-2];
	}
	return data[n];
}

Running time is O(n).

Running space O(n),store number

third three

// function Fibonacci dp
int Fibonacci_dp(int n)
{
	if( n<0 ) return -1;
	else if( n==0 ) return 0;
	else if( n==1 ) return 1;
	queue<int> * Q = new queue<int>;
	Q -> push(0);
	Q -> push(1);
	int head;
	for(int i=2;i <= n;i++)
	{
		head=Q->front();
		Q->pop();
		Q->push(head+Q->front());
	}
	Q->pop();
	head = Q->front();
	delete Q;
	return head;
}

Running time is O(n).

Running space O(2),store Fibonacci(n-1) and Fibonacci(n-2)

• 实验

• 代码

test.cpp

#include <iostream>
#include <queue>
#include <Windows.h>
#include <ctime>
using namespace std ;

// function Fibonacci recursion
int Fibonacci_re(int n);
// function Fibonacci dp
int Fibonacci_dp(int n);
// function Fibonacci array
int Fibonacci_ar(int n);

// function main
int main( )
{
	DWORD s,e;
	int r=0;
	for(int i=0;i<40;i++)
	{
		s = GetTickCount();
		r = Fibonacci_re(i);
		e = GetTickCount();
		cout<<"Fibonacci n="<<i<<endl;
		cout<<r<<" re "<<" ms "<<e-s<<endl;
		s = GetTickCount();
		r = Fibonacci_dp(i);
		e = GetTickCount();
		cout<<r<<" dp "<<" ms "<<e-s<<endl;
		s = GetTickCount();
		r = Fibonacci_ar(i);
		e = GetTickCount();
		cout<<r<<" ar "<<" ms "<<e-s<<endl;
		cout<<endl;
	}

	system("pause");
	return 0;
}

// function Fibonacci recursion
int Fibonacci_re(int n)
{
	if(n<0) return -1;
	else if(n==0) return 0;
	else if(n==1) return 1;
	return Fibonacci_re(n-1)+Fibonacci_re(n-2);
}

// function Fibonacci dp
int Fibonacci_dp(int n)
{
	if( n<0 ) return -1;
	else if( n==0 ) return 0;
	else if( n==1 ) return 1;
	queue<int> * Q = new queue<int>;
	Q -> push(0);
	Q -> push(1);
	int head;
	for(int i=2;i <= n;i++)
	{
		head=Q->front();
		Q->pop();
		Q->push(head+Q->front());
	}
	Q->pop();
	head = Q->front();
	delete Q;
	return head;
}

// function Fibonacci array
int Fibonacci_ar(int n)
{
	if( n<0 ) return -1;
	else if( n==0 ) return 0;
	else if( n==1 ) return 1;
	int * data = new int[n+1];
	data[0] = 0;
	data[1] = 1;
	for(int i = 2;i <= n;i++)
	{
		data[i] = data[i-1]+data[i-2];
	}
	return data[n];
}

算法之数列 Fibonacci