算法之数列 Fibonacci

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 recursionint 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 arrayint 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 dpint 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 recursionint Fibonacci_re(int n);// function Fibonacci dpint Fibonacci_dp(int n);// function Fibonacci arrayint Fibonacci_ar(int n);// function mainint 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 recursionint 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 dpint 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 arrayint 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];}