16.O(logn)求Fibonacci数列

#include "stdafx.h"
#include <iostream>
using namespace std;

/*
f(0) = 0.
f(1) = 1.
f(N) = f(N-1) + f(N-2)_ (N>=2)

see http://blog.linjian.org/articles/fibonacci-essay/ for more detail
*/


// recursive
unsigned int rfib(unsigned int n)
{// o(2^n)
    if (n<2)
    {
        return n;
    }
    else
    {
        return rfib(n-1)+rfib(n-2);
    }
}

// use table to reuse value : forward
#define MAX 1000
unsigned int f[MAX]={0};
unsigned int tfib_forward(unsigned int n)
{// o(n)
    f[0] = 0; 
    f[1] = 1;
    for (unsigned int i=2;i<=n;++i)
    {
        f[i] = f[i-1] + f[i-2];
    }
    return f[n];
}

// use table to reuse value : backward
unsigned int tfib_backward(unsigned int n)
{
    if (n<2)
    {
        f[n] = n;
        return f[n];
    }
    else
    {
        if(f[n]==0)
            f[n] = tfib_backward(n-1) + tfib_backward(n-2);
        return f[n];
    }
}

// use temp value instead of table
unsigned int fib(unsigned int n)
{// o(n)
    if (n<2)
    {
        return n;
    }
    else
    {
        unsigned int a=0,b=1,c;
        for (unsigned int i=2;i<=n;++i)
        {
            c = a + b;
            a = b;
            b = c;
        }
        return c;
    }
}

// use template meta programming #1 struct-enum
// enum has value range
#define FIBE(N) FibE<N>::Val

template<int N>
struct FibE
{
    enum
    {
        Val = FibE<N-1>::Val + FibE<N-2>::Val
    };
};

template<>
struct FibE<0>
{
    enum
    {
        Val = 0
    };
};

template<>
struct FibE<1>
{
    enum
    {
        Val = 1
    };
};

// use template meta programming # class-static const
#define FIBC(N) FibC<N>::val

template<int N>
class FibC
{
public:
    static const unsigned int val = FibC<N-1>::val + FibC<N-2>::val;
};

template<>
class FibC<0>
{
public:
    static const unsigned int val = 0;
};

template<>
class FibC<1>
{
public:
    static const unsigned int val = 1;
};

// use calss-function
class Fib
{
public:
    Fib() : a(0), b(1), n(0)
    {
    }
    unsigned int operator()()
    {
        if (n <= 1) {
            n++;
            return n - 1;
        } else {
            int c;
            c = a + b;
            a = b;
            b = c;
            return c;
        }
    }
private:
    int a, b, n;
};


// test
void test_tfib_forward()
{
    for (int i=0;i<MAX;++i)
    {
        cout<< tfib_forward(i)<<" ";
    }
}

void test_metaFibE()
{
    cout<<FIBE(50)<<endl;
}

void test_metaFibC()
{
    cout<<FIBC(50)<<endl;
}

void test_cfib()
{
    int i=10;
    Fib fib;
    do {
        cout << fib() << endl;
    } while (i--);
}

int main()
{
    //test_tfib_forward();
    test_metaFibE();
    test_metaFibC();
    test_cfib();

    system("pause");
    return 0;
}