16.O(logn)求Fibonacci数列[Fibonacci]

【题目】

log(n)时间Fib(n),本质log(n)求a^n。

【代码】

C++ Code

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#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)
)
    {
        return n;
    }
    else
    {
        );
    }
}

// use table to reuse value : forward

};
unsigned int tfib_forward(unsigned int n)
{
    // o(n)
;
    f[;
    ; i <= n; ++i)
    {
        f[i] = f[i - ];
    }
    return f[n];
}

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

// use temp value instead of table
unsigned int fib(unsigned int n)
{
    // o(n)
)
    {
        return n;
    }
    else
    {
        , c;
        ; 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 -  >::Val
    };
};

template<>
>
{
    enum
    {
        Val =
    };
};

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

template<int N>
class FibC
{
public:
>::val;
};

template<>
>
{
public:
;
};

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

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

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

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

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

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

system("pause");
;
}

【参考】

http://zhedahht.blog.163.com/blog/static/25411174200722991933440/

http://blog.****.net/foolishwolf_x/article/details/8774874

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16.O(logn)求Fibonacci数列[Fibonacci]

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