《剑指offer》第六十四题（求1+2+…+n）

// 面试题64：求1+2+…+n
// 题目：求1+2+…+n，要求不能使用乘除法、for、while、if、else、switch、case
// 等关键字及条件判断语句（A?B:C）。

#include <iostream>

// ====================方法一====================
//使用构造函数
class Temp
{
public:
    Temp() { ++N; Sum += N; }

    static void Reset() { N = 0; Sum = 0; }
    static unsigned int GetSum() { return Sum; }

private:
    static unsigned int N;
    static unsigned int Sum;//静态成员，所有实例共享
};

unsigned int Temp::N = 0;
unsigned int Temp::Sum = 0;

unsigned int Sum_Solution1(unsigned int n)
{
    Temp::Reset();

    Temp *a = new Temp[n];//建立n次，实现sum加和
    delete[]a;
    a = NULL;

    return Temp::GetSum();
}

// ====================方法二====================
//使用虚函数
class A;
A* Array[2];

class A
{
public:
    virtual unsigned int Sum(unsigned int n)
    {
        return 0;
    }
};

class B : public A
{
public:
    virtual unsigned int Sum(unsigned int n)
    {
        return Array[!!n]->Sum(n - 1) + n;
    }
};

int Sum_Solution2(int n)
{
    A a;
    B b;
    Array[0] = &a;
    Array[1] = &b;

    int value = Array[1]->Sum(n);//当n大于0时，总是执行B类中的sum，直到n=0，!!n=0，然后变成了Array[0]->Sum(n)，即A类，注意Array设成全局变量

    return value;
}

// ====================方法三====================
//使用函数指针
typedef unsigned int(*fun)(unsigned int);

unsigned int Solution3_Teminator(unsigned int n)
{
    return 0;
}

unsigned int Sum_Solution3(unsigned int n)
{
    static fun f[2] = { Solution3_Teminator, Sum_Solution3 };//静态成员，第一次调用时候建立
    return n + f[!!n](n - 1);
}

// ====================方法四====================
//使用模版类型
template <unsigned int n> struct Sum_Solution4
{
    enum Value { N = Sum_Solution4<n - 1>::N + n };//Sum_Solution4<number>::N就是我们要的值
};

template <> struct Sum_Solution4<1>
{
    enum Value { N = 1 };
};

template <> struct Sum_Solution4<0>
{
    enum Value { N = 0 };
};

// ====================测试代码====================
void Test(int n, int expected)
{
    printf("Test for %d begins:
", n);

    if (Sum_Solution1(n) == expected)
        printf("Solution1 passed.
");
    else
        printf("Solution1 failed.
");

    if (Sum_Solution2(n) == expected)
        printf("Solution2 passed.
");
    else
        printf("Solution2 failed.
");

    if (Sum_Solution3(n) == expected)
        printf("Solution3 passed.
");
    else
        printf("Solution3 failed.
");
}

void Test1()
{
    const unsigned int number = 1;
    int expected = 1;
    Test(number, expected);
    if (Sum_Solution4<number>::N == expected)
        printf("Solution4 passed.
");
    else
        printf("Solution4 failed.
");
}

void Test2()
{
    const unsigned int number = 5;
    int expected = 15;
    Test(number, expected);
    if (Sum_Solution4<number>::N == expected)
        printf("Solution4 passed.
");
    else
        printf("Solution4 failed.
");
}

void Test3()
{
    const unsigned int number = 10;
    int expected = 55;
    Test(number, expected);
    if (Sum_Solution4<number>::N == expected)
        printf("Solution4 passed.
");
    else
        printf("Solution4 failed.
");
}

void Test4()
{
    const unsigned int number = 0;
    int expected = 0;
    Test(number, expected);
    if (Sum_Solution4<number>::N == expected)
        printf("Solution4 passed.
");
    else
        printf("Solution4 failed.
");
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    system("pause");
    return 0;
}