面试题46：求1+2+3+4+……n

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题目：求1+2+3+……+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）。

    解法一：利用构造函数求解，将类的数据成员声明为静态类型，外部定义，求n个数的和，我们可以创建n个实例，构造函数会被调用n次，代码如下：

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;};unsigned int Temp::N;unsigned int Temp::Sum;unsigned int Sum_Solution(unsigned int n){Temp::Reset();Temp* a = new Temp[n];delete[] a;a = NULL;return Temp::GetSum();}

解法二：利用虚函数求解（递归）

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_Soulation2(int n){A a;B b;Array[0] = &a;Array[1] = &b;int value = Array[1]->Sum(n);return value;}

解法三：利用函数指针求解：在纯C的编程环境下我们不能使用虚函数

typedef unsigned int(*fun)(unsigned int n);unsigned int Solution_3(unsigned int n){return 0;}unsigned int Sum__(unsigned int n){static fun f[2] = { Solution_3, Sum__ };return n + f[!!n](n - 1);}

解法四：利用模板函数求解

template<unsigned int n> struct Sum_Solution4{enum Value{N=Sum_Solution4<n-1>::N+n};};template<> struct Sum_Solution4<1>{enum Value{ N = 1 };};Sum_Solution4<100>::N就是1+2+3+4......n的结果