这个C++问题可解么？
定义：
向量相乘 à 对应位置的数相乘。(v1, v2)*(v3, v4) = (v1*v3, v2*v4)
向量与数相乘 à 向量每一个位置的数与该数相乘。(v1, v2)*a = (v1*a, v2*a)
数与向量相乘 à 数与向量中各维的平均数相乘。a*(v1,v2) = (a*v1, a*v2)
数与数相乘 à 两数的普通乘法。
请提供Math, Vector, Number的类声明和定义，使得任意向量或数可以相乘。测试函数如下，直接使用请勿修改。
注：假设Vector为10维向量。用随机数生成所需要的数（包括Vector的每一维或Number的值）。
void main(){
srand((unsigned)time(NULL));
Vector a,b;
Number c,d;
Math* p[2]={&a, &c};

for (int i = 0; i < 2; i++)
{
//与向量相乘
cout < < "乘数: " < < p[i]-> toString() < < endl;
cout < < "被乘数: " < < b.toString() < < endl;
p[i]-> multiply(&b);//p[i]=p[i]*b;
cout < < "积: " < < p[i]-> toString() < < endl;

cout < < "--------------- " < < endl;

//与实数相乘
cout < < "乘数: " < < p[i]-> toString() < < endl;
cout < < "被乘数: " < < d.toString() < < endl;
p[i]-> multiply(&d);//p[i]=p[i]*d;
cout < < "积: " < < p[i]-> toString() < < endl;

cout < < "--------------- " < < endl;
}
}


[解决办法]
#include <iostream>
#include <string>
#include <strstream>
#include <ctime>
#include <vector>

using namespace std;


class Math
{
public:
Math(){};
~Math(){};

virtual string toString(){ return " "; }
virtual void multiply(Math* other) {}
virtual double mean() {return 0;}

virtual void GetData(vector <double> & _data){}
virtual void SetData(const vector <double> & _data) {}
};

class Number:public Math
{
public:
Number() { data = rand();}
~Number(){}

virtual string toString()
{
strstream stream;
stream < <data;
string str;
stream> > str;
return str;
}

virtual void multiply(Math* other)
{
data *= other-> mean();
}

virtual double mean() { return data;}

double GetData() { return data;}
void SetData( double _data) { data = _data;}

virtual void GetData(vector <double> & _data)
{ _data.push_back(data);}

virtual void SetData(const vector <double> & _data)
{if (_data.size()> 0) data = _data[0];}

private:
double data;
};


class Vector:public Math
{
public:
Vector()
{ for (int i=0; i <10; ++i) data[i] = rand();}
~Vector(){}

virtual string toString()
{
strstream stream;
stream < < "( ";
for (int i=0; i <9; ++i) {
stream < <data[i] < < ", ";
}

stream < <data[9] < < ") ";
string str;
stream> > str;
return str;
}

virtual void multiply(Math* other)
{
vector <double> vother;
other-> GetData(vother);
if (vother.size()==1) {
for (int i=0; i <10; ++i) data[i] *= vother[0];
}
else {
for (int i=0; i <10; ++i) data[i] *= vother[i];
}

}

virtual double mean()
{
double sum = 0;
for (int i=0; i <10; ++i) sum += data[i];
return sum /10;
}


virtual void GetData(vector <double> & _data)
{
for (int i=0; i <10; ++i) _data.push_back(data[i]);
}

virtual void SetData(const vector <double> & _data)
{
int _dataSize = _data.size();
for (int i=0; i < min(10, _dataSize); ++i) data[i] = _data[i];
}

private:

double data[10];
};


int main()
{
srand((unsigned)time(NULL));
Vector a,b;
Number c,d;
Math* p[2]={&a, &c};

for (int i = 0; i < 2; i++)
{
//与向量相乘
cout < < "乘数: " < < p[i]-> toString() < < endl;
cout < < "被乘数: " < < b.toString() < < endl;
p[i]-> multiply(&b);//p[i]=p[i]*b;
cout < < "积: " < < p[i]-> toString() < < endl;

cout < < "--------------- " < < endl;

//与实数相乘
cout < < "乘数: " < < p[i]-> toString() < < endl;
cout < < "被乘数: " < < d.toString() < < endl;
p[i]-> multiply(&d);//p[i]=p[i]*d;
cout < < "积: " < < p[i]-> toString() < < endl;

cout < < "--------------- " < < endl;
}

system( "pause ");
}