c++实现多项式乘法

题目大概要求如下：

自己写的出现了比较多的问题，数组大小没有定义，局限性很大，多项式个数多了会出现问题，#include
using namespace std;
int main()
{
int i, j, m, n,p[m],q[n],s[m+n]; //数组个数要搞清！易错点在这！
cout<<"输入第一行的个数："; cin>>m;
cout<<"输入系数: ";
for (i = m-1; i >=0; i--) //为第一列系数
{
cin>>p[i];
}
cout<<"P(X)=";
for (i=m-1; i>=0; i--)
{
if(i==0) {cout<<p[i];break;}
cout<<p[i]<<"×X^"<<i<<"+";
}
cout<<"\n\n";
cout<<"输入第二行的个数：";cin>>n;
cout<<"输入系数: ";
for (i = n-1; i >=0; i--) //第二列系数
{
cin>>q[i];
}
cout<<"Q(X)=";
for (i=n-1; i>=0; i--)
{
if(i==0) {cout<<q[i];break;}
cout<<q[i]<<"×X^"<<i<<"+";
}
cout<<"\n\n";
for (i = m + n-2; i >=0; i--) //都是零
{s[i] = 0;}

for (i = m-1; i>=0; i--)
{
    for (j = n-1; j >=0; j--)
        {
            s[i + j] += p[i] * q[j];
        } 
} 
cout<<"它们乘积多项式：S(X)=";
for (i=m+n-2; i>=0; i--)    //输出所搞的 
{
     if(i==0){cout<<s[i];break;} 
      cout<<s[i]<<"×X^"<<i<<"+";
   
   }

}
希望有人可以帮忙解决题目问题，最好要有注释在函数后面。谢谢

给你重新写一个，可以把

#include <iostream>
using namespace std;
void mulit_poly(int p[], int n1, int q[], int n2, int s[]);
const int MAX_POLY = 20;
int main() {
    int p[MAX_POLY], q[MAX_POLY], s[MAX_POLY * 2];
    int n1, n2;
    cin >> n1 >> n2;
    for (int i = n1 - 1; i >= 0; i--) {
        cin >> p[i];
    }
    for (int i = n2 - 1; i >= 0; i--) {
        cin >> q[i];
    }
    mulit_poly(p, n1, q, n2, s);
    bool first = true;
    for (int i = n1 + n2 - 1; i >= 0; i--) {
        if (s[i] != 0) {
            if (!first)
                cout << "+";
            cout << s[i];
            if (i != 0)
                cout << "x^" << i;
            first = false;
        }
    }
    return 0;
}
void mulit_poly(int p[], int n1, int q[], int n2, int s[]) {
    for (int i = 0; i < n1 + n2; i++) {
        s[i] = 0;
    }
    for (int i = 0; i < n1; i++) {
        for (int j = 0; j < n2; j++) {
            s[i + j] += p[i] * q[j];
        }
    }
}