仅总汇，没注释
1，加法

#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
vector<int>add(vector<int>&A,vector<int>&B)
{
    int t=0;//表示进位
    vector<int>C;
    if(A.size()<B.size())return add(B,A);
    for(int i=0;i<A.size();i++)
    {
        t+=A[i];
        if(i<B.size())t+=B[i];
        C.push_back(t%10);
        t/=10;
    }
    if(t>0)C.push_back(1);
    return C;
}
int main()
{
    string a,b;
    vector<int>A,B;
    cin>>a>>b;
    for(int i=a.size()-1;i>=0;i--)A.push_back(a[i]-'0');
    for(int i=b.size()-1;i>=0;i--)B.push_back(b[i]-'0');
    auto C=add(A,B);
    for(int i=C.size()-1;i>=0;i--)cout<<C[i];


    return 0;
}

2、减法

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
bool cmp(vector<int>&A,vector<int>&B)
{
    if(A.size()!=B.size())return A.size()>B.size();
    for(int i=A.size()-1;i>=0;i--)
    {
        if(A[i]!=B[i])return A[i]>B[i];
    }
    return true;
}
vector<int>sub(vector<int>&A,vector<int>&B)
{
    vector<int>C;
    int t=0;
    for(int i=0;i<A.size();i++)
    {
        t=A[i]-t;
        if(i<B.size())t-=B[i];
        C.push_back((t+10)%10);
        if(t<0)t=1;
        else t=0;
    }
    while(C.size()>1&&C.back()==0)C.pop_back();
    return C;
}
int main()
{
    string a,b;
    vector<int>A,B,C;
    cin>>a>>b;
    for(int i=a.size()-1;i>=0;i--)A.push_back(a[i]-'0');
    for(int i=b.size()-1;i>=0;i--)B.push_back(b[i]-'0');
    if(cmp(A,B))
    {
        C=sub(A,B);
    }
    else C=sub(B,A),cout<<"-";
    for(int i=C.size()-1;i>=0;i--)cout<<C[i];



    return 0;
}

3,乘法

#include<iostream>
#include<vector>
using namespace std;
vector<int>mul(vector<int>&A,int b)
{
    vector<int>C;
    int t=0;
    for(int i=0;i<A.size()||t;i++)
    {
        if(i<A.size())t+=A[i]*b;
        C.push_back(t%10);
        t/=10;
    }
    while(C.size()>1&&C.back()==0)C.pop_back();
    return C;
}
int main()
{
    string a;
    int b;
    vector<int>A;
    cin>>a>>b;
    for(int i=a.size()-1;i>=0;i--)A.push_back(a[i]-'0');
    auto C=mul(A,b);
    for(int i=C.size()-1;i>=0;i--)cout<<C[i];

    return 0;
}

4，减法

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
vector<int>div(vector<int>&A,int b,int &r)
{
    vector<int>C;
    r=0;
    for(int i=A.size()-1;i>=0;i--)
    {
        r=r*10+A[i];
        C.push_back(r/b);
        r%=b;
    }
    reverse(C.begin(),C.end());
    while(C.size()>1&&C.back()==0)C.pop_back();
    return C;
}
int main()
{
    string a;
    int b,r=0;
    vector<int>A;
    cin>>a>>b;
    for(int i=a.size()-1;i>=0;i--)A.push_back(a[i]-'0');
    auto C=div(A,b,r);
    for(int i=C.size()-1;i>=0;i--)cout<<C[i];
    cout<<endl<<r<<endl;


    return 0;
}