算法简要

高精度加法（A + B）：遍历 低位 -> 高位，push求和后该位的结果
高精度减法 (A - B) ：低位 -> 高位，大减小，在可借位之下，push每位之差
高精度乘法 (A × b) : 遍历 低位 -> 高位，求A每位和b的乘积，并只push每位的结果
高精度除法  (A ÷ b): 遍历A 高位 -> 低位 在有余数之下，push每次t（余数与该位的和）大于b的商

注意事项：
* 用string 读取高精度数
* 用vector数组逆序存入（加法、乘法为了方便进位，减法逆序方便运算，除法用不用都可以）
* 进行减法、乘法、除法要考虑前导0的情况

高精度加法代码：

#include <iostream>
#include <algorithm>
#include <vector>
#include <cstring>

using namespace std;

const int N = 100010;

vector <int> A, B;

vector <int> add(vector <int> a, vector <int> b)
{
    vector <int> c;
    if (a.size() < b.size()) return add(b, a);
    int t = 0;//进位
    for (int i = 0; i < a.size(); i ++)
    {
        if (i < b.size()) t += b[i];
        c.push_back((a[i] + t) % 10);
        t = (a[i] + t) / 10;
    }
    if (t > 0) c.push_back(t);
    // for (int i = c.size() - 1; i >= 0; i --) if(c[i] == 0) c.pop_back();
    return c;
}
string a, b;
int main()
{
    cin >> a >> b;
    for (int i = 0; i < a.size(); i ++) A.push_back(a[i] - '0');
    for (int i = 0; i < b.size(); i ++) B.push_back(b[i] - '0');
    reverse(A.begin(), A.end());
    reverse(B.begin(), B.end());
    auto C = add(A, B);

    for (int i = C.size() - 1; i >= 0; i --) cout << C[i];
    return 0;
}

高精度减法代码：

#include <iostream>
#include <vector>
#include <cstring>
#include <algorithm>

using namespace std;

//判断两个数大小
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> diff(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 = 0;
        else t = 1;
    }
    for (int i = C.size() - 1; i >= 0; i --) printf("%d", C[i]);
    while(C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}
int main()
{
    string a, b;
    cin >> a >> b;
    vector <int> c, d;
    for(int i = a.size() - 1; i >= 0; i --) c.push_back(a[i] - '0'); 
    for(int i = b.size() - 1; i >= 0; i --) d.push_back(b[i] - '0');

    if (cmp(c, d)) 
    {
        auto C = diff(c, d);
        // for (int i = C.size() - 1; i >= 0; i --) printf("%d", C[i]);
    }
    else
        {
            auto C = diff(d, c);
            cout << "-";
            for (int i = C.size() - 1; i >= 0; i --) printf("%d", C[i]);
        }
    return 0;
}

高精度乘法代码：

#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

vector <int> mul(vector <int> A, int b)
{
    vector <int> C;
    int t = 0, cnt = 0;
    for (int i = 0; i < A.size(); i ++)
    {
       t += A[i] * b;
       C.push_back(t % 10);
       t /= 10;
    }
    if (t) C.push_back(t);
    //去前导0
    while(C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}
int main()
{
    vector <int> A;
    int b;
    string 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;
}

高精度除法代码：

#include <iostream>
#include <cstring>
#include <vector>
#include <algorithm>

using namespace std;

vector <int> A;

int t;
vector <int> div(vector <int> A, int b)
{
    vector <int> C;
    for (int i = A.size() - 1; i >= 0; i --)
    {
        t = t * 10 + A[i];
        C.push_back(t / b);
        t %= b;
    }
    reverse(C.begin(), C.end());
    // for (int i = 0; i < C.size(); i ++) cout << C[i];
    while(C.size() > 1 && C.back() == 0) C.pop_back();
    // cout << endl;
    // for (int i = 0; i < C.size(); i ++) cout << C[i];
    return C;
}
int main()
{
    string a;
    int b;
    cin >> a >> b;
    for (int i = a.size() - 1; i >= 0; i --) A.push_back(a[i] - '0');
    auto C = div(A, b);
    for (int i = C.size() - 1; i >= 0; i --) cout << C[i];
    cout << endl << t;
    return 0;
}