A+B（18:40 - 27.20）

使用vector

#include <iostream>
#include <vector>
using namespace std;
vector<int> add(vector<int> &A, vector<int> &B){
    vector<int> C;
    for(int i = 0, t = 0; i < A.size() || i < B.size() || t != 0; i++){
        if(i < A.size()) t += A[i];
        if(i < B.size()) t += B[i];
        C.push_back(t % 10);
        t /= 10;
    }
    return C;
}
int main(){
    string a, b; cin >> a >> b;
    vector<int> 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--) printf("%d", C[i]);
    return 0;
}

使用string

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
using namespace std;
int main(){
    string a, b; cin >> a >> b;
    string res;
    reverse(a.begin(), a.end());
    reverse(b.begin(), b.end());
    for(int i = 0, t = 0; i < a.size() || i < b.size() || t != 0; i++){
        if(i < a.size()) t += a[i] - '0';
        if(i < b.size()) t += b[i] - '0';
        res += to_string(t % 10);
        t /= 10;
    }
    reverse(res.begin(), res.end());
    cout <<res;
    return 0;
}

A-B（32:00 - 45:10）

使用vector

#include <iostream>
#include <vector>

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;
    for(int i = 0, t = 0; i < A.size(); i++){
        t = A[i] - t;
        if(i < B.size()) t -= B[i];
        //一个表达式把A[i] >= B[i] 或 A[i] < B[i]的情况都考虑了
        C.push_back((t + 10) % 10);
        if(t < 0) t = 1;
        else t = 0;
    }
    //去掉前面的0；
    //比如 999 - 997 按照这个算法的到的是 C【3，0，0】
    while(C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}
int main(){
    string a,b; cin >> a >> b;
    vector<int> 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');

    //判断A是否大于等于B
    if(cmp(A, B)){
        auto C = sub(A, B);
        for(int i = C.size() - 1; i >= 0; i--) printf("%d", C[i]);
    }else{
        auto C = sub(B, A);
        printf("-");
        for(int i = C.size() - 1; i >= 0; i--) printf("%d", C[i]);
    }

    return 0;
}

使用string

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

using namespace std;
bool cmp(string &A, string &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] - '0' > B[i] - '0';
    }
    return true;
}
string sub(string &A, string &B){
    string C;
    for(int i = 0, t = 0; i < A.size(); i++){
        t = (A[i] - '0') - t;
        if(i < B.size()) t -= (B[i] - '0');
        //一个表达式把A[i] >= B[i] 或 A[i] < B[i]的情况都考虑了
        C += (t + 10) % 10 + '0';
        if(t < 0) t = 1;
        else t = 0;
    }
    //去掉前面的0；
    //比如 999 - 997 按照这个算法的到的是 C【3，0，0】
    int k = C.size();
    while(k > 1 && C[k - 1] == '0') k--;
    return C.substr(0, k);
}
int main(){
    string a,b; cin >> a >> b;
    reverse(a.begin(), a.end());
    reverse(b.begin(), b.end());
    //判断A是否大于等于B
    if(cmp(a, b)){
        auto c = sub(a, b);
        reverse(c.begin(), c.end());
        cout << c;
    }else{
        auto c = sub(b, a);
        reverse(c.begin(), c.end());
        cout <<"-" << c;
    }

    return 0;
}

A * b（48:30 - 58:00）

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

using namespace std;
int main(){
    string a; int b; cin >>a >>b;
    vector<int> A;
    vector<int> C;
    for(int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    string res;
    for(int i = 0, t = 0; i < A.size() || t != 0; i++){
        t += A[i] * b;
        C.push_back(t%10);
        t /= 10;
    }
    //为什么要去前导0呢，12345 * 0 = 00000
    while(C.size() > 1 && C.back() == 0) C.pop_back();
    for(int i = C.size() - 1; i >= 0; i--) cout<< C[i];
    return 0;
}

A * B

class Solution {
public:
    string multiply(string num1, string num2) {
        vector<int> A, B;
        int n = num1.size(), m = num2.size();
        vector<int> C(m + n);
        for(int i = n - 1; i >= 0; i--) A.push_back(num1[i] - '0');
        for(int i = m - 1; i >= 0; i--) B.push_back(num2[i] - '0');

        for(int i = 0; i < n; i++){
            for(int j = 0; j < m; j++){
                C[i + j] += A[i] * B[j];
            }
        }
        int k = C.size();
        for(int i = 0, t = 0; i < k; i++){
            t += C[i];
            C[i] = t % 10;
            t /= 10; 
        }
        // k为长度，保证长度大于1，k = 2 while循环结束得到的也是长度
        while(k > 1 && C[k-1] == 0) k--;
        string res;
        //取数的时候，要从长度-1的地方开始取
        for(int i = k - 1; i >= 0; i--){
            res += C[i] + '0';
        }
        // k--;
        // while(k >= 0) res += C[k--] + '0';
        return res;
    }
};

A / b（1:01:10 - 1:11:30）

#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;
    vector<int> A;

    int B;
    cin >> a >> B;
    for (int i = a.size() - 1; i >= 0; i -- ) A.push_back(a[i] - '0');

    int r;
    auto C = div(A, B, r);

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

    cout << endl << r << endl;

    return 0;
}