005高精度加减乘除

1. 加法

#include <iostream>
#include <vector>
using namespace std;
const int N = 1e6 + 10;
vector<int> add(vector<int> A, vector<int> B){
    vector<int> C;
    int t = 0;
    for(int i = 0; i < A.size() || i < B.size(); i++){
        if(i < A.size()) t+=A[i];
        if(i < B.size()) t+=B[i];
        C.push_back( t % 10);
        t /= 10;
    }
    if(t == 1) 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 --) printf("%d", C[i]);
    return 0;
}

2. 减法

#include <iostream>
#include <vector>

using namespace std;


int cmp(vector<int> &A, vector<int> &B){
    if(A.size() != B.size()) return A.size() > B.size(); //如果A比B大，则返回1
    //A,B 相同位数的情况，逐一比较，从最高位开始，即vector的末尾开始比较（因为是尾插法，vector中为逆序）
    for(int i = A.size() - 1; i >= 0; i--)
        if(A[i] != B[i]) return A[i] > B[i]; //如果A大于B，则返回1
    return 1; //A≥B时，A-B
}
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];
        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;
    cin >> a >> b;
    for(int i = a.size() - 1;i >= 0; i --) A.push_back(a[i] - '0');//-‘0’转换类型，char变成数字int
    for(int i = b.size() - 1; i >= 0; i -- ) B.push_back(b[i] - '0');
    if(cmp(A,B)){
        //A大于等于B
        auto C = sub(A,B);
        for(int i = C.size() - 1; i >= 0; i--) cout << C[i];
    }else{
        //C== -sub(B,A)
        auto 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++ ){ // 如果有进位，还需要加上进位
        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');
    vector<int> C = mul(A, b);
    for(int i =C.size() - 1; i >= 0; i--) cout << C[i];
    return 0; 
}

4. 除法

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;


vector<int> div(vector<int> &A, int b, int &r){
    vector<int> C; //商
    for(int i = A.size() - 1; i >= 0; i -- ){
        r = r * 10 + A[i];
        C.push_back(r / b);
        r %= b;
    }
    //现在C表示的商是正序，为了方便运算，进行逆置
    reverse(C.begin(), C.end());
    while(C.size() > 1 && C.back() == 0 ) C.pop_back();//末尾是0，则删去

    return C;
}

int main(){
    string a;
    int b;

    cin >> a >> b;

    vector<int> A; 
    for (int i = a.size() - 1; i >= 0; i -- ) A.push_back(a[i] - '0'); //a=123 A=321

    int r;
    auto C = div(A, b, r); //r为余数，b除数， A被除数存放在数组中

    for (int i = C.size() - 1; i >= 0; i -- ) printf("%d", C[i]);
    cout << endl << r << endl;

    return 0;


}