高精度 加减乘除

• add：

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

using namespace std;

vector<int> a, b, c;//c = a + b

void add(){
    int t = 0;//代表进位
    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)c.push_back(t);
}

int main(){
    string s1,s2;    
    cin >> s1 >> s2;
    
    for(int i = s1.size()-1;i >= 0;--i)a.push_back(s1[i] - '0');
    for(int i = s2.size()-1;i >= 0;--i)b.push_back(s2[i] - '0');
    
    add();
    
    for(int i = c.size()-1;i >= 0;--i)cout << c[i];      
}

• mul：

#include <iostream>
#include <vector>

using namespace std;

//a*b = c
void mul(vector<int>& a,int b,vector<int>& c){
    int t = 0;
    for(int i = 0;i < a.size();++i){
        c.push_back((a[i]*b + t) % 10);
        t = (a[i]*b + t) / 10; 
    }    
    if(t)c.push_back(t);
}

int main(){
    string s;
    int b;
    cin >> s >> b;
    vector<int> a;
    for(int i = s.size()-1;i >= 0;--i)a.push_back(s[i] - '0');
    
    vector<int> c;
    mul(a,b,c);
    for(int i = c.size()-1;i >= 0;--i)cout << c[i];
    
    return 0;
}

• div：

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

using namespace std;

void div(vector<int>& a,int b,vector<int>& c,int& r){
    for(int i = 0;i < a.size();++i){
        r = r * 10 + a[i];
        c.push_back(r/b);
        r %= b;
    }
}

int main(){
    string s;
    cin >> s;
    vector<int> a;
    for(int i = 0;i < s.size();++i)a.push_back(s[i] - '0');
    int b;
    cin>>b;
    
    int r = 0;
    vector<int> c;
    div(a,b,c,r);
    bool flag = true;
    for(int i = 0;i < c.size();++i){
        if(c[i] != 0)flag = false;
        if(flag == false)cout << c[i];
    }
    cout << endl << r;
    return 0;
}

• sub：

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

using namespace std;

//a >= b return true else return false
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;
}

//a >= b
void sub(vector<int>& a, vector<int>& b, vector<int>& c){
    int t = 0;//代表借位
    for(int i = 0;i < a.size();++i){
        t = a[i] - t;
        if(i < b.size())
            t -= b[i];
        //这句包含了t > 0 and t < 0，结果都是t+10 % 10
        c.push_back((t+10)%10);
        if(t >= 0)t = 0;//代表不需要借位
        else t = 1;//借位
    }
    //去掉前面的0
    while(c.size() > 1 && c.back() == 0)c.pop_back();
}

int main(){
    string s1, s2;
    cin >> s1 >> s2;
    vector<int> a, b, c;
    
    for(int i = s1.size()-1;i >= 0;--i)a.push_back(s1[i]-'0');
    for(int i = s2.size()-1;i >= 0;--i)b.push_back(s2[i]-'0');
    
    if(cmp(a,b)){
        sub(a, b, c);
        for(int i = c.size()-1;i >= 0;--i)cout << c[i];
    }
    else{
        sub(b, a, c);
        cout << '-';
        for(int i = c.size()-1;i >= 0;--i)cout << c[i];
    } 
    
    return 0;
}