高精度算法

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

vector<int> add(vector<int> a,vector<int> b){
    vector<int> res;
    int i=0,j=0;
    int t=0;
    while(i<a.size()&&j<b.size()){
        t+=(a[i]+b[i]);
        res.push_back(t%10);
        t/=10;
        i++;
        j++;
    }
    while(i<a.size()){
        t+=a[i];
        res.push_back(t%10);
        t/=10;
        i++;
    }
    while(j<b.size()){
        t+=b[i];
        res.push_back(t%10);
        t/=10;
        j++;
    }
    while(t){
        res.push_back(t%10);
        t/=10;
    }
    reverse(res.begin(),res.end());
    return res;
}

int main(){
    string a;
    string 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 j=b.size()-1;j>=0;j--){
        B.push_back(b[j]-‘0‘);
    }
    vector<int> c=add(A,B);
    for(int i=0;i<c.size();i++){
        cout<<c[i];
    }
    cout<<endl;
}

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

vector<int> sub(vector<int> a,vector<int> b){
    //a>b那么a一定不会小于b的位数
    vector<int> c;
    int t=0;
    int i=0;
    for(;i<b.size();i++){
        t=a[i]-t;
        t-=b[i];
        c.push_back((t+10)%10);
        if(t<0)t=1;
        else t=0;
    }
    while(i<a.size()){
        t=a[i]-t;
        c.push_back((t+10)%10);
        if(t<0)t=1;
        else t=0;
        i++;
    }
    int n=c.size()-1;
    for(int j=n;j>=0;j--){
        if(c[j]>0)break;
        c.pop_back();
    }
    reverse(c.begin(),c.end());
    return c;
}

bool cmp(vector<int> a,vector<int> b){
    if(a.size()>b.size())return true;
    if(b.size()>a.size())return false;
    for(int i=a.size()-1;i>=0;i--){
        if(a[i]>b[i])return true;
        if(b[i]>a[i])return false;
    }
    return true;
}

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‘);
    }
    if(cmp(A,B)){
        vector<int> c=sub(A,B);
        if(c.size()==0){
            cout<<0<<endl;
            return 0;
        }
        for(int i=0;i<c.size();i++){
            cout<<c[i];
        }
        cout<<endl;
    }
    else {
        vector<int> c=sub(B,A);
        cout<<‘-‘;
        for(int i=0;i<c.size();i++){
            cout<<c[i];
        }
        cout<<endl;
    }
}

#include <iostream>
#include <algorithm>
#include <vector>
#include <cstring>
#include <string>
#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();i++){
        t+=(A[i]*b);
        C.push_back(t%10);
        t/=10;
    }
    while(t){
        C.push_back(t%10);
        t/=10;
    }
    reverse(C.begin(),C.end());
    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‘);
    }
    vector<int> C=mul(A,b);
    for(int i=0;i<C.size();i++){
        cout<<C[i];
    }
    cout<<endl;
}

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

vector<int> divv(vector<int> a,int b,int &r){
    //从高位向低位除模拟余数
    vector<int> c;
    r=0;
    bool flag=true;
    //用来判断是不是有前导零
    for(int i=0;i<a.size();i++){
        r=r*10+a[i];
        if(r/b==0&&flag){
            r%=b;
            continue;
        }
        c.push_back(r/b);
        flag=false;
        r%=b;
    }
    return c;
}

int main(){
    string a;
    int b;
    cin>>a;
    cin>>b;
    vector<int>A;
    for(int i=0;i<a.size();i++){
        A.push_back(a[i]-‘0‘);
    }
    int r;
    vector<int> c=divv(A,b,r);
    for(int i=0;i<c.size();i++){
        cout<<c[i];
    }
    cout<<endl;
    cout<<r<<endl：
}