高精度算法

高精度加法

AcWing.791高精度加法

# include <iostream>
# include <string>
# include <vector>
using namespace std;
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 = t / 10;
    }
    if(t) 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');
    
    vector<int> C = add(A, B);
    for(int i = C.size() - 1; i >= 0; i --) cout << C[i];
    
    return 0;
}

高精度减法

AcWing.792高精度减法

# include <iostream>
# include <string>
# include <vector>
using namespace std;
bool cmp(vector<int>& A, vector<int>& B){
    if(A.size() != B.size()) return A.size() > B.size(); // A和B长度不相等
    for(int i = A.size() - 1; i >= 0; i --){ //A和B长度相等
        if(A[i] != B[i]) return A[i] > B[i];
    }
    return true; //A和B一样
}

vector<int> sub(vector<int>& A, vector<int>& B){ //规定 A 比 B 大
    vector<int> C;
    int t = 0; //借位
    int res; // res = A[i] - B[i] - t
    for(int i = 0; i < A.size(); i ++){
        res = A[i] - t;
        if(i < B.size()) res -= B[i]; //如果B有数,则减去B[i]
        if(res >= 0){  //不用借位
            C.push_back(res);
            t = 0;
        }
        else{ //需要借位
            C.push_back(res + 10);
            t = 1;
        }
    }
    while(C.size() > 1 && C.back() == 0) C.pop_back(); //去除前导0
    
    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');
    
    if(cmp(A, B)){
        vector<int> C = sub(A, B);
        for(int i = C.size() - 1; i >= 0; i --) cout << C[i];
    }else{
        vector<int> C = sub(B, A);
        cout << "-";
        for(int i = C.size() - 1; i >= 0; i --) cout << C[i];
    }
    
    return 0;
}

高精度乘法(大精度×小精度)

AcWing.793高精度乘法

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

vector<int> mul(vector<int>& A, int b){
    vector<int> C;
    int res, t = 0;
    for(int i = 0; i < A.size(); i ++){
        res = A[i] * b + t;
        C.push_back(res % 10);
        t = res / 10;
    }
    if(t) C.push_back(t);
    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');
    vector<int> C = mul(A, b);
    for(int i = C.size() - 1; i >= 0; i --) cout << C[i];
    
    return 0;
}

高精度除法(高精度除以低精度)

AcWing.794高精度除法

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

vector<int> div(vector<int>& A, int b, int& r){
    vector<int> C; //商
    r = 0; //余数
    int res;
    for(int i = A.size() - 1; i >= 0; i --){
        res = r * 10 + A[i];
        C.push_back(res / b);
        r = res % b;
    }
    reverse(C.begin(), C.end());
    while(C.size() > 1 && C.back() == 0) C.pop_back();
    
    return C;
}
int main(){
    string a;
    int b, r;
    vector<int> A;
    cin >> a >> b;
    
    for(int i = a.size() - 1; i >= 0; i --) A.push_back(a[i] - '0');
    
    vector<int> C = div(A, b, r);
    
    for(int i = C.size() - 1; i >=0; i --) cout << C[i];
    cout << endl;
    cout << r << endl;
    
    return 0;
}