算法学习——大整数运算（高精度）C++

1.大整数加法

用数组来存储大整数的每一位，然后模拟人工运算，用for循环按位运算和处理，原理十分简单，直接上模板。

#include<iostream>
#include<vector>
using namespace std;
//大整数加法
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) 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--) cout<<C[i];

    cout<<endl;

    return 0;
}

#include<iostream>
#include<vector>
using namespace std;
//判断A是否大于等于B
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 1;
}

//C = 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;
}

//C = A + B
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) 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‘);

    if(cmp(A,B)){
        auto C = sub(A,B);
        for(int i = C.size()-1;i>=0;i--) cout<<C[i];
        cout<<endl;
    }else{
        auto C = sub(B,A);
        cout<<"-";
        for(int i = C.size()-1;i>=0;i--) cout<<C[i];
        cout<<endl;
    }

    return 0;
}

#include <iostream>
#include <vector>

using namespace std;

vector<int> mul(vector<int> A, vector<int> B)
{
    vector<int> C(A.size() + B.size());

    for (int i = 0; i < A.size(); i ++ )
        for (int j = 0; j < B.size(); j ++ )
            C[i + j] += A[i] * B[j];

    for (int i = 0, t = 0; i < C.size() || t; i ++ )
    {
        t += C[i];
        if (i >= C.size()) C.push_back(t % 10);
        else C[i] = t % 10;
        t /= 10;
    }

    while (C.size() > 1 && !C.back()) 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‘);
    auto C = mul(A, B);

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

    return 0;
}

#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;
}

原文地址：https://www.cnblogs.com/Flydoggie/p/12235396.html