大整数加法减法与乘法

模拟运算

用数组逆向保存大数每一位 加法直接从尾向前相加（尾部已对齐） 注意进位

减法类似 确保大数减小数 不够减了向前减一 需要注意符号的有无问题

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

int a[11000], b[11000];
string s1, s2;

void Add()
{
    int len1 = s1.length();
    int len2 = s2.length();
    int Max = max(len1, len2);
    int k;
    for (int i = len1-1, k = 0; i >= 0; i--)
        a[k++] = s1[i] - '0';
    for (int i = len2-1, k = 0; i >= 0; i--)
        b[k++] = s2[i] - '0';

    int up = 0;
    for (int i = 0; i < Max+1; i++) {
        a[i] = a[i] + b[i] + up;
        up = a[i] / 10;
        a[i] %= 10;
    }
    int first;
    for (first = Max+1; first >= 0; first--)
        if (a[first])
            break;

    if (first == -1)
        cout << "0";
    for (int i = first; i >= 0; i--)
        cout << a[i];

}

void Sub(string Max, string Min)  //a - b
{
    int len1 = Max.length();
    int len2 = Min.length();
    int MaxLen = max(len1, len2);

    int k;
    for (int i = len1-1, k = 0; i >= 0; i--)
        a[k++] = Max[i] - '0';
    for (int i = len2 - 1, k = 0; i >= 0; i--)
        b[k++] = Min[i] - '0';

    int up = 0;
    for (int i = 0; i < MaxLen+1; i++) {
        a[i] = a[i] - b[i] - up;
        if (a[i] < 0) {
            up = 1;
            a[i] += 10;
        }
        else
            up = 0;
    }

    int first;
    for (first = MaxLen+1; first >= 0; first--)
        if (a[first])
            break;

    if (first == -1)
        cout << "0";
    else {
        for (int i = first; i >= 0; i--)
            cout << a[i];
    }
}

int main()
{
    cin >> s1 >> s2;

    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));

    if (s1[0] == '-' && s2[0] == '-')
    {
        cout << '-';
        s1.erase(0, 1);
        s2.erase(0, 1);
        Add();
    }
    else if (s1[0] == '-' || s2[0] == '-')
    {
        string Max, Min;
        if (s1[0] == '-') {
            if (s1.length()-1 > s2.length())
                cout << "-";
            if (s1.length()-1 == s2.length())
            {
                if (s1[1] > s2[0])
                    cout << "-";
            }
            s1.erase(0, 1);
        }

       if (s2[0] == '-') {

            if (s2.length()-1 > s1.length())
                cout << "-";
            if (s1.length() == s2.length()-1)
            {
                if (s2[1] > s1[0])
                    cout << "-";
            }
            s2.erase(0, 1);
        }

        if(s1.length() > s2.length())
        {
            Max = s1;
            Min = s2;
        }
        else if (s1.length() == s2.length() && s1[0] > s2[0])
        {
            Max = s1;
            Min = s2;
        }
        else {
            Min = s1;
            Max = s2;
        }
      Sub(Max, Min);
    }
    else
        Add();

    return 0;
}

 乘法

先乘再进位

#include <iostream>
#include <string>
#include <cstring>
using namespace std;
int a[1100], b[1100], c[2300];

void big_number_multipy(string s1, string s2)
{
    int lenth1 = s1.length();
    int lenth2 = s2.length();
    int MaxLen = lenth1 + lenth2;

    int i, j, k;
    for (i = lenth1-1, k = 0; i >= 0; i--)
        a[k++] = s1[i] - '0';
    for (i = lenth2-1, k = 0; i >= 0; i--)
        b[k++] = s2[i] - '0';

    for (i = 0; i < lenth1; i++)
        for (j = 0; j <lenth2; j++)
            c[i+j] += a[i] * b[j];

    for (i = 0; i < MaxLen; i++) {
        c[i+1] += c[i] / 10;
        c[i] %= 10;
    }

    int first;
    for (first = MaxLen; first >= 0; first--)
        if (c[first])
            break;
    if (first == -1)
        cout << "0";
    for (int i = first; i >= 0; i--)
        cout << c[i];
}

int main()
{
    string s1, s2;

    cin >> s1 >> s2;
    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));
    memset(c, 0, sizeof(c));
    big_number_multipy(s1, s2);


    return 0;
}