C++高精度整数加减乘除模板

其中高精度乘法通过了POJ2389，其他没有测过，不过应该是没有问题的。

其中高精度除法返回一对string，分别表示商和余数。

代码：

#include <bits/stdc++.h>

using namespace std;

const int maxn = 100010;

int a[maxn], b[maxn], res[maxn];

string add(string s1, string s2) {  // under condition: s1,s2>=0

    // 初始化部分

    int n = s1.length(), m = s2.length();

    for (int i = 0; i < n; i ++) a[i] = s1[n-1-i] - '0';

    for (int i = 0; i < m; i ++) b[i] = s2[m-1-i] - '0';

    int len = max(n, m) + 1;

    for (int i = n; i < len; i ++) a[i] = 0;

    for (int i = m; i < len; i ++) b[i] = 0;

    for (int i = 0; i < len; i ++) res[i] = 0;

    // 处理部分

    for (int i = 0; i < len; i ++) {

        res[i] += a[i] + b[i];

        if (res[i] >= 10) {

            res[i+1] += res[i] / 10;

            res[i] %= 10;

        }

    }

    // 返回部分

    int i = len-1;

    while (res[i] == 0 && i > 0) i --;

    string s = "";

    for (; i >= 0; i --) {

        char c = (char) (res[i] + '0');

        s += c;

    }

    return s;

}

string sub(string s1, string s2) {  // under condition: s1>=s2>=0

    // 初始化部分

    int n = s1.length(), m = s2.length();

    for (int i = 0; i < n; i ++) a[i] = s1[n-1-i] - '0';

    for (int i = 0; i < m; i ++) b[i] = s2[m-1-i] - '0';

    int len = max(n, m);

    for (int i = n; i < len; i ++) a[i] = 0;

    for (int i = m; i < len; i ++) b[i] = 0;

    for (int i = 0; i < len; i ++) res[i] = 0;

    // 处理部分

    for (int i = 0; i < len; i ++) {

        res[i] += a[i] - b[i];

        if (res[i] < 0) {

            res[i+1] --;

            res[i] += 10;

        }

    }

    // 返回部分

    int i = len-1;

    while (res[i] == 0 && i > 0) i --;

    string s = "";

    for (; i >= 0; i --) {

        char c = (char) (res[i] + '0');

        s += c;

    }

    return s;

}

bool cmp(string s1, string s2) {    // under condition: s1,s2 >= 0

    int n = s1.length(), m = s2.length();

    int i;

    for (i = 0; i < n-1 && s1[i] == '0'; i ++);

    s1 = s1.substr(i);

    for (i = 0; i < m-1 && s2[i] == '0'; i ++);

    s2 = s2.substr(i);

    if (s1.length() != s2.length()) return s1.length() < s2.length();

    return s1 < s2;

}

string Add(string s1, string s2) {

    if (s1[0] == '-' && s2[0] == '-') {

        return "-" + add(s1.substr(1), s2.substr(1));

    }

    else if (s1[0] == '-') {

        s1 = s1.substr(1);

        if (cmp(s1, s2) == true) {

            return sub(s2, s1);

        } else {

            return "-" + sub(s1, s2);

        }

    }

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

        s2 = s2.substr(1);

        if (cmp(s1, s2) == true) {

            return "-" + sub(s2, s1);

        } else {

            return sub(s1, s2);

        }

    }

    else {

        return add(s1, s2);

    }

}

string Sub(string s1, string s2) {

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

        s2 = s2.substr(1);

        return Add(s1, s2);

    }

    else {

        return Add(s1, "-" + s2);

    }

}

string multi(string s1, string s2) {    // under condition: s1,s2>=0

    // 初始化部分

    int n = s1.length(), m = s2.length();

    for (int i = 0; i < n; i ++) a[i] = s1[n-1-i] - '0';

    for (int i = 0; i < m; i ++) b[i] = s2[m-1-i] - '0';

    int len = n + m;

    for (int i = n; i < len; i ++) a[i] = 0;

    for (int i = m; i < len; i ++) b[i] = 0;

    for (int i = 0; i < len; i ++) res[i] = 0;

    // 处理部分

    for (int i = 0; i < n; i ++)

        for (int j = 0; j < m; j ++)

            res[i+j] += a[i] * b[j];

    for (int i = 0; i < len; i ++) {

        res[i+1] += res[i] / 10;

        res[i] %= 10;

    }

    // 返回部分

    int i = len-1;

    while (res[i] == 0 && i > 0) i --;

    string s = "";

    for (; i >= 0; i --) {

        char c = (char) (res[i] + '0');

        s += c;

    }

    return s;

}

pair<string, string> divide(string s1, string s2) { // under condition: s1>=0,s2>0

    string s = "", t = "";

    int n = s1.length(), m = s2.length();

    bool flag = false;

    for (int i = 0; i < n; i ++) {

        s += s1[i];

        int num = 0;

        while (cmp(s, s2) == false) {

            num ++;

            s = sub(s, s2);

        }

        if (num > 0) {

            flag = true;

            char c = (char)(num + '0');

            t += c;

        }

        else if (flag) {

            t += '0';

        }

    }

    if (t.length() == 0) t = "0";

    while (s[0] == '0' && s.length() > 1) s = s.substr(1);

    return make_pair(t, s);

}

string s1, s2;

int main() {

    while (cin >> s1 >> s2) {

        cout << "add:\t" << Add(s1, s2) << endl;

        cout << "sub:\t" << Sub(s1, s2) << endl;

        cout << "multi:\t" << multi(s1, s2) << endl;

        pair<string, string> divide_pair = divide(s1, s2);

        cout << "divide:\t" << divide_pair.first << " ...... " << divide_pair.second << endl;

    }

    return 0;

}

测试数据：

100 9

add:    109

sub:    91

multi:  900

divide: 11 ...... 1

1000000 87

add:    1000087

sub:    999913

multi:  87000000

divide: 11494 ...... 22