将大数当做字符串进行处理，也就是将大数用十进制字符数组进行表示，然后模拟人们手工进行“竖式计算”的过程得到乘法的结果。

#include<iostream>
using namespace std;
#define MAXN 100

string multiply(char line1[], char line2[])
{
    short number1[MAXN], number2[MAXN], result[MAXN];//number1，number2：两个乘数；result：乘积的结果

    short len1 = strlen(line1);
    short len2 = strlen(line2);

    short len = len1 + len2;

    bool line1isNegativeNumber = false;// 是否是负数
    bool line2isNegativeNumber = false;// 是否是负数

    for (int i = 0; i < len1; i++) {
        char number = line1[i];

        if (i == 0) {
            if (number == '-' && len1 > 1) {
                line1isNegativeNumber = true;
            }
            else if (number == '-' && len1 == 1){
                string invalidString("Invalid input");
                return invalidString;
            }
            else if (number > '9' || number < '0'){
                string invalidString("Invalid input");
                return invalidString;
            }
        }
        else {
            if (number > '9' || number < '0'){
                string invalidString("Invalid input");
                return invalidString;
            }
        }

        if (number != '-') {
            number1[len1 - i - 1] = number - '0';
        }
    }

    for (int i = 0; i < len2; i++) {
        char number = line2[i];
        if (i == 0) {
            if (number == '-' && len2 > 1) {
                line2isNegativeNumber = true;
            }
            else if (number == '-' && len2 == 1){
                string invalidString("Invalid input");
                return invalidString;
            }
            else if (number > '9' || number < '0'){
                string invalidString("Invalid input");
                return invalidString;
            }
        }
        else {
            if (number > '9' || number < '0'){
                string invalidString("Invalid input");
                return invalidString;
            }
        }

        if (number != '-') {
            number2[len2 - i - 1] = number - '0';
        }

    }

    if (line1isNegativeNumber) {
        len1--;
    }

    if (line2isNegativeNumber) {
        len2--;
    }
    memset(result, 0, sizeof(short) * (MAXN - 1));

    for (int i = 0; i < len1; i++) {
        for (int j = 0; j < len2; j++) {
            result[i + j] = result[i + j] + number1[i] * number2[j];//逐位相乘
        }
    }

    int carry = 0;
    for (int i = 0; i <= len; i++){//进位
        int k = result[i] + carry;
        result[i] = k % 10;
        carry = k / 10;
    }

    int realLen = 0;//实际的计算结果长度
    for(int i = len - 1; i >= 0; i--) {
        if (result[i] != 0) {//处理多余的零
            realLen = i + 1;
            break;
        }
    }

    if (line1isNegativeNumber ^ line2isNegativeNumber) {
        realLen++ ;
    }

    char *line = new char[realLen + 1];
    if (realLen == 0) {
        line[0] = 0 + '0';
        line[1] = '\0';//字符串的结束标志
    }
    else {
        int i = 0;
        if (line1isNegativeNumber ^ line2isNegativeNumber) {
            line[0] = '-';
            i = 1;
        }

        for (; i < realLen; i++) {
            line[i] = result[realLen - i - 1] + '0';
        }

        line[realLen] = '\n';
    }
    return line;

}

int main(int argc, const char * argv[]) {
    @autoreleasepool {
        char line1[MAXN], line2[MAXN];
        while(cin >> line1 >>line2)
        {
            cout << multiply(line1, line2) << endl;
        }

    }
    return 0;
}

参考https://www.cnblogs.com/king-ding/p/bigIntegerMul.html