大数开方，大数相乘

                   计算两个很大的数的开方后的乘积

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

//两个字符串相乘
string strMultiply(string str1 , string str2)
{
    string strResult = "";
    int len1 = str1.length();
    int len2 = str2.length();
    int num[500] = {0};
    int i = 0, j = 0;
    for(i = 0; i < len1; i++)
    {
        for(j = 0; j < len2; j++)
        {
            num[len1-1 - i + len2-1 - j] += (str1[i] - '0')*(str2[j] - '0');
        }
    }

    for(i = 0; i < len1 + len2; i++)
    {
        num[i+1] += num[i] / 10;

        num[i] = num[i] % 10;
    }

    for(i = len1 + len2 - 1; i >= 0 ; i--)
    {
        if(0 != num[i]) break;
    }

    for(j = i; j >= 0; j--)
    {
        strResult += num[j] + '0';
    }
    return strResult;
}

//str1 * 10^pos后(即在str1后添上pos个0)，与str2作比较
int compare(string str1, string str2, int pos)
{
    int len1 = str1.length();
    int len2 = str2.length();
    if(len2 > len1+pos) return 0;
    if(len2 < len1+pos) return 1;
    int i = 0;
    for(i = 0; i < len2; i++)
    {
        if(str1[i]-'0' > str2[i]-'0') return 1;
        if(str1[i]-'0' < str2[i]-'0') return 0;
    }
    return 0;
}

//对大数str开方取整
string sqrtLarge(string str)
{
    int len = str.length();
    int i = 0;
    int j = 0;
    string strResult = "";
    string str1 = "";
    if(len&1)
        len=len/2+1;
    else
        len=len/2;
    for(i = 0; i < len; i++)
    {
        for(j = 0; j < 10; j++)//枚举当前位从0~9每一个数
        {
            str1 = strResult;
            str1 += j + '0';
            if(1 == compare(strMultiply(str1, str1) , str , 2*(len-i-1)) )//判断当前这个数的平方与str的大小
            {
                //由于str1后少了len/2-i-1个0，所以平方以后少了2*(len/2-i-1)个
                strResult +=  j-1 + '0';
                break;
            }
            if(9 == j) strResult += '9';
        }
    }
    return strResult;
}
int main()
{
    string str1;
    string str2;
    string strResult;
    cin>>str1>>str2;

    cout<<strMultiply(sqrtLarge(str1) , sqrtLarge(str2))<<endl;

    return 0;
}