043_Multiply Strings

//the intergers are too big to compute in ordinary arithmetrics.
class Solution {
public:
    string multiply(string num1, string num2) {
        int l1 = num1.length(), l2 = num2.length();
        if( l1 ==0 || l2==0) return "0";
        
        vector<int> reverse(l1+l2, 0);
        for (int i = 0; i < l1; i++)
        {
            int digit1 = num1[l1 - i - 1] - '0';
            int carry = 0;
            for (int j = 0; j < l2; j++)
            {
                int digit2 = num2[l2 - j - 1] - '0';
                int sum = digit1 * digit2 + reverse[i+j] + carry;
                carry = sum/10;
                reverse[i+j] = sum%10;
            }
            if (carry>0) reverse[i + l2] += carry;
        }
        int start = l1 + l2 -1;
        while( start > -1 && reverse[start]==0) start--;
        if(start == -1) return "0";
        
        string ans="";
        
        for (int i = start; i >= 0; i-- ) 
        {
            ans += (char)(reverse[i]+'0');
        }
        
        return ans;
    }
};