LeetCode OJ--Multiply Strings **

https://oj.leetcode.com/problems/multiply-strings/

用字符串实现大数乘法，细节题，细节很多

 
class Solution {
public:
    string multiply(string num1, string num2) {
        if(num1.empty() || num1.size() == 0 || num2.empty() || num2.size() == 0)
            return "";
        //0
        if(num1 == "0" || num2 == "0")
            return "0";
        
        //keep num2 the smaller
        if(num1.size() < num2.size())
        {
            //exchange
            string t = num1; num1 = num2; num2 = t;
        }
        string ans = "";
        ans.resize(num1.size());
        
        //initialize
        for(size_t i = 0; i < num1.size(); i++)
            ans[i] = '0';
            
        int pos = 0;
        int times = 0;
        int sum = 0;
        
        for(int index2 = num2.size() - 1; index2 >= 0; index2--)
        {
            pos = ans.size() - 1 - times;
            times++;
            int carry = 0;
            for(int index1 = num1.size() - 1; index1 >=0; index1--)
            {
                sum = carry + (num1[index1] - '0')*(num2[index2] - '0') + ans[pos] - '0';
                carry = sum/10;
                ans[pos] = sum%10 + '0';
                pos--;
                // ans has been the beginning while index1 not, and ans has been the beginning and here are carry
                if(pos == -1 &&(carry > 0|| index1 != 0))
                {
                    string t = "0";
                    t[0] = carry + '0';
                    ans = t + ans;
                    carry = 0;
                    pos = 0;
                }
            }
        }
        return ans;
    }
};