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class Solution {//draw it out and then observe it to find out the regular pattern//more practice is neededpublic:	string multiply(string num1, string num2) {		// Start typing your C/C++ solution below		// DO NOT write int main() function		if(num1.size() == 0 || num2.size() == 0) return string("");		string ans(num1.size()+num2.size()+1, '0');//important observation		reverse(num1.begin(), num1.end());		reverse(num2.begin(), num2.end());		for (int digIdx2 = 0; digIdx2 < num2.size(); ++digIdx2)//the below number num2		{			int dig2 = num2[digIdx2]-'0';			int carry = 0;			for (int digIdx1 = 0; digIdx1 < num1.size(); ++digIdx1)//the up number num1 			{				int dig1 = num1[digIdx1]-'0';				int tmp = ans[digIdx1+digIdx2]-'0';				int sum_cur = carry+dig1*dig2+tmp;				ans[digIdx1+digIdx2] = sum_cur%10+'0';				carry = sum_cur/10;			}			ans[digIdx2+num1.size()] = carry+'0';			}		reverse(ans.begin(), ans.end());		int posStart = ans.find_first_not_of('0');		if(posStart < 0 || posStart >= ans.size()) //in case of ""000"			posStart = ans.size()-1;		int len = ans.size()-posStart;		return ans.substr(posStart, len);	}};

second time

class Solution {public:    string multiply(string num1, string num2) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        reverse(num1.begin(), num1.end());        reverse(num2.begin(), num2.end());        int carry = 0;        string result;        for(int len = 0; ;++len)        {            int sum = 0;            bool flag = false;            for(int i = 0; i < num1.size(); ++i)            {                int j = len-i;                if(j < 0 || j >= num2.size()) continue;                sum += (num1[i]-'0')*(num2[j]-'0');                flag = true;            }            if(!flag) break;            sum += carry;            result.push_back(sum%10+'0');            carry = sum/10;        }                while(carry > 0)        {            result.push_back(carry%10+'0');            carry /= 10;        }        reverse(result.begin(), result.end());        if(result.find_first_not_of('0') == string::npos) return "0";        else return result.substr(result.find_first_not_of('0'), result.size()-result.find_first_not_of('0'));    }};

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