stringMathFunctions.cpp

string sum(string str1, string str2)
{
    if (str1.length() > str2.length())
        swap(str1, str2);
 
    string str = "";
 
    int n1 = str1.length(), n2 = str2.length();
 
    reverse(str1.begin(), str1.end());
    reverse(str2.begin(), str2.end());
 
    int carry = 0;
    for (int i=0; i<n1; i++)
    {
        int sum = ((str1[i]-'0')+(str2[i]-'0')+carry);
        str.push_back(sum%10 + '0');
 
        carry = sum/10;
    }
 
    for (int i=n1; i<n2; i++)
    {
        int sum = ((str2[i]-'0')+carry);
        str.push_back(sum%10 + '0');
        carry = sum/10;
    }
 
    if (carry)
        str.push_back(carry+'0');
 
    reverse(str.begin(), str.end());
 
    return str;
}

string product(string num1, string num2)
{
    int n1 = num1.size();
    int n2 = num2.size();
    if (n1 == 0 || n2 == 0)
       return "0";
 
    vector<int> result(n1 + n2, 0);
 
    int i_n1 = 0; 
    int i_n2 = 0; 
 
    for (int i=n1-1; i>=0; i--)
    {
        int carry = 0;
        int n1 = num1[i] - '0';
        i_n2 = 0; 
         
        for (int j=n2-1; j>=0; j--)
        {
            int n2 = num2[j] - '0';
            int sum = n1*n2 + result[i_n1 + i_n2] + carry;
            carry = sum/10;
            result[i_n1 + i_n2] = sum % 10;
            i_n2++;
        }
 
        if (carry > 0)
            result[i_n1 + i_n2] += carry;
        i_n1++;
    }
 
    int i = result.size() - 1;
    while (i>=0 && result[i] == 0)
       i--;
 
    if (i == -1)
       return "0";
 
    string s = "";
    while (i >= 0)
        s += std::to_string(result[i--]);
 
    return s;
}

inline string divideby2(string a) {
	int la = a.length();

	if(la == 0) return a;

	ll carry = 0;
	string ans;
	fo(i,0,la) {
		int curr = 10*carry + (a[i] - '0');
		carry = (curr%2);
		ans += ((curr/2) + '0');
	}
	if(ans == "0") return ans;
	if(ans[0] == '0') ans.erase(ans.begin());
	return ans;
}