43. Multiply Strings

class Solution {
public:
    string multiply(string num1, string num2) {
        if(num1 == "0" || num2 == "0")
            return "0";
        int l1 = num1.length(), l2 = num2.length();

        vector<int> v(l1 + l2);

        //pf is power factor 
        int i = l2-1, pf = 0;

        while(i >= 0)
        {
            int ival = num2[i] -'0';

            int j = l1 - 1, carry = 0;

            //travesing the result array from left to right
            int k = v.size() - 1 - pf;

            while(j>=0 || carry != 0)
            {
                int jval = j>=0 ? num1[j] - '0' : 0;

                int prod = (ival * jval) + v[k] +  carry;

                v[k] = prod % 10;
                carry = prod /10;

                k--;
                j--; 
            }
            pf++;
            i--;
        }

        string ans = "";
        bool flag = true;

        for(int i = 0; i<v.size(); i++)
        {
            if(v[i] == 0 && flag == true)
            {
                continue;
            }
            else
            {
                flag = false;
                ans += (v[i] + '0') ;
            }
        }

        return ans;

    }
};