Improving the time complexity of the program - vector, find, lower_bound

Question

I have a few questions about how to adjust my program so that the speed is O (log (n)) - at least for the invoice and audit methods.

In the newCompany method, I insert an element into a vector and then sort by ID? There is a need to sort after inserting, can't it be done differently? At the same time, I search here using the find () method, I can't use lower_bound () because I have elements sorted by ID.

I have two invoice methods. In the first I look for id, and I use lower_bound, I don't see the problem in that. I'm looking for a different variant using the addr and name string, so I can't use lower_bound again from the same problem as with the new method.

Are there any ways to replace the problems described above? Thank you in advance.

The whole program https://onecompiler.com/cpp/3xybks89x

class Company
{
...
    private:
        string name;
        string addr;
        string id;
        unsigned int totalIncome;
        unsigned int numberOrders;
        unsigned int amount;
};
bool CVATRegister::newCompany ( const string &name, const string &addr, const string &taxID )
{
    Company cmp(name, addr, taxID);
    
    if ( find(DCompany.begin(), DCompany.end(), cmp) == DCompany.end() )
    {
        DCompany.push_back(cmp);
        
        sort(DCompany.begin(), DCompany.end(), [](const Company & a, const Company & b)
        { 
            return a.getId() < b.getId(); 
        });

        return true;
    }
    return false;
}
bool CVATRegister::invoice ( const string &taxID, unsigned int amount )
{
    Company cmp("", "", taxID);

    auto itr = lower_bound(DCompany.begin(), DCompany.end(), cmp);
    if(itr != DCompany.end() && itr->getId() == taxID)
     {   
        TotalInvoice.push_back(amount);

        DCompany[distance(DCompany.begin(), itr)].saveInvoice(amount);        
        return true;
     }
     
     return false;    
}

bool CVATRegister::invoice ( const string  &name, const string &addr, unsigned int amount )
{
    Company cmp(name, addr,"-1");

    auto itr = find(DCompany.begin(), DCompany.end(), cmp);

    if(itr != DCompany.end())
     {   
        TotalInvoice.push_back(amount); 
        DCompany[distance(DCompany.begin(), itr)].saveInvoice(amount);
        return true;
     }
     return false;
}

bool CVATRegister::audit ( const string &name, const string  &addr, unsigned int &sumIncome ) const
{
    Company cmp(name, addr,"-1");

    auto itr = find(DCompany.begin(), DCompany.end(), cmp);

    if(itr != DCompany.end())
     {   
        sumIncome = itr->getTotalIncome(); 
        return true;
     }
     return false;

}

bool CVATRegister::audit ( const string  &taxID, unsigned int &sumIncome) const
{
    Company cmp("", "", taxID);

    auto const itr = lower_bound(DCompany.begin(), DCompany.end(), cmp);

    if(itr != DCompany.end() && itr->getId() == taxID)
     {   
        sumIncome = DCompany[distance(DCompany.begin(), itr)].getTotalIncome();
        return true;
     }
     
     return false;

}

EDIT:

auto itr = lower_bound(DCompany.begin(), DCompany.end(), cmp, [](const Company & a, const Company & b)
        { 
            if (strcasecmp(a.getName().c_str(), b.getName().c_str()) == 0)
                return strcasecmp(a.getName().c_str(), b.getName().c_str()) < 0;
                
            return strcasecmp(a.getAddr().c_str(), b.getAddr().c_str()) < 0;
        });