Relational algebra one to many, division - sql

Question

I have seen many examples of division but none helped me understand how to solve the following problem:
Relations are:
Patient (Pid, Did, Pname, Disease, Severity)
Doctor (Did, Cname, Dname, Specialty)
Clinic (Cname, Mname, Type, City)
Question is: Find all pairs of patient ID and city such that the patient doesn't suffer from flu, and was treated in all the clinics in that city.
From what I've seen I need to divide the patients without flu by....? I think that it should be a table with all the clinics in a certain city, but how do I get that, and for each possible city?
Thanks

Answer 1

so... this is kind of complicated... pay special attention to the sample data I included in the tables.
http://sqlfiddle.com/#!2/04eac4/15/0
http://sqlfiddle.com/#!2/04eac4/17/0
I have no idea where division was supposed to take place...?
First we need to know how many clinics are in each city:
select city, count(cid) as c_count from clinic group by city
Then we need to know where each patient has been treated for anything besides the flu...
select patient.pid, patient.pname, clinic.city,
count(distinct clinic.cid) as p_c_count
from patient
join patient_doctor
on patient.pid = patient_doctor.pid
join doctor
on patient_doctor.did = doctor.did
join clinic
on doctor.cid = clinic.cid
where patient_doctor.disease not in ('Flu')
group by patient.pid, patient.pname, clinic.city
This joins all the tables together so that we can link PID and CID. Then we want only information that on patients that does not include a diagnosis of the flu. After, we group by the patient information and the clinic city so that we can count the number of clinics that patient went to for each city. Keep in mind, Patient A can go to Clinic 1 in the first city and be treated for the flu and even if he gets treated for the flu at a different clinic in a different city, the way you phrased the question allows that person to show up in results for the first city/clinic.... Does that makes any sense?
Then we need to join those two results. If the number of clinics in each city is equal to the number of clinics a patient visited per city, without being diagnosed with the flu, we get this:
select p_info.pid, c_ct_info.city
from (select city, count(cid) as c_count from clinic group by city) as c_ct_info
join (
select patient.pid, patient.pname, clinic.city,
count(distinct clinic.cid) as p_c_count
from patient
join patient_doctor
on patient.pid = patient_doctor.pid
join doctor
on patient_doctor.did = doctor.did
join clinic
on doctor.cid = clinic.cid
where patient_doctor.disease not in ('Flu')
group by patient.pid, patient.pname, clinic.city ) as p_info
on c_ct_info.city = p_info.city
where c_count = p_c_count;
Now. This excludes anyone who just visited one clinic and wasn't diagnosed with the flu but didn't go any of the other clinics in that city.
Just in case that sqlfiddle dies one day... here is the tables and data I used:
Create table Clinic (
CID int not null primary key,
Cname varchar(100),
Mname varchar(100),
Type tinyint,
City varchar(100)
);
insert into Clinic values (1,'Clinic 1','Mname 1', 1, 'City 1');
insert into Clinic values (2,'Clinic 2','Mname 2', 1, 'City 1');
insert into Clinic values (3,'Clinic 3','Mname 3', 1, 'City 2');
Create table Doctor (
DID int not null primary key,
Dname varchar(100),
Specialty varchar(100),
CID int,
foreign key (CID) references Clinic (CID)
);
insert into Doctor values (1, 'House', 'Internal Medicine', 1);
insert into Doctor values (2, 'Dr Who', 'General Practice', 1);
insert into Doctor values (3, 'Dr Dave', 'General Practice', 1);
insert into Doctor values (4, 'Dr Four', 'General Practice', 2);
insert into Doctor values (5, 'Dr Five', 'General Practice', 3);
insert into Doctor values (6, 'Dr Six', 'General Practice', 3);
create Table Patient (
PID int not null primary key,
PName varchar(100)
);
insert into Patient values (1, 'P. One');
insert into Patient values (2, 'P. Two');
insert into Patient values (3, 'P. Three');
insert into Patient values (4, 'P. Four');
insert into Patient values (5, 'P. Five');
Create table Patient_Doctor (
PDID int not null auto_increment primary key,
PID int not null,
DID int,
Disease varchar(100),
Severity tinyint,
foreign key (PID) references Patient (PID),
foreign key (DID) references Doctor (DID)
);
insert into Patient_Doctor values (null, 1, 1, 'Flu', 1);
insert into Patient_Doctor values (null, 1, 4, 'Flu', 1);
insert into Patient_Doctor values (null, 1, 5, 'Flu', 1);
-- shouldn't be in our results because they were diagnosed with the flu in each city
insert into Patient_Doctor values (null, 2, 2, 'Other', 1);
insert into Patient_Doctor values (null, 2, 4, 'Other', 1);
insert into Patient_Doctor values (null, 2, 5, 'Other', 1);
-- should be in our results because they attended every clinic in every city and
-- did not get diagnosed with the flu at any location
insert into Patient_Doctor values (null, 3, 1, 'Other', 1);
insert into Patient_Doctor values (null, 3, 4, 'Other', 1);
insert into Patient_Doctor values (null, 3, 6, 'Flu', 1);
-- should show up in our results for City 1 because they attended all the clinics in that
-- city and were not diagnosed with the flu. this person should NOT show up in our results
-- for city 2 because they were diagnosed with the flu at a clinic there.
insert into Patient_Doctor values (null, 4, 3, 'Other', 1);
-- should NOT show up in any results. although they weren't diagnosed with the flu, they
-- did not attend each clinic in that city.
insert into Patient_Doctor values (null, 5, 2, 'Flu', 1);
-- should NOT show up in results... meets none of the criteria
if we would add this data:
insert into Patient values (6, 'P. Six');
insert into Patient_Doctor values (null, 6, 5, 'Other', 1);
we should expect to see that person in our results because there's only one clinic in city 2 and they were not diagnosed with the flu there...
Things I changed:
Patient_Doctor: PID, DID, Disease, Severity
Patient: PID, PName
Clinic and Doctor are now joined by CID instead of CName
I highly suggest you create another table for Disease so that you are not repeating the same information over and over again. This table would include the fields Disease_ID and Disease_Description. The disease would then be linked to the patient by the Disease_ID.