Question

From this site:

Tables:

CREATE TABLE PilotSkills
(pilot_name CHAR(15) NOT NULL,
plane_name CHAR(15) NOT NULL,
PRIMARY KEY (pilot_name, plane_name));

CREATE TABLE Hangar
(plane_name CHAR(15) NOT NULL PRIMARY KEY);

Query:

SELECT DISTINCT pilot_name
  FROM PilotSkills AS PS1
  WHERE NOT EXISTS
       (SELECT *
          FROM Hangar
         WHERE NOT EXISTS
               (SELECT *
                  FROM PilotSkills AS PS2
                 WHERE (PS1.pilot_name = PS2.pilot_name)
                   AND (PS2.plane_name = Hangar.plane_name)));

I understand the problem it’s used for (set division), including the analogy that describes it as “There ain’t no planes in this hangar that I can’t fly!”. What I don’t understand is exactly what’s at work here, and how it comes together to do what it says its doing.

Having trouble stating with specifics my difficulty at the moment…

---

Edit: Let me just first ask what something like this does, exactly:

SELECT DISTINCT pilot_name
  FROM PilotSkills
  WHERE NOT EXISTS
       (SELECT *
          FROM Hangar)

I think I’m missing some fundamental understanding here…

Edit: Irrelevant, and it wouldn’t be a meaningful without the third nested SELECT, right?

Answer 1

What we want is a distinct list of pilots that can fly every plane in the hanger. For that to be true, for a given pilot, there cannot exist a plane they cannot fly. So, we want to get a list of all planes for each pilot and see if there is one they cannot fly. If there is one (the pilot cannot fly) we remove them from the list. Whomever is left, can fly all planes in the hanger.

Said more formally, find a distinct list of pilot names such that for a given pilot, there does not exist a plane in the set of planes (Hanger) such that the plane does not exist in the set of the given pilot’s skills.

“find a distinct list of pilot
names…”

Select Distinct pilot_name
From PilotSkills As PS1
...

“…such that for a given pilot, there
does not exist a plane in the set of
planes (Hanger)…”

Select Distinct pilot_name
From PilotSkills As PS1
Where Not Exists    (
                    Select 1
                    From Hanger

“…such that the plane does not exist
in the set of the given pilot’s
skills.”

Select Distinct pilot_name
From PilotSkills As PS1
Where Not Exists    (
                    Select 1
                    From Hanger As H
                    Where Not Exists    (
                                        Select 1
                                        From PilotSkills As PS2
                                        Where PS2.pilot_name = PS1.pilot_name
                                            And PS2.plane_name = H.plane_name
                                        )
                    )