Calculating weighted marks within weighted marks - sql

Question

I have a maths / SQL problem that I've been grappling with.
I have two tables with the following structure:
CREATE TABLE Exams
(
ExamID INT PRIMARY KEY,
ExamName VARCHAR(100),
CourseID INT,
RelatedExamID INT NULL,
Weighting DECIMAL (5,3)
)
CREATE TABLE ExamMarks
(
ExamMarkID INT IDENTITY PRIMARY KEY,
StudentID VARCHAR(8),
ExamID INT FOREIGN KEY REFERENCES Exams(ExamID),
ExamMark DECIMAL (5,4)
)
The exams table contains the following data:
INSERT INTO Exams (ExamID, ExamName, CourseID, RelatedExamID, Weighting)
VALUES (1, 'English',1,NULL,1),
(2, 'French',2,NULL,1),
(3, 'Maths',3,NULL,0.6),
(4, 'Statistics',3,NULL,0.4),
(5, 'Physics Part 1',4,NULL,0.5),
(6, 'Physics Part 2',4,NULL,0.5),
(7, 'Heat and Mass',4,6,0.25)
The Exam Marks table contains the following data:
INSERT INTO ExamMarks (StudentID, ExamID, ExamMark)
VALUES ('00112233', 1, 0.75),
('00112233', 2, 0.52),
('00112233', 3, 0.68),
('00112233', 4, 0.8),
('00112233', 5, 0.50),
('00112233', 6, 0.66),
('00112233', 7, 0.45)
The idea here is that a given course may have
A single exam (such as with English and French)
Multiple exams (such as with course 3, which has 2 exams called "Maths" and "Physics") which have independent weightings - in this case, the course is structured so that the Maths exam is 60% of the total, and the Physics exam contributes 40%
Exams with sub-exams, such as with Course 4, more on which shortly.
If I want to get the weighted total marks for each candidate for each exam - forgetting about course 4 for the moment - I do the following:
SELECT em.StudentID,e.CourseID, SUM(em.ExamMark * e.Weighting)/SUM(e.Weighting)
FROM Exams e
INNER JOIN ExamMarks em ON e.ExamID = em.ExamID
GROUP BY em.StudentID,e.CourseID
However, Course 4 is made up of 3 parts:
Physics Part 1 - 50% of the total, and
Physics Part 2 - also 50% of the total
Heat and Mass, which makes up 25% of Physics Part 2 (thus its ID in the 'RelatedExamID' column)
To be clear, Heat and Mass makes up 25% of Physics Part 2, which itself makes up 50% of the course.
I've put these figures into an Excel spreadsheet, and after a lot of head-scratching, was able to figure that our student should end up with a mark for Course 4 of 55.375%.
However, unfortunately, my SQL (and maths / logic) skills are not good enough to get to this result in a SQL query.
The data above represents something of a simplification. There are, in fact, around 10000 marks to be considered (around 500 students involved), for about 200 different exams, of which perhaps 30 are "sub-exams". Each year, these have to be totalled up to give the student their mark per course, given these weightings.

Answer 1

Okay, so I have managed to find a solution. I'd still be grateful for any others which might be more efficient or robust from those who know more than me.
--Get SubComponent marks
WITH SubComponents
AS
(SELECT
em.StudentID
,em.ExamID
,e.RelatedExamID
,e.Weighting
,e.Weighting * em.ExamMark AS WeightedMark
FROM Exams e
INNER JOIN ExamMarks em
ON e.ExamID = em.ExamID
WHERE e.RelatedExamID IS NOT NULL),
--Get marks for those components which have subcomponents
ParentComponents
AS
(SELECT
em.StudentID
,e.CourseID
,em.ExamID
,e.RelatedExamID
,e.Weighting
,((1 - SubComponents.Weighting) * em.ExamMark)
+ SubComponents.WeightedMark AS OverallComponentMark
FROM Exams e
INNER JOIN ExamMarks em
ON e.ExamID = em.ExamID
INNER JOIN SubComponents
ON SubComponents.RelatedExamID = e.ExamID
AND SubComponents.StudentID=em.StudentID),
--Get marks for those components which are neither parent nor child components
StandaloneComponents
AS
(SELECT
em.StudentID
,e2.CourseID
,em.ExamID
,e2.RelatedExamID
,e2.Weighting
,em.ExamMark
FROM Exams e2
INNER JOIN ExamMarks em
ON e2.ExamID = em.ExamID
WHERE NOT EXISTS (SELECT
*
FROM Exams
WHERE RelatedExamID = e2.ExamID)
AND e2.RelatedExamID IS NULL),
-- Bring all the above together
ComponentMarks
AS
(SELECT
StudentID
,CourseID
,ExamID
,Weighting
,ExamMark
FROM StandaloneComponents
UNION
SELECT
StudentID
,CourseID
,ExamID
,Weighting
,OverallComponentMark
FROM ParentComponents)
-- Finally group and combine marks at course level
SELECT
StudentID
,CourseID
,SUM(ExamMark * Weighting) / SUM(Weighting)
FROM ComponentMarks
GROUP BY StudentID
,CourseID