Relational Algebra and SQL

In this lab, you will work on querying databases using relational algebra and SQL. The exercises in this lab are similar to the examples that you studied during the lecture. The purpose of the lab sessions is to get the hands-on experience that is required for future carrier.

The exercises in this lab are based on the university database from the Database System Concepts.

University database
Relational algebra

Write the following queries in relational algebra:

  1. Find the titles of courses in the Comp. Sci. department that have 3 credits.

\[\pi_{title}(\sigma_{dept\_name = 'Comp. Sci.'\ \wedge \ credits = 3}(course)) \]

  1. Find the IDs of all students who were taught by an instructor named Einstein.

\[ \pi_{ID}(takes \bowtie \pi_{course\_id}(teaches\bowtie\sigma_{name = 'Einstein'}(instructor)))\] c. Find the highest salary of any instructor.

\[\gamma_{max(salary)}(instructor)\] d. Find all instructors earning the highest salary (there may be more than one with the same salary).

\[\sigma_{salary = \gamma_{max(salary)}(instructor)} (instructor) \]

  1. Find the enrollment of each section that was offered in Fall 2009.

\[ _{sec\_id} \gamma_{count(*)\ as\ enrolment} (\sigma_{year = 2009 \ \wedge\ semester = 'Fall'}(takes))\]

SQL

For SQL, we will have two types of exercises. Type1, you need to interpret and understand the outcomes of an SQL Query. Type2, You will need to write your SQL query to extract specific piece of data.

Running SQL queries

To run these queries, download the university database univdb-sqlite.db from here. The database contains a table time_slot that is not included in the schema diagram. After that, execute these queries and describe the task that they are supposed to perform and comment on the query outputs.

Q1. SELECT-FROM-WHERE

    SELECT ID, name, dept_name
        FROM student
        WHERE dept_name < "Finance";

This query will display the ‘ID’, ‘name’, ‘dept_name’ of students who belong to a department with name precedes the name ‘Finance’ according to the oreder of letter based on their ASCII code. In the university database, these departments will be ‘Biology’, ‘Comp. Sci.’ and ‘Elec. Eng.’.

Q2. Using DISTINCT

    SELECT DISTINCT dept_name          
        FROM student;

It will return the names of the departments who has students records in the database. For the university database, this will be ‘Comp. Sci.’, ‘History’, ‘Finance’, ‘Physics’, ‘Music’, ‘Elec. Eng.’, ‘Biology’. The name of the department will appear only one time regardless of the number of students in the department.

Q3. Using ALL

    SELECT ALL dept_name                 
            FROM student

It will return the names of the departments who has students records in the database. The name of the department will appear as many times as the number of students in the department. For example, ‘Comp. Sci.’ will appear 4 times according to the records in the university database.

Q4. Using named literal attribute

    SELECT 'MyName' as 'V1';

Will return a relation with a single attribute ‘V1’and this attribute has a single value ’MyName’.

Q5. Using literal attribute with FROM

    SELECT 'A'  FROM student;

Will return a relation with a single attribute ‘A’ and this attribute has 13 cells (similar to the number of records in the student relation) with a value ‘A’.

Q6. Performing calculations on the Query output

    SELECT dept_name, building, budget, (budget + (budget * 0.15)) as new_budget 
    FROM department;

This query will return a relation with attributes ‘dept_name’, ‘building’, ‘budget’, and ‘new_budget’. The new_budget is increased by 15% than the original budget.

Q7. Join

    SELECT name, course_id, sec_id
        FROM student, takes
        WHERE student.ID = takes.ID 
                and sec_id = 2;

This query will return a relation with attributes ‘name’, ‘course_id’, ‘sec_id’ who are attending in the section with sec_id = 2.

Q8. Self-join

    SELECT * FROM student as S1, student as S2 
        WHERE S1.dept_name = S2.dept_name 
            AND S1.name <> S2.name;

This query will return a relation with the information of students who are in the same department. Each record in the new relation will contain the information of two students from the same department.

Q9. Left-outer-join

    SELECT * FROM student 
    JOIN takes  
    ON student.ID = takes.ID;

This query will return a relation with the information of the students and the courses they have taken with their grades. The records that will be in the resulting relation should have the student ID in both tables.

  • What will be the difference when using LEFT OUTER JOIN instead of JOIN

In this case, all students should appear in the resulting relation even if the student didn’t take any courses. If a student didn’t take any courses, the course information will be replaced by null.

Writing SQL queries

In this part, you will write your own SQL queries to perform the following tasks.

  1. Write a query that returns the information of the students and the courses they have taken.
    SELECT * FROM student 
    JOIN takes  
    ON student.ID = takes.ID;
  1. SQLite supports LEFT OUTER JOIN only. How do we rewrite the following query on SQLite.
    SELECT * FROM studen 
    Right outer JOIN takes  
    ON student.ID = takes.ID;

We can do that by changing RIGHT OUTER JOIN to LEFT OUTER JOIN and switch the position of the tables around the join operator as follows:

    SELECT * FROM takes 
    LEFT outer JOIN studen  
    ON student.ID = takes.ID;
  1. SQLite supports only LEFT OUTER JOIN. How can rewrite the following query on SQLite.
    SELECT * FROM student 
    FULL outer JOIN takes  
    ON student.ID = takes.ID;

We can do that by performing LEFT OUTER JOIN twice where both table will switch places around the join operator and taking the union of the results of both queries as follows:

    SELECT S.ID, S.name, S.tot_cred, S.dept_name, T.course_id, 
        T.sec_id, T.semester, T.year, T.Grade  FROM student S
    lEFT outer JOIN takes T  
    ON S.ID = T.ID
    UNION 
    SELECT S.ID, S.name, S.tot_cred, S.dept_name, T.course_id, 
        T.sec_id, T.semester, T.year, T.Grade FROM takes T
    LEFT outer JOIN student S  
    ON S.ID = T.ID;

We are listing the set of attributes so that the order of the values will not change when taking the union. For this database, taking student left outer join takes will produce the required results but this is not true for general cases.

  1. Write a query that finds the names of all students that contain the substring “an” in their names
    SELECT name FROM student 
    WHERE name LIKE '%an%';
  1. Write a query that returns the names and tot_cred of students with total credits between 32 and 80 (inclusive)
  SELECT name, tot_cred FROM student 
  WHERE tot_cred >= 32 and tot_cred <= 80;
  1. Write a query that returns the information of the students in the department Biology and Physics using set operations
  SELECT * FROM student 
  WHERE dept_name = 'Biology' 
  union  
  SELECT * FROM student 
  WHERE dept_name = 'Physics';
  1. Write a query that returns the information of all students except the students in the computer science department using set operations
  SELECT * FROM student
  Except 
  SELECT * FROM student WHERE dept_name = 'Comp. Sci.';
  1. Given the query:
    SELECT dept_name, avg(salary) avg_salary 
    FROM instructor
    Group by dept_name
    HAVING avg_salary > 70000;
  • What does this query do? This query will return the names of the departments where the average instructor salary is strictly greater than 70000 with the average salary of the instructors in those departments.
  • Why we used HAVING? Because we used GROUP BY so we cannot use WHERE to specify the condition.
  • What about replacing HAVING by WHERE? If we would like to replace HAVING by WHERE the we need to use a subquery as follows:
  SELECT dept_name, avg_salary FROM 
    (SELECT dept_name, avg(salary) avg_salary FROM instructor
    Group by dept_name)
  WHERE avg_salary > 70000;
  1. Write a query to return the names of students with the largest and smallest number of tot_cred.
  SELECT name FROM student
  WHERE tot_cred = (Select max(tot_cred) from student) 
  OR tot_cred = (Select min(tot_cred) from student);
  1. Write a query to return the number of departments that have more than one student.
SELECT DISTINCT dept_name from student;
  1. Write a query to return the number of students in the Comp. Sci., Physics, Finance and History.
  SELECT dept_name, num_students FROM
  (SELECT dept_name, count (*) num_students FROM student S GROUP BY S.dept_name )
  WHERE dept_name IN ('Comp. Sci.', 'Physics', 'Finance', 'History');

We can even write a simpler query using HAVING since we have GROUP BY. We can rewrite the query as:

  SELECT dept_name, count (*) num_students 
  FROM student S GROUP BY S.dept_name
  HAVING dept_name IN ('Comp. Sci.', 'Physics', 'Finance', 'History');