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Database Systems &Applications

Lec 12Relational Algebra

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3

Building Complex Expressions

Combine operators with parentheses andprecedence rules.

Three notations, just as in arithmetic:

1. Sequences of assignment statements.

2. Expressions with several operators.

3. Expression trees.

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4

Sequences of Assignments

Create temporary relation names.

Renaming can be implied by giving relations a listof attributes.

Example: R3 := R1 C R2 can be written:

R4 := R1 X R2

R3 := C(R4)

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5

Expressions in a Single Assignment

Example: the theta-join R3 := R1C

R2 can

written: R3 := C

(R1 X R2)

Precedence of relational operators:1. [SELECT, PROJECT, RENAME] (highest).

2. [PRODUCT, JOIN].

3. INTERSECTION.

4. [UNION, DIFFERENCE]

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6

Expression Trees

Leaves are operands --- either variables standingfor relations or particular constant relations.

Interior nodes are operators, applied to their childor children.

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7

Example

students_t(st_id, name)

st_courses_t(st_id1, c_no, sem, year, grade)

Find the st_ids of all the students those are eitherA7 or grade = B.

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8

As a Tree:

students_tst_courses_t

SELECTdiscipline = A7 SELECTgrade = B

PROJECTst_id

RENAMER(st_id)

PROJECTst_id1

UNION

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Example

st_courses_t(st_id1, c_no, sem, year, grade)

Find the students who got same grade in two

different courses.

Strategy: by renaming, define a copy ofst_courses_t, called stc(st_id1, c_no1, sem, year,

grade). The natural join ofst_courses_t and stcconsists of (st_id1, c_no, c_no1, sem,year,grade) such that the students who gotsame grade in two different courses.

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The Tree

st_courses_tst_courses_t

RENAMEstc(st_id1, c_no1, sem, year, grade)

JOIN

PROJECTst_id1

SELECTc_no != c_no1

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11

Schemas for Results ---(1)

Union, intersection, and difference: theschemas of the two operands must be thesame, so use that schema for the result.

Selection: schema of the result is the same asthe schema of the operand.

Projection: list of attributes tells us theschema.

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Schemas for Results --- (2)

Product: schema is the attributes of bothrelations.

Use R.A, etc., to distinguish two attributesnamedA.

Theta-join: same as product.

Natural join: union of the attributes of the tworelations.

Renaming: the operator tells the schema.

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Consider the following schema.

People(PID,name,address,gender,age)

Planet(Plname,colour,shade,Galaxy)

Live(PID,Plname,migratedfrom,status)

(A person can be migrated from one planet to anotherplanet at any time. Depending on that the status will be

living or shifted. By birth the value of migratedfrom for

a given PID is NULL)

Property(PrID,PID,Plname,type)

GuestHouse(GID,No.of.Bed rooms)

Haveasite(SID,sqfts)

Another Example

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a. Find the names of people who live on redplanet.

b. Find the names of people who live on blueplanet at present but never lived on greenplanet

c. Find the plnames in the order of demand.(The demand is more for dark shadeplanets and then for the planets which are inMilky Way Galaxy and then for others.

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1 .Draw the expression tree for the followingquery.Find the names of male people who is having a

guest house with 3 bed rooms on green colourplanet.

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