Selection and Projection

Transcription

1 Tutorial - Relational Algebra CSC343 - Introduction to Databases Fall 008 TA: Lei Jiang CSC343: Intro. to Databases 1 Selection and Projection σ (R) = {s R s satisfies condition c} c --- selection based on condition c π (R) = R a 1,...,an a 1,...,an --- projection onto the columes a... a 1 n Relation R Relation R selection projection CSC343: Intro. to Databases 1

2 Selection and Projection Given following database schema, write following queries in relational algebra. doctors (dnum, dname, rank, phone) Q1: Who are the patients 10 years old or younger? σ ( ) age 10 patients Q: Who σ are the surgeons? ( doctors rank= surgeon ) Q3: What are the phone numbers of doctors? π, ( doctors dname phonenum ) Q4: What π are the phone numbers of surgeons?, ( σ dname phonenum rank surgeon( doctors = )) order matters CSC343: Intro. to Databases 3 Set Operations R I R = {s s R and s R } --- intersection of R and R, which must be "schema compatible" R U R = {s s R or s R } --- union of R and R, which must be "schema compatible" R - R = { s s R and s R } --- set difference of tuples from R and R, which must be "schema compatible" CSC343: Intro. to Databases 4

3 Set Operations Q5: Restate the expression σ ( ) age 10 age 60 patients using set operations. find the set A of patients with age >= 60; find the set B of patients with age <=10; take A union B. σ ( patients) Uσ ( patients) age 10 age 60 CSC343: Intro. to Databases 5 Set Operations Q6: Restate the expression σ ( ) rank surgeon rank oculist doctors using set operations without and. find the set A of oculists; find the set B of surgeon; find the set C of all doctors; (d) take C (A union B). doctors ( σ ( doctors) Uσ ( doctors)) rank= surgeon rank = oculist CSC343: Intro. to Databases 6 3

4 Set Operations Q7: Find all the patients who saw doctor 801 but not 80 (i.e. dnum=801, dnum 80) find the set A of patients who saw doctor 801 find the set B of patients who saw doctor 80; take A B. π σ ( visits) π σ ( visits) pnum dnum= 801 pnum dnum= 80 CSC343: Intro. to Databases 7 Cartesian Product and Join R 1 R = {<s 1,s > s1 R 1 and s R } --- cartesian product of R and R Ra 1 θ Rb σ R1a θ Rb 1 R R = (R R ) --- θ join, where θ can be <,, >,, =,, etc Ra 1 = Rb σ R1a = Rb 1 R R = (R R ) --- equi-join, same as θ join where θ is = R 1 R = σ R1a 1=Rb 1,...,R1a n=rb (R n 1 R ) --- nature join, same as equi-join on all common attributes May also project out R.b x CSC343: Intro. to Databases 8 4

5 Cartesian Product and Join Q8: Form peer groups for patients, where a peer group is a pair of patients where age difference is less than 10 years (can use the rename operator ρ A (R)) form the set A of all patient peer groups; select the pairs from A such that the age difference is less than 10 years σ ( ρ ( π ( patients)) ρ ( π ( patients))) A. age B. age A. age B. age+ 10 A. pnum B. pnum A pnum, age B pnum, age CSC343: Intro. to Databases 9 Cartesian Product and Join Q9: Who are the surgeons who visited the patient 101 (i.e. pnum = 101)? find the set A of visits by patient 101; find the set B of surgeons; join A and B on dnum. σ ( π ( )) π ( doctors))) visits. dnum= doctors. num rank = surgeon pnum= 101 pnum, dnum visits dnum, rank CSC343: Intro. to Databases 10 5

6 Cartesian Product and Join Q10: Who has seen a surgeon after April 11, 001? find the set A of patient visits after April 11, 001; find the set B of surgeons; join A and B on dnum and project onto pnum. π σ ( σ ( visits) σ ( doctors)) pnum visits. dnum= doctors. dnum date rank = surgeon CSC343: Intro. to Databases 11 Cartesian Product and Join Q11: Is there any non-surgeon doctors who performed a surgeon (a doctor performed a surgeon if the visit record shows diagnosis= operation for him)? The way of thinking: find the set A of non-surgeon; find the set B of patient visits where an operation is performed; join A and B on dnum and project onto dnum. Answer: πdnumσdoctors. dnum= visits. dnum( σrank surgeon( doctors) σdiagnosis= operation( visists)) CSC343: Intro. to Databases 1 6

7 Division Given two relation schemas R 1 (A,B) and R (A) where R 1.A and R.A has the same domain, R 1 / R = {x x is a A value such that for every B value y in (a tuple of) R there is a tuple <x,y> in R 1 } CSC343: Intro. to Databases 13 Divison Q1: Who has seen all the surgeons after April 11, 001? find the set A of patients who has seen some surgeon projected onto pnum and dnum; find the set B of all surgeon projected onto dnum; take A / B π ( σ ( visits)) π ( σ ( doctors)) pnum, dnum date dnum rank = surgeon CSC343: Intro. to Databases 14 7

8 Division Q13: Find all patients except for the youngest ones? find the Y set of the youngest patients by forming the set P of pairs of patients (A, B) where A.age <= B.age; dividing P by the set of all patients (so we get the set of patients who is younger than or has the same age as all patients) subtract Y from the set of all patients. π ( patients) ( σ ( ρ ( π ( patients)) ρ ( π ( patients))) π ( patients)) pnum, age A. age B. age A pnum, age B pnum, age pnum, age CSC343: Intro. to Databases 15 Division Given two relation schemas R 1 (A,B) and R (A), express division R 1 /R in terms of other RA operators. find the set S of A values that does not appear with some B values in a tuple of R1 by finding the set of P of all possible (A,B) pairs; subtracting P by R1 and projecting onto A find the set of L of all A values in R1 taking L S. R 1 / R = π A (R 1 ) π A ((π A (R 1 ) R ) R 1 ) CSC343: Intro. to Databases 16 8