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1 . Projection, selection and join operations Witold Rekuć Data Processing Technology 9

2 Operations on tables Relational operations Set theoretic operations Projection Union Selection Intersection Join Difference Division Complement Rename Witold Rekuć Data Processing Technology 0

3 Projection Projection results in a table that has a header restricted to the given set of column names r(r) - table r of a header R that is a projection argument X a header of a new table a set of column names (X R) q(x) = π X ( r (R) ) = { t[x] : t r } where t[x] denotes a row obtained by a restriction of the row t to values of X R X Witold Rekuć Data Processing Technology

4 Example r({a,b,c,d}) A B C D a5 b c d a6 b4 c5 d a6 b4 c d a6 b4 c d a b c d π {C,D} ( r ({A,B,C,D}) ) = q({c,d}) C c c5 c c c D d d d d d π {A,B} ( r ({A,B,C,D}) ) = q({a,b}) A a5 a6 a B b b4 b Witold Rekuć Data Processing Technology

5 Example Give names and telephone numbers of all companies q({name, Telephone}) = π {Name, Telephone} (Companies ({Id, Name, Street, City Id, Telephone})) q Companies Name Telephone Id Name Street City Id Telephone Our Company Abeja Audi Pafawag Iase Dolmed π {Name, Telephone} Our Company Abeja Audi Pafawag Iase Dolmed Our Street Abejow Street Audi Blvd. Wagon Place Energetic Lane Medical Street rows restricted to X={Name, Telephone} Witold Rekuć Data Processing Technology

6 Witold Rekuć Data Processing Technology 4

7 Example: Give city ids of the companies q({cityid}) = π {City Id} (Company ({Id,Name,Street,City Id,Telephone})) Witold Rekuć Data Processing Technology 5

8 q City Id π {City Id} Companies Id Name 0 Our Company Abeja Audi Pafawag Street Our Street Abejow Street Audi Blvd. Wagon Place City Id Telephone Iase Energetic Lane 56 5 Dolmed Medical Street Why there are duplictes of rows in the table q? Witold Rekuć Data Processing Technology 6

9 Witold Rekuć Data Processing Technology 7

10 Example: Give unique list of city ids of the companies q({cityid}) = π {City Id} (Company ({Id,Name,Street,City Id,Telephone})) Witold Rekuć Data Processing Technology 8

11 Companies q Id 0 Name Our Company Street Our Street City Id Telephone 4 City Id Abeja Abejow Street 4 55 Pafawag Wagon Place π {KodMjc} Audi Audi Blvd. 4 Iase Energetic Lane 56 5 Dolmed Medical Street Witold Rekuć Data Processing Technology 9

12 Example Having a table MonthTurnover we would like to calculate an average value of the month turnover. q({turnover}) = π {Obrót} ( MonthTurnover ({Month,Turnover}) ) q MonthTurnover Turnover Month Turnover π {Turnover} January February March April Mai June Leave duplicates in the result table Avg = ( )/6 = 66,67 Avg = ( )/ = 00 Witold Rekuć Data Processing Technology 40

13 Expressing projection by means of SQL select Name, Telephone from Companies; select distinct Name, Telephone from Companies; select * from Companies; Witold Rekuć Data Processing Technology 4

14 Selection Selection results in a table that has a header equal to the header of the argument table but with rows restricted to those satisfying a given condition r(r) F table r of a header R that is a selection argument selection condition (logical expression) q(r) = σ F ( r (R) ) = { t : t r i F(t) = true } rows satisfying the selection condition Witold Rekuć Data Processing Technology 4

15 Przykład r({a,b,c,d}) A B C D a5 a a6 4 a5 a6 4 a a6 4 a a a σ σ B=4 B=4 and D< ( r ({A,B,C,D}) ) = q ({A,B,C,D}) A B C D a6 4 a5 a6 4 a a6 4 a ( r ({A,B,C,D}) ) = q ({A,B,C,D}) A B C D a6 4 a σ B=4 or D< ( r ({A,B,C,D}) ) = q ({A,B,C,D}) A B C D a5 a a6 4 a5 a6 4 a a6 4 a a a Witold Rekuć Data Processing Technology 4

16 Example Give the list of cities from the province DL q({id,name,prov Id}) = σ Prov Id = DL ( Cities ({Id,Name,Prov Id}) ) Cities q Id Name Wrocław Prov Id DL Wrocław DL σ Prov Id = DL Wałbrzych DL Id Name Prov Id Opole OP Wałbrzych DL 4 Warszawa MZ 5 6 Katowice Kraków SL MP Witold Rekuć Data Processing Technology 44

17 Witold Rekuć Data Processing Technology 45

18 q({... })=σ (City Id=) and (Companies({Id,Name,Street,City Id,Telephone})) (Telephone is NULL) Witold Rekuć Data Processing Technology 46

19 q({... })=σ (City Id=) or (Companies({Id,Name,Street,City Id,Telephone})) (Telephone is NULL) Witold Rekuć Data Processing Technology 47

20 Expressing selection by means of the SQL select * from Cities where [Prov Id] = DL ; select * from Companies where ([City Id] = ) and (Telephone IS NULL); select * from Companies where ([City Id] = ) or (Telephone IS NULL); Witold Rekuć Data Processing Technology 48

21 Composition of projection and selection operations q(x) = π X (σ F ( r (R) ) Example Give names of companies from Opole, which telephone number is unknown. q({name})=π {Name} (σ (City id=) and (Companies({Id,Name,Street,City id,telephone}))) (Telephone is NULL) q Companie sid Name 0 Our Company Street Our Street City Id Telephone 4 Name Abeja Abejow Street 4 55 Audi Pafawag π {Name} ( σ (City Id=) and (Telephone is NULL) Audi Pafawag Audi Blvd. Wagon Place 4 Iase Energetic Lane 56 5 Dolmed Medical Street Witold Rekuć Data Processing Technology 49

22 q({name})=π {Name} (σ (City Id=) and (Companies({Id,Name,Stret,City Id,Telephone}))) (Telephone is NULL) Witold Rekuć Data Processing Technology 50

23 Expressing projection and selection by means of the SQL select Name from Companies where [City Id] = and Telephone IS NULL; Witold Rekuć Data Processing Technology 5

24 Join operation The problem: we would like to get the list of companies and city names Companies Id Name Street 0 Our Our Street Company Abeja Abejow Street Audi Audi Blvd. Pafawag Wagon Place City Id Telephone Cities Id Name Wrocław Opole Wałbrzych Prov Id DL OP DL Comp007.accdb Province Id Name DL Dolnośląskie OP Opolskie 4 Iase Energetic Lane 56 5 Dolmed Invoices Id SellerId Medical Street BuyerId Date Invoice items DocI BuyerId d /0 0 ItemN o ProdId 00 NetPrice,00 Quantity 0 / / ,50 00 / / ,00 50 / /0 00,00 00 / /0 00,00 0 / / ,50 0 4/ /0 0 00,00 45 Products /0 / ,50 7, id 00 Name Pâté Unit kg VatRate 7% /0 / ,0, Sausage Mortadela Crisps Coffee Jakobs kg packet 400g packet 00g 7% 7% 7% /0 4/ ,60, Mackerel can 50g 7% Witold Rekuć Data Processing Technology 5

25 Companies Id 0 Name Our Company Street Our Street City Id Telephone 4 Cities Abeja Abejow Street 4 55 Id Name Prov Id Audi Audi Blvd. Wrocław DL 4 Pafawag Iase Wagon Place Energetic Lane 56 Opole Wałbrzych OP DL 5 Dolmed Medical Street Witold Rekuć Data Processing Technology 5

26 Equijoin (equi-join) operation r(r) table r having header R, attribute A R s(s) table s having header S, attribute B S R i S are disjoint, don't have common names (R S = Ø) q(r S) = r [ A=B ] s = { t : t[r] r, t[s] s i t[a] = t[b] } r R A s S B v v t v v Witold Rekuć Data Processing Technology 54

27 Companies Id Name Street 0 Our Our Street Company Abeja Abejow Street Audi Audi Blvd. Pafawag Wagon Place 4 Iase Energetic Lane City Id Telephone Cities Id Name Wrocław Opole Wałbrzych Prov Id DL OP DL 5 Dolmed Medical Street Companies [ City Id = Id ] Cities List of compnies Id Name Street City Id Telephone Cities.Id Cities.Name Prov Id 0 Our Company Our Comapny 4 Wrocław DL Abeja Abejow Street 4 55 Wałbrzych DL Audi Audi Bvld. Opole OP Pafawag Wagon Lane Opole OP 4 Iase Energetic Lane 56 Wałbrzych DL 5 Dolmed Medcal Street Wrocław DL Witold Rekuć Data Processing Technology 55

28 Companies [ City Id = Id ] Cities Witold Rekuć Data Processing Technology 56

29 Companies [ ] Cities = Companies Cities Witold Rekuć Data Processing Technology 57

30 Composition of projection, selection and equi-join operations q(x) = π X (σ F ( r [A=B] s ) Example π {Invoices.Date} (σ Cities.Name= Wałbrzych ( Invoices [Buyer Id=Id] Companies [City Id=Id ] Cities )) Witold Rekuć Data Processing Technology 58

31 Composition of projection, selection and equi-join operations Witold Rekuć Data Processing Technology 59

32 Cartesian product Witold Rekuć Data Processing Technology 60

33 Equi-join of many tables Witold Rekuć Data Processing Technology 6

34 Expressing projection, selection and equi-join by means of SQL select Companies.Name, Cities.Name from Companies inner join Cities on Companies.[City Id]=Cities.Id; select Companies.Name, Cities.Name from Companies inner join Cities on Companies.[City Id]=Cities.Id where Companies.Telephone is Null; select Invoices.Id, Companies.Name, Invoices.Date from ( [Invoice Items] inner join Invoices on ([Invoice Items].[Seller Id] = Invoices.[Seller Id]) and ([Invoice Items].Id = Invoices.Id) ) inner join Companies on Invoices.[Seller Id] = Companies.Id; Witold Rekuć Data Processing Technology 6

35 Examples C( Id, Name ) P ( Id, Name ) n a na n b nb n c nc 4 n4 In (Id, SiD, BiD,Date) InI ( InvId, SiD, Id, PiD Pr Qua) d a 0 d b 5 d a 0 4 d a d b 7 c 4 5 a 5 c b 4 4 c 0 5 Witold Rekuć Data Processing Technology 6

36 Compute: ) π{date}(in) ) σsid= and BiD=(In), σsid= or BiD=(In) ) π{nrd,nrs}(σsmb=a(ini)) 4) In [SiD=Id] C, In [BiD=Id] C, In [Id=InvId, SiD=SiD] InI Write expressions for the following queries given in the natural language: ) Give names of the companies, which bought something on 'd'. ) Give names of the products bought by the company of the name 'n'. ) Give dates at which product of the name 'na' was bought. 4) Give the names of products that was bought at price >. Witold Rekuć Data Processing Technology 64

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