sol practice1
TRANSCRIPT
7/28/2019 Sol Practice1
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C S E 2 3 2 F a l l , 2 0 0 0
S o l u t i o n s t o p r a c t i c e p r o b l e m s o n q u e r i e s
1 . ( a ) L i s t t h e b a r s t h a t s e r v e a b e e r t h a t J o e l i k e s .
( i ) t u p l e c a l c u l u s :
f b : b a r j 9 s 2 s e r v e s 9 l 2 l i k e s
( s ( b a r ) = b ( b a r ) ̂ s ( b e e r ) = l ( b e e r ) ̂ l ( d r i n k e r ) = J o e ) g :
( i i ) d o m a i n c a l c u l u s :
f b : b a r j 9 c : b e e r ( s e r v e s ( b ; c ) ̂ l i k e s ( c ; J o e ) ) g :
( i i i ) r e l a t i o n a l a l g e b r a :
b a r
( s e r v e s 1
d r i n k e r = J o e
( l i k e s ) ) :
( i v ) S Q L :
s e l e c t s e r v e s . b a r
f r o m s e r v e s , l i k e s
w h e r e s e r v e s . b e e r = l i k e s . b e e r
A N D l i k e s . d r i n k e r = \ J o e "
( v ) Q B E :
s e r v e s b a r b e e r
b c
l i k e s d r i n k e r b e e r
J o e c
a n s w e r b a r
I . b
( b ) L i s t t h e d r i n k e r s t h a t f r e q u e n t a t l e a s t o n e b a r t h a t s e r v e s a b e e r
t h e y l i k e .
( i ) t u p l e c a l c u l u s :
f d : d r i n k e r j 9 f 2 f r e q u e n t s 9 s 2 s e r v e s 9 l 2 l i k e s
( f ( d r i n k e r ) = d ( d r i n k e r ) ̂ f ( b a r ) = s ( b a r )
̂ s ( b e e r ) = l ( b e e r ) ̂ l ( d r i n k e r ) = d ( d r i n k e r ) ) g
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( i i ) d o m a i n c a l c u l u s :
f d : d r i n k e r j 9 b 9 c f r e q u e n t s ( d ; b ) ̂ s e r v e s ( b ; c ) ̂ l i k e s ( d ; c ) ] g
( i i i ) r e l a t i o n a l a l g e b r a :
d r i n k e r
( f r e q u e n t s 1 s e r v e s 1 l i k e s )
( i v ) S Q L :
s e l e c t f r e q u e n t s . d r i n k e r
f r o m f r e q u e n t s , s e r v e s , l i k e s
w h e r e f r e q u e n t s . b a r = s e r v e s . b a r
a n d s e r v e s . b e e r = l i k e s . b e e r
a n d l i k e s . d r i n k e r = f r e q u e n t s . d r i n k e r
( v ) Q B E :
f r e q u e n t s d r i n k e r b a r
d b
s e r v e s b a r b e e r
b c
l i k e s d r i n k e r b e e r
d c
a n s w e r d r i n k e r
I . d
( c ) L i s t t h e d r i n k e r s t h a t f r e q u e n t o n l y b a r s t h a t s e r v e s o m e b e e r
t h a t t h e y l i k e .
( A s s u m e e a c h d r i n k e r l i k e s a t l e a s t o n e b e e r a n d f r e q u e n t s a t l e a s t
o n e b a r . )
( i ) t u p l e c a l c u l u s :
f d : d r i n k e r j 8 f 2 f r e q u e n t s f ( d r i n k e r ) = d ( d r i n k e r ) !
9 s 2 s e r v e s 9 l 2 l i k e s ( s ( b a r ) = f ( b a r ) ̂
s ( b e e r ) = l ( b e e r ) ̂ l ( d r i n k e r ) = d ( d r i n k e r ) ) g
( i i ) d o m a i n c a l c u l u s :
f d : d r i n k e r j 8 b f r e q u e n t s ( d ; b ) !
9 c ( s e r v e s ( b ; c ) ̂ l i k e s ( d ; c ) ) ] g
( i i i ) r e l a t i o n a l a l g e b r a :
d r i n k e r
( f r e q u e n t s )
d r i n k e r
f r e q u e n t s
d r i n k e r ; b a r
( s e r v e s 1 l i k e s ) ] :
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( i v ) S Q L :
s e l e c t d r i n k e r
f r o m f r e q u e n t s
w h e r e d r i n k e r n o t i n
( s e l e c t f . d r i n k e r
f r o m f r e q u e n t s f
w h e r e f . b a r n o t i n
( s e l e c t b a r
f r o m s e r v e s , l i k e s
w h e r e s e r v e s . b e e r = l i k e s . b e e r
a n d l i k e s . d r i n k e r = f . d r i n k e r ) )
( v ) Q B E :
S t a g e I ( n d c o m p a t i b l e d r i n k e r - b a r p a i r s ) :
s e r v e s b a r b e e r
b c
l i k e s d r i n k e r b e e r
d c
c o m p a t i b l e d r i n k e r b a r
I . d b
S t a g e I I ( n d d r i n k e r s w h o f r e q u e n t s o m e i n c o m p a t i b l e b a r ) :
f r e q u e n t s d r i n k e r b a r
d b
c o m p a t i b l e d r i n k e r b a r
: d b
b a d d r i n k e r
I . d
S t a g e I I I ( n d a n s w e r b y t a k i n g t h e c o m p l e m e n t ) :
f r e q u e n t s d r i n k e r b a r
d
b a d d r i n k e r
: d
a n s w e r d r i n k e r
I . d
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( d ) L i s t t h e d r i n k e r s t h a t f r e q u e n t n o b a r t h a t s e r v e s a b e e r t h a t t h e y
l i k e .
T h i s i s j u s t t h e c o m p l e m e n t o f ( b ) .
2 . ( a ) L i s t t h e a c t o r s c a s t i n a t l e a s t o n e m o v i e b y K u r o s a w a ( h e r e a n d
b e l o w , K s t a n d s f o r K u r o s a w a ) .
( i ) d o m a i n c a l c u l u s :
f a : a c t o r j 9 t f i l m ( t ; K ; a ) g :
( i i ) r e l a t i o n a l a l g e b r a :
a c t o r
(
d i r e c t o r = K
( f i l m ) ) :
( i i i ) S Q L :
s e l e c t a c t o r
f r o m l m
w h e r e d i r e c t o r = K
( i v ) Q B E :
l m t i t l e d i r e c t o r a c t o r
K P .
( b ) L i s t t h e a c t o r s c a s t i n e v e r y m o v i e b y K u r o s a w a .
( i ) d o m a i n c a l c u l u s :
f a : a c t o r j 8 t 9 x ( f i l m ( t ; K ; x ) ) ! f i l m ( t ; K ; a ) g :
( i i ) r e l a t i o n a l a l g e b r a :
a c t o r
( f i l m )
a c t o r
t i t l e
(
d i r e c t o r = K
( f i l m ) ) 1
a c t o r
( f i l m )
t i t l e ; a c t o r
(
d i r e c t o r = K
( f i l m ) ) ]
A l s o ,
t i t l e ; a c t o r
( f i l m )
t i t l e
(
d i r e c t o r = K
( f i l m ) ) :
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( i i i ) S Q L :
s e l e c t a c t o r
f r o m l m
w h e r e a c t o r n o t i n
( s e l e c t f . a c t o r
f r o m l m f g
w h e r e g . d i r e c t o r = K a n d f . a c t o r n o t i n
( s e l e c t a c t o r
f r o m l m
w h e r e t i t l e = g . t i t l e ) )
( i v ) Q B E :
S t a g e I
l m t i t l e d i r e c t o r a c t o r
a
t K
: t a
b a d - a c t o r s a c t o r
I . a
S t a g e I I
l m t i t l e d i r e c t o r a c t o r
a
b a d - a c t o r s a c t o r
: a
a n s w e r a c t o r
I . a
( c ) L i s t t h e a c t o r s c a s t o n l y i n m o v i e s b y K u r o s a w a .
( i ) d o m a i n c a l c u l u s :
f a : a c t o r j 8 t 8 d f i l m ( t ; d ; a ) ! d = K ] g
( i i ) r e l a t i o n a l a l g e b r a :
a c t o r
( f i l m )
a c t o r
(
d i r e c t o r 6= K
( f i l m ) ) :
( i i i ) S Q L :
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s e l e c t a c t o r
f r o m l m
w h e r e a c t o r n o t i n
( s e l e c t a c t o r
f r o m l m
w h e r e d i r e c t o r 6= K )
( i v ) Q B E :
S t a g e I
l m t i t l e d i r e c t o r a c t o r
6= K a
b a d - a c t o r s a c t o r
I . a
S t a g e I I
l m t i t l e d i r e c t o r a c t o r
a
b a d - a c t o r s a c t o r
: a
a n s w e r a c t o r
I . a
( d ) L i s t a l l p a i r s o f a c t o r s w h o a c t t o g e t h e r i n a t l e a s t o n e m o v i e .
( i ) d o m a i n c a l c u l u s :
f a
1
: a c t o r
1
; a
2
: a c t o r
2
j 9 t 9 d ( f i l m ( t ; d ; a
1
) ̂ f i l m ( t ; d ; a
2
) ) g
( i i ) r e l a t i o n a l a l g e b r a :
a c t o r
1
; a c t o r
2
a c t o r ! a c t o r
1
( f i l m ) 1
a c t o r ! a c t o r
2
( f i l m ) ]
( i i i ) S Q L :
s e l e c t f . a c t o r , g . a c t o r
f r o m l m f g
w h e r e f . t i t l e = g . t i t l e
( i v ) Q B E :
l m t i t l e d i r e c t o r a c t o r
t a
1
t a
2
a n s w e r a c t o r
1
a c t o r
2
I . a
1
a
2
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( e ) L i s t a l l p a i r s o f a c t o r s c a s t i n e x a c t l y t h e s a m e m o v i e s .
( i ) d o m a i n c a l c u l u s :
f a
1
: a c t o r
1
; a
1
: a c t o r
2
j 8 t 8 d f i l m ( t ; d ; a
1
) $ f i l m ( t ; d ; a
2
) ] g
( i i ) r e l a t i o n a l a l g e b r a :
C o n s i d e r r s t t h e q u e r y q a s k i n g f o r p a i r s o f a c t o r s < a ; a
0
>
s u c h t h a t a a c t s i n e v e r y m o v i e w h e r e a
0
a c t s . T h i s i s e x -
p r e s s e d b y :
a c t o r
( f i l m )
a c t o r ! a c t o r
0
(
a c t o r
( f i l m ) )
a c t o r ; a c t o r
0
a c t o r
( f i l m )
a c t o r ! a c t o r
0
( f i l m ) f i l m
a c t o r ! a c t o r
0
(
a c t o r
( f i l
T h e g i v e n q u e r y i s n o w e x p r e s s e d b y :
q 1
a c t o r ; a c t o r
0
! a c t o r
0
; a c t o r
( q ) :
( i i i ) S Q L :
s e l e c t f . a c t o r , g . a c t o r
f r o m l m f g
w h e r e < f . a c t o r , g . a c t o r > n o t i n Q
a n d < g . a c t o r , f . a c t o r > n o t i n Q
w h e r e Q i s :
s e l e c t x . a c t o r , y . a c t o r
f r o m l m x y
w h e r e y . a c t o r n o t i n
( s e l e c t a c t o r
f r o m l m
w h e r e t i t l e = x . t i t l e )
( i v ) Q B E :
S t a g e I
l m t i t l e d i r e c t o r a c t o r
a
1
t a
2
: t a
1
b a d a c t o r
1
a c t o r
2
I . a
1
a
2
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S t a g e I I
l m t i t l e d i r e c t o r a c t o r
a
1
a
2
b a d a c t o r
1
a c t o r
2
: a
1
a
2
: a
2
a
1
a n s w e r a c t o r
1
a c t o r
2
I . a
1
a
2
( f ) L i s t t h e d i r e c t o r s s u c h t h a t e v e r y a c t o r i s c a s t i n o n e o f h i s / h e r
l m s .
( i ) d o m a i n c a l c u l u s :
f d : d i r e c t o r j 8 a 9 t 9 e ( f i l m ( t ; e ; a ) ) ! 9 t f i l m ( t ; d ; a ) ] g
( i i ) r e l a t i o n a l a l g e b r a :
d i r e c t o r ; a c t o r
( f i l m )
a c t o r
( f i l m ) :
( i i i ) S Q L :
s e l e c t d i r e c t o r
f r o m l m
w h e r e d i r e c t o r n o t i n
( s e l e c t f . d i r e c t o r
f r o m l m f g
w h e r e f . d i r e c t o r n o t i n
( s e l e c t d i r e c t o r
f r o m l m
w h e r e a c t o r = g . a c t o r ) )
( i v ) Q B E :
S t a g e I
l m t i t l e d i r e c t o r a c t o r
d
a
: d a
b a d - d i r e c t o r s d i r e c t o r
I . d
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S t a g e I I
l m t i t l e d i r e c t o r a c t o r
d
b a d - d i r e c t o r s d i r e c t o r
: d
a n s w e r d i r e c t o r
I . d
3 . ( a ) T r u e . T h e p r o o f u s e s d i s t r i b u t i v i t y o f e x i s t e n t i a l q u a n t i c a t i o n
o v e r d i s j u n c t i o n .
( b ) F a l s e ( n o t e t h a t t h i s s a y s , e s s e n t i a l l y , t h a t e x i s t e n t i a l q u a n t i c a
t i o n d i s t r i b u t e s o v e r c o n j u n c t i o n ) . A c o u n t e r e x a m p l e i s :
R A B
0 0
S A B
0 1
( c ) F a l s e . S a m e c o u n t e r x a m p l e a s f o r ( b ) .
4 . O n e w a y t o m a k e t h e e v a l u a t i o n m o r e e c i e n t i s t o r e w r i t e t h e q u e r y
a s
d i r e c t o r
t i t l e ; d i r e c t o r
( m o v i e ) 1
t i t l e
(
t h e a t e r 6= " C o v e "
( s c h e d u l e ) ) ]
T h i s c u t s d o w n t h e s i z e o f r e l a t i o n s p a r t i c i p a t i n g i n t h e j o i n a n d a v o i d s
b u i l d i n g u p a n u n n e c e s s a r i l y l a r g e i n t e r m e d i a t e r e s u l t ( r e s u l t i n g f r o m
t h e j o i n ) .
5 . C o n s i d e r t h e f o l l o w i n g r s p j a l g e b r a q u e r y ( R i s a r e l a t i o n w i t h a t -
t r i b u t e s A B C ) :
A C
A B
( R ) 1
B C
( R ) ] 1
A
A C
( R ) 1
C B
( R ) ] :
( a ) T h e t a b l e a u c o r r e s p o n d i n g t o t h e q u e r y i s :
A B C
a b
1
c
1
a
1
b
1
c
a b
2
c
2
a
2
b
3
c
2
a c
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( b ) T h e r e i s a h o m o m o r p h i s m o f t h e t a b l e a u m a p p i n g t h e 2 n d a n d
3 r d r o w s t o t h e r s t . S o t h e m i n i m i z e d t a b l e a u i s :
A B C
a b
1
c
1
a
1
b
1
c
a c
( c ) A n r s p j a l g e b r a q u e r y c o r r e s p o n d i n g t o t h e m i n i m i z e d t a b l e a u i s :
A C
(
A B
( R ) 1
B C
( R ) ) :
( d ) R e d o ( a ) , ( b ) , ( c ) f o r t h e q u e r y :
A C
A B
( R ) 1
B C
(
B = 8
( R ) ) ] 1
A
A C
(
A = 5
( R ) ) 1
C B
( R ) ] :
T h e c o r r e s p o n d i n g t a b l e a u i s :
A B C
5 8 c
1
a
1
8 c
5 b
1
c
2
a
2
b
2
c
2
5 c
T h e l a s t t w o r o w s c a n b e m a p p e d t o t h e r s t . T h e m i n i m i z e d
t a b l e a u i s :
A B C
5 8 c
1
a
1
8 c
5 c
A c o r r e s p o n d i n g a l g e b r a q u e r y i s :
A C
(
A = 5
B = 8
( R ) ) 1
C
(
B = 8
( R ) ) :
1 0
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6 . ( i ) T h e t a b l e a u T c o r r e s p o n d i n g t o q i s
A B C
a b
1
c
1
a
1
b c
1
a
2
b c
2
a
2
b
2
c
a b c
C h a s i n g w i t h r e s p e c t t o = f A C ! B ; B ! C ; C ! A g y i e l d s :
C H A S E
( T ) =
A B C
a b c
1
a b c
1
a b c
1
a b
2
c
a b c
E l i m i n a t i n g d u p l i c a t e r o w s f r o m C H A S E
( T ) y i e l d s t h e m i n i m a l t a b l e a u :
A B C
a b c
1
a b
2
c
a b c
a n d t h e c o r r e s p o n d i n g r s p j q u e r y i s
A B
( R ) 1
A C
( R ) :
( i i ) T h e t a b l e a u T c o r r e s p o n d i n g t o q i s
A B C
a b
1
5
a
1
b 5
8 b c
2
8 b
2
c
a b c
C h a s i n g w i t h r e s p e c t t o = f A C ! B ; B ! C ; C ! A g y i e l d s ( a f t e r
e l i m i n a t i n g d u p l i c a t e r o w s ) :
1 1