Tema 3B

3,/$
'(),1,&,Ð1'(3,/$
'HVFULEDQVHODVVLJXLHQWHVLPDJHQHV
'HILQLFLyQGHOWLSROLQHDO
¢3RUTXp
GLJR3,/$"
¢(QTXpVHSDUHFHHVWD
'HVDSLODUHOOLEUR
LPDJHQDODDQWHULRU"
(6758&785$
/,)2/DVW,Q)LUVW2XW
´HO~OWLPRTXHHQWUDHVHOSULPHURTXHVDOHµ
‡/DVLQVHUFLRQHVVHUHDOL]DQSRUXQH[WUHPR\
ODVH[WUDFFLRQHVSRUHOPLVPRH[WUHPRWRSH
‡ (O HOHPHQWR TXH VH SXHGH FRQVXOWDU HQ WRGR
PRPHQWRHVHO~OWLPRTXHVHLQVHUWyWRSH
$SLODUHOOLEUR
VLJXH'(),1,&,Ð1'(3,/$
23(5$&,21(6
(63(&,),&$&,Ð1'(3,/$R7$'
&RQVWUXFWRUDVGHOWLSR
◆FUHDSSFUHDXQDSLODYDFtDS
0RGLILFDGRUDGHOWLSR
◆DSLODUSHLQVHUWDXQHOHPHQWRHQODSLOD
7,32 SLOD [HOHPHQWR]
6,17$;,6
SURFHGLPLHQWRFUHDSVDOSSLOD
SURFHGLPLHQWRDSLODUHQWVDOSSLODHQWHHOHPHQWR
SURFHGLPLHQWRGHVDSLODUHQWVDOSSLOD
IXQFLyQWRSHSSSLODGHYXHOYHHOHPHQWR
IXQFLyQYDFLDS"SSLODGHYXHOYHOyJLFR
6(0É17,&$
◆GHVDSLODUSH[WUDHXQHOHPHQWRGHODSLOD
&RQVXOWRUDVGHOWLSR
◆WRSHSSREWLHQHHOHOHPHQWRWRSHGHODSLOD
◆ YDFLDS"SGHYXHOYH&,(572VLODSLODHVWiYDFtD
\)$/62HQFDVRFRQWUDULR
{}
creap(p)
{p=λ}
{p=P1 P2 .. Pn ∧ e=E}
apilar(p,e)
{p=P1 P2 .. Pn E}
FRQWLQXD➠
&2/$
VLJXH7$'3,/$
'HVFULEDQVHODVVLJXLHQWHVLPDJHQHV
'HILQLFLyQGHOWLSROLQHDO
VLJXH6(0É17,&$
{p=P1 P2 .. Pn ∧ p<>λ}
desapilar(p)
{p= P1 .. Pn-1}
¢3RUTXp
GLJR&2/$"
..
{p=P1 P2 .. Pn ∧ p<>λ}
e:=topep (p)
{p=P1 P2 .. Pn ∧ e = Pn }
¢(QTXpVHSDUHFH
HVWDLPDJHQ
{p=P1 P2 .. Pn}
b:=vaciaq?(p)
3RQHUVHDODFROD
{p=P1 P2 .. Pn ∧ b=(p=λ)}
´(OVLJXLHQWHµ
23(5$&,21(6
(6758&785$
),)2)LUVW,Q)LUVW2XW
´HOSULPHURTXHHQWUDHVHOSULPHURTXHVDOHµ
‡/DVLQVHUFLRQHVVHUHDOL]DQSRUXQH[WUHPR\
ODVH[WUDFFLRQHVSRUHORWUR
‡ (O HOHPHQWR TXH VH SXHGH FRQVXOWDU HQ WRGR
PRPHQWRHVHOTXHSULPHURVHLQVHUWy
VLJXH'(),1,&,Ð1'(&2/$
'(),1,&,Ð1'(&2/$
DHVWD"
&RQVWUXFWRUDVGHOWLSR
◆FUHDTTFUHDXQDFRODYDFtDT
◆HQFRODUTHLQVHUWDXQHOHPHQWRHQODFRODT
0RGLILFDGRUDGHOWLSR
◆GHVHQFRODUTHOLPLQDHOSULPHUHOHPHQWRGHT
&RQVXOWRUDVGHOWLSR
◆SULPHURTREWLHQHHOSULPHUHOHPHQWRGHT
◆ YDFLDT"T GHYXHOYH &,(572 VL OD FROD T HVWi
YDFtD\)$/62HQFDVRFRQWUDULR
(63(&,),&$&,Ð1'(&2/$R7$'
VLJXH7$'&2/$
VLJXH6(0É17,&$
7,32 FROD [HOHPHQWR]
6,17$;,6
{q=Q1 Q2 .. Qn ∧ q<>λ}
desencolar(q)
{q= Q2 .. Qn}
SURFHGLPLHQWRFUHDTVDOTFROD
SURFHGLPLHQWRHQFRODUHQWVDOTFRODHQWHHOHPHQWR
SURFHGLPLHQWRGHVHQFRODUHQWVDOTFROD
IXQFLyQSULPHURTFRODGHYXHOYHHOHPHQWR
IXQFLyQYDFLDT"TFRODGHYXHOYHOyJLFR
{q=Q1 Q2 .. Qn ∧ q<>λ}
e:=primero (q)
{q=Q1 Q2 .. Qn ∧ e = Q1}
6(0É17,&$
{q=Q1 Q2 .. Qn ∧ e=E}
encolar(q,e)
{q=Q1 Q2 .. Qn E}
{}
creaq(q)
{q=λ}
FRQWLQXD➠
'HILQLFLyQGHOWLSROLQHDO/,67$FRQSXQWR
'HVFULEDQVHODVVLJXLHQWHVLPDJHQHV
GHLQWHUpV
¢3RUTXp
GLJROLVWD"
{q=Q1 Q2 .. Qn }
b:=vaciaq?(q)
{q=Q1 Q2 .. Qn ∧ b=(q=λ)}
'(),1,&,Ð1'(/,67$FRQSXQWR
GHLQWHUpV
(6758&785$
8QDOLVWDHVXQDVHFXHQFLDGHHOHPHQWRVGHXQWLSR
GDGR RUGHQDGRV OLQHDOPHQWH VHJ~Q OD SRVLFLyQ TXH
RFXSDQHQODPLVPD
8QDOLVWDFRQSXQWRGHLQWHUpVHVXQDOLVWDTXH
WLHQHXQDSRVLFLyQHVSHFLDORGLVWLQJXLGDVREUHODTXH
VHDSOLFDQODVGLVWLQWDVRSHUDFLRQHV
¢(QTXpVHSDUHFH
HVWDLPDJHQ
/D3ULPHUD
´/DVLJXLHQWHµ
¢4XpFDUWDHV"
(OLPLQDUOD
DHVWD"
(OSXQWRGHLQWHUpVVHSXHGHFDPELDUFRQORTXHHV
SRVLEOH RSHUDU VREUH ORV GLVWLQWRV HOHPHQWRV GH OD
OLVWD
VLJXH'(),1,&,Ð1'(/,67$FRQSXQWR
GHLQWHUpV
23(5$&,21(6
VLJXH23(5$&,21(6GHOD/,67$FRQ
SXQWRGHLQWHUpV
② 2SHUDFLRQHVSDUDFDPELDUHOSXQWRGHLQWHUpV:
① 2SHUDFLRQHVSDUDPDQLSXODUODOLVWD:
◆SULQFLSLROVLW~DHOSXQWRGHLQWHUpVGHODOLVWDO
◆FUHDOOFUHDXQDQXHYDOLVWDYDFtDO
◆LQVHUWDOH LQVHUWD XQ HOHPHQWR HQ OD OLVWD O HQ OD
DOSULQFLSLR
SRVLFLyQLQPHGLDWDPHQWHDQWHULRUDODGLVWLQJXLGD
◆ILQOVLW~DHOSXQWRGHLQWHUpVDOILQDO
◆ VXSULPHO HOLPLQD HO HOHPHQWR TXH HVWi HQ OD
◆ VLJXLHQWHO FDPELD HO SXQWR GH LQWHUpV GH OD
SRVLFLyQGLVWLQJXLGDGHODOLVWDO
OLVWDODODVLJXLHQWHSRVLFLyQ
◆
UHFXSHUDO: GHYXHOYH HO HOHPHQWR TXH HVWi HQ OD
SRVLFLyQGLVWLQJXLGDGHODOLVWDO
VLJXH23(5$&,21(6GHOD/,67$FRQ
SXQWRGHLQWHUpV
③ 2SHUDFLRQHVSDUDFRQVXOWDUHOHVWDGRGHODOLVWD
◆HVYDFLDOOGHYXHOYH&,(572VLODOLVWDOHVWiYDFtD\
)$/62HQFDVRFRQWUDULR
◆ HVILQO GHYXHOYH &,(572 VL HO SXQWR GH LQWHUpV GH
OD OLVWD O HV SRVWHULRU DO ~OWLPR HOHPHQWR \ )$/62 HQ
FDVRFRQWUDULR
(63(&,),&$&,Ð1'(/,67$R7$'
7,32 OLVWD [HOHPHQWR]
6,17$;,6
SURFHGLPLHQWRFUHDOVDOOOLVWD
SURFHGLPLHQWRLQVHUWDHQWVDOOOLVWDHQWHHOHPHQWR
SURFHGLPLHQWRVXSULPHHQWVDOOOLVWD
IXQFLyQUHFXSHUDOOLVWDGHYXHOYHHOHPHQWR
SURFHGLPLHQWRSULQFLSLRHQWVDOOOLVWD
SURFHGLPLHQWRILQHQWVDOOOLVWD
SURFHGLPLHQWRVLJXLHQWHHQWVDOOOLVWD
IXQFLyQHVYDFLDOOOLVWDGHYXHOYHOyJLFR
IXQFLyQHVILQOOOLVWDGHYXHOYHOyJLFR
FRQWLQXD➠
(VSHFLILFDFLyQGHO7$'/,67$
VLJXH7$'/,67$
6(0É17,&$
1RWDFLyQXWLOL]DGD
6(0É17,&$
{}
O ///Q∧≤QGRQGHQ HTXLYDOHDO λ
creal(l)
SRV≤SRV≤QHVODSRVLFLyQGHOSXQWRGHLQWHUpV
{l
=λ ∧ pos=1}
{l =L1L2...Ln ∧ pos=i ∧ 1≤pos≤n }
suprime(l)
{l=L’1 L’2...L’n-1 ∧(L’1=L1...L’i-1= Li-1)∧
(L’i=Li+1...L’n-1= Ln)∧ pos=i }
{l =L1L2..Ln ∧ pos=i ∧ 1≤pos≤n+1 ∧ e=E }
inserta(l,e)
{l=L’1L’2...L’n+1∧ ( L’1=L1 ∧ .. ∧ L’i-1=Li-1 )
∧ L’i=E ∧ pos=i+1
{l = L1L2...Ln ∧ 1≤pos≤n }
e:=recupera(l)
{l = L1L2...Ln ∧ e=Lpos}
∧ (L’i+1=Li ∧ .. ∧ L’n+1=Ln)}
FRQWLQXD➠
FRQWLQXD➠
(VSHFLILFDFLyQGHO7$'/,67$
6(0É17,&$
{l=L1 L2...Ln ∧ 0≤n}
principio(l)
{l=L1L2...Ln ∧ pos=1}
{l=L1L2...Ln ∧ 0≤n}
b:=esvacial(l)
{b=(n=0)}
{l=L1L2...Ln ∧ 0≤n}
fin(l)
{l=L1L2...Ln ∧ pos=n+1}
{l=L1L2...Ln ∧ 0≤n}
b:=esfin(l)
{b=(pos=n+1)}
,PSOHPHQWDFLRQHVGHORVWLSRV
OLQHDOHV
•$VLJQDFLyQGLQiPLFDGHPHPRULDSXQWHURV
•,PSOHPHQWDFLRQHVGHOWLSR3LOD
•,PSOHPHQWDFLRQHVGHOWLSR&ROD
•,PSOHPHQWDFLRQHVGHOWLSR/LVWDFRQSXQWRGH
LQWHUpV
{l=L1L2...Ln ∧ 1≤pos≤n ∧ pos=i}
siguiente(l)
{ l=L1L2...Ln ∧ pos=i+1}