DVOSTRUKO POVEZANE

LISTE

Strukture podataka i algoritmi 1

Dvostruko povezane liste (1)

Dvostruko povezana lista - DPL (doubly-linked list - DLL) se sastoji od sekvence čvorova koji su povezani vezama u oba smera.

Svaki čvor DPL sadrži element liste i veze ka čvoru prethodniku i čvoru sledbeniku (ili null veze).

Zaglavlje DPL sadrži veze ka prvom i ka poslednjem čvoru (ili null veze ako je lista prazna).

pig dog rat cat

dog

Dvostruko povezane liste (2)

Java klasa koja implementira čvor DPL: public class DLLNode {

protected Object element;

protected DLLNode pred, succ;

public DLLNode (Object elem,

DLLNode pred, DLLNode succ) {

this.element = elem;

this.pred = pred;

this.succ = succ;

}

}

Dvostruko povezane liste (3)

Java klasa koja impementira zaglavlje

DPL: public class DLL {

private DLLNode first, last;

public DLL () {

// Construct an empty DLL.

this.first = null;

this.last = null;

}

…

}

DLL methods (to follow)

ant bat cat first

last

Prolazak kroz DPL (1)

Metod u klasi DLL koji ispisuje elemente liste od

poslednjeg do prvog:

public void printLastToFirst () {

// Stampa sve elemente od poslednjeg do prvog. for (DLLNode curr = this.last;

curr != null; curr = curr.pred)

System.out.println(curr.element);

}

Demonstracija:

curr

ant bat cat first

last

curr

ant bat cat first

last

curr

ant bat cat first

last

curr

ant bat cat first

last

Prolazak kroz DPL (2)

Metod u klasi DLL koji ispisuje elemente liste

od prvog do poslednjeg:

public void printFirstToLast () {

// Stampa sve elemente od prvog do poslednjeg.

for (DLLNode curr = this.first;

curr != null; curr = curr.succ)

System.out.println(curr.element);

}

Operacije sa DPL (1)

Metod u klasi DLL koji briše prvi čvor: public void deleteFirst () {

// Brise prvi element liste.

if (this.first != null)

if (this.first.succ != null) {

DLLNode second = this.first.succ;

second.pred = null;

this.first = second;

} else {

this.first = null;

this.last = null;

}

}

Demonstracija:

ant bat cat first

last

second

ant bat cat first

last

second

ant bat cat first

last

second

ant bat cat first

last

Operacije sa DPL (2)

Metod u klasi DLL koji briše poslednji čvor: public void deleteLast () {

// Brise poslednji element.

if (this.last != null)

if (this.last.pred != null){

DLLNode penult = this.last.pred;

penult.succ = null;

this.last = penult;

} else {

this.first = null;

this.last = null;

}

}

Demonstracija:

ant bat cat first

last

penult

ant bat cat first

last

penult

ant bat cat first

last

penult

ant bat cat first

last

DPL = unapred i unazad povezana JPL

ant bat cat DPL:

ant bat cat Unapred

JPL:

ant bat cat Unazad

JPL:

Ubacivanje

Problem: Ubaciti novi element na proizvoljnu poziciju u

listi.

4 slučaja:

1) Ubacivanje u praznu listu;

2) Ubacivanje pre prvog elementa neprazne liste;

3) Ubacivanje posle poslednjeg elementa neprazne liste;

4) Ubacivanje između čvorova neprazne liste.

Algoritmu za ubacivanje je porteban pokazivač na

prethodnika/sledbenika novog čvora.

11

Ubacivanje u DPL (1)

Algoritam: Ubacujemo novi čvor elem na određenu poziciju u DPL

listi (spoljašnji pokazivači su first, last):

1. Neka je ins pokazivač na novokreirani čvor sa elementom elem, pokazivači na prethodni i na sledeći element su inicijalno null. 2. Ubaciti ins na željeno mesto u unapred povezanoj JPL koja počinje sa first. 3. Neka je pomoćni pokazivač succ sukcesor od ins’s u unapred povezanoj JPL (ili null ako ins nema sledbenika). 4. Ubaciti ins posle čvora na koji pokazuje succ u unazad povezanoj JPL koja počinje sa last. 5. Kraj.

Ubacivanje u DPL (2)

Pomoćni algoritam za ubacivanje u unapred povezanu JPL:

Ubaciti elem na datu poziciju u unapred povezanoj JPL koja počinje sa first:

1. Ako je potrebno ubaciti novi čvor na početak ili u praznu listu: 1.1. Postaviti vezu sledećeg od ins na first. 1.2. Postaviti first na ins. 2. Ako je potrebno ubaciti novi čvor iza čvora na koji pokazuje pred: 2.1. Postaviti vezu sledećeg od ins na vezu sledećeg od pred. 2.2. Postaviti vezu sledećeg od pred na ins. 3. Kraj.

Ubacivanje u DPL (3)

Pomoćni algoritam za ubacivanje u unazad povezanu JPL:

Ubaciti elem posle čvora succ u unazad povezanoj JPL koja počinje sa last:

1. Ako je potrebno ubaciti novi čvor na početak ili u praznu listu: 1.1. Postaviti vezu prethodnog od ins na last. 1.2. Postaviti last na ins. 2. Ako je potrebno ubaciti novi čvor iza čvora na koji pokazuje succ: 2.1. Postaviti vezu prethodnog od ins na vezu prethodnog od succ. 2.2. Postaviti vezu prethodnog od succ na ins. 3. Kraj.

Ubacivanje u DPL (4)

Demostracija (ubacivanje pre prvog čvora):

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

bat cat first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins ant

bat cat first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins ant

bat cat first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins ant

bat cat first

last

succ

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins ant

bat cat first

last

succ

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ant

bat cat first

last

Ubacivanje u DPL (5)

Demonstracija (ubacivanje posle poslednjeg čvora):

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

bat cat first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins dog

bat cat first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins dog

bat cat first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins dog

bat cat first

last

succ

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins dog

bat cat first

last

succ

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

dog

bat cat first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

fox dog first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins

fox dog

eel

first

last

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins

fox dog

eel

first

last

Ubacivanje u DPL (6)

Demonstracija (ubacivanje u sredinu liste):

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins

fox dog

eel

first

last

succ

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

ins

fox dog

eel

first

last

succ

To insert elem at a given point in the DLL headed by (first, last):

1. Make ins a link to a newly-created node with element elem,

predecessor null, and successor null.

2. Insert ins at the insertion point in the forward SLL headed by first.

3. Let succ be ins’s successor (or null if ins has no successor).

4. Insert ins after node succ in the backward SLL headed by last.

5. Terminate.

fox dog

eel

first

last

Ubacivanje u DPL - metod (1)

public void insert (Object elem, DLLNode pred) {

// Ubacuje elem na datu poziciju u DPL posle cvora

// pred, ili pre prvog cvora ako je pred null.

DLLNode ins = new DLLNode(elem, null, null);

if (pred == null) {

// ubacivanje na pocetak

ins.succ = this.first;

this.first = ins;

if (this.last == null)

// ubacivanje u praznu listu

this.last = ins;

else

this.first.succ.pred = ins;

...

Ubacivanje u DPL - metod (2)

...

} else {

ins.succ = pred.succ;

pred.succ = ins;

if (ins.succ == null){

// ubacivanje na kraj

ins.pred = this.last;

this.last = ins;

} else {

ins.pred = ins.succ.pred;

ins.succ.pred = ins;

}

}

}

Brisanje

Problem: Obrisati zadati čvor iz liste.

Četiri slučaja:

1) Brisanje jedinog čvora;

2) Brisanje prvog, ali ne i poslednjeg čvora;

3) Brisanje poslednjeg ali ne i prvog čvora;

4) Brisanje čvora u sredini.

Potrebno je da algoritam ima pokazivač na čvor

koji brišemo.

Brisanje iz DPL (1)

Algoritam:

Brisati čvor na koji pokazuje del iz DPL (spoljašnji pokazivači su first, last):

1. Neka pred i succ pokazuju na čvorove prethodnika i sledbenika od čvora del. 2. Obrisati čvor del, čiji je prethodnik pred, iz unapred povezane JPL koja počinje sa first. 3. Obrisati čvor del, čiji je prethodnik succ, iz unazad povezane JLP koja počinje sa last. 4. Kraj.

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

ant bat cat first

last

del

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

pred

ant bat cat first

last

succ

del

Brisanje iz DPL (2)

Demonstracija (brisanje prvog ali ne i poslednjeg

čvora):

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

pred

ant bat cat first

last

succ

del

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

pred

ant bat cat first

last

succ

del

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

ant bat cat first

last

Brisanje iz DPL (3)

Demonstracija (brisanje unutrašnjeg čvora):

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

del

fox dog eel first

last

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

del

fox dog eel first

last

pred succ

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

del

fox dog eel first

last

pred succ

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

del

fox dog eel first

last

pred succ

To delete node del from the DLL headed by (first, last):

1. Let pred and succ be node del’s predecessor and successor.

2. Delete node del, whose predecessor is pred, from the forward

SLL headed by first.

3. Delete node del, whose successor is succ, from the backward SLL

headed by last.

4. Terminate.

fox dog eel first

last

Brisanje iz DPL – metod (1)

public void delete (DLLNode del) {

if (del.pred == null && del.succ == null) {

// brisemo jedini element

this.first = null;

this.last = null;

} else if (del.pred == null) {

// brisemo prvi

del.succ.pred = null;

this.first = del.succ;

...

Brisanje iz DPL – metod (2)

...

} else if (del.succ == null) {

// brisemo poslednji

del.pred.succ = null;

this.last = del.pred;

} else {

// brisemo unutrasnji

del.pred.succ = del.succ;

del.succ.pred = del.pred;

}

}

Poređenje algoritama za ubacivanje

i izbacivanje

Algoritam JPL DPL

Ubacivanje O(1) O(1)

Brisanje O(n) O(1)