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1. Danh sch mc ni n l g?

1.1. Khi nim

Danh sch mc ni n (Singly-linked list) gm cc nt c ni vi nhau theo

mt chiu. Mi nt l mt bn ghi (record) gm hai trng:

- Trng info cha gi tr lu trong nt .

- Trng link cha lin kt (con tr) ti nt k tip, tc l cha mt thng tin

bit nt k tip nt trong danh sch l nt no. Vi nt cui cng (khng c nt

k tip), trng lin kt ny c gn vi mt gi tr c bit, chng hn con tr

nil.

Cu trc nt ca danh sch mc ni n

Code

Type

PNode=^Node; {Kiu con tr ti mt nt}

Node=Record {Kiu bin ng cha thng tin

trong mt nt}

info: ;

link: PNode;

End;

Nt u tin (head) ng vai tr quan trng trong danh sch ni n. duyt

danh sch ni n. duyt danh sch ni n, ta bt u t nt u tin, da vo

trng lin kt i sang nt k tip, n khi gp gi tr c bit (duyt qua nt cui)

th dng li.

Danh sch ni n

1.2. Truy cp cc phn t trong danh sch mc ni n

Bn thn danh sch mc ni n l mt kiu d liu tru tng. ci t

kiu d liu tru tng ny, c th dng mng cc nt (trng link cha ch s ca nt

k tip) hoc bin cp pht ng (trng link cha con tr tr ti nt k tip). Tuy

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nhin, vic xc nh phn t ng th p trong danh sch bt buc phi duyt t u

danh sch qua p nt, vic ny mt thi gian trung bnh O(n) v t ra khng hiu qu

nh thao tc trn mng. Ni cch khc, danh sch ni n tin cho vic truy cp tun

t nhng khng hiu qu nu chng ta thc hin nhiu php truy cp ngu nhin.

2. To danh sch mc ni n

2.1. tng

Chng ta c th bt u to dn danh sch t tri hoc phi qua u c, cch

c cp ti y l t tri qua phi:

- u tin ta to mt nt u tin, nt ny ng vai tr va l nt Head.

- Sau t nt th 2 tr i, mi ln to thm 1 nt ta gn nt trung gian bng nt

va to. Gn trng Link hp l theo nh ngha danh sch ni n.

2.2. Code

{Th tc to mi danh sch}

Procedure Readf;

Var P:PNode;

Begin

Assign(f,fi);Reset(f);

Readln(f,N,K);

New(P);

Read(f,P^.info);

Head:=P;

Q:=P;

For i:=2 to n do Begin

New(P);

P^.Next:=Nil;

Read(f,P^.Info);

Q^.Next:=P;

Q:=P;

End;

Close(f);

End;

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3. Chn phn t vo danh sch ni n

3.1. tng

chn thm mt nt cha gi tr v vo v tr ca nt p trong danh sch ni n,

trc ht ta to ra mt nt mi Newnode cha gi tr v v cho nt ny lin kt ti p.

Nu p ang l nt u tin ca danh sch (head) th cp nht head bng NewNode,

cn nu p khng phi l nt u tin ca danh sch, ta tm nt q l nt ng lin trc

nt p v chnh li lin kt: q lin kt ti NewNode thay v lin kt thng ti p.

Chn phn t vo danh sch ni n

3.2. Code

{Th tc chn phn t V vo v tr nt P}

Procedure Insert(p: Pnode; const v: );

Var NewNode, q, head: Pnode;

Begin

New(NewNode);

NewNode^.info := v;

NewNode^.link := p;

If head = p then head := NewNode

Else

Begin

q := head;

while q^.link q do q:=q^.link;

q^.link := NewNode;

End;

End;

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Vic chnh li lin kt trong th tc chn phn t vo danh sch ni n mt

thi gian O(1). Tuy nhin, vic tm ra nt ng lin trc nt p yu cu phi duyt t

u danh sch, vic ny mt thi gian trung bnh O(n). Vy th tc chn mt phn t

vo danh sch ni n mt thi gian thc hin trung bnh O(n).

4. Xa phn t khi danh sch mc ni n

4.1. tng

xa nt p khi danh sch ni n, gi next l nt ng lin sau p trong danh

sch. Xt hai trng hp:

- Nu p l nt u tin trong danh sch head = p th ta t li head = next.

- Nu p khng phi nt u tin trong danh sch, tm q l nt ng lin trc nt p

v chnh li lin kt: q lin kt ti next thay v lin kt ti p.

Vic cui cng l hy nt p.

4.2. Code

{Th tc xa nt P}

Procedure Delete(p:PNode);

Var next, q, head: PNode

Begin

Next := p^.link;

If p = head then head := next

Else

Begin

Q:= head;

While q^.link p do q := q^.link;

Q^.link:= next;

End;

Dispose(P);

End;

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Xa phn t khi danh sch ni n

Cng ging nh th tc chn, th tc xa mt phn t khi danh sch ni n

cng mt thi gian thc hin trung bnh l O(n).

5. Biu din ngn xp (Stack) bng danh sch ni n kiu LIFO

5.1. Khi nim:

Ngn xp l mt dng c bit ca danh sch m vic b sung hay loi b mt

phn t u c thc hin 1 u ca danh sch gi l nh. Ni cch khc, ngn

xp l 1 cu trc d liu c 2 thao tc c bn: b sung (push) v loi b phn t (pop),

trong vic loi b s tin hnh loi phn t mi nht c a vo danh sch.

Chnh v tnh cht ny m ngn xp cn c gi l kiu d liu c nguyn tc LIFO

(Last In First Out - Vo sau ra trc).

Ta s trnh by cch ci t ngn xp bng danh sch ni n bng bin ng v

con tr.

- Li vo v li ra u l nh ca Stack c qun l bi nt Top.

- Khng xt trng hp trn Stack bi n cn ph thuc vo nhiu th khc.

- Stack rng khi nt Top trng (nil).

5.2. Code

Type

PNode=^Node;

Node=Record

Info: ;

Link: PNode;

End;

Var Top:PNode;

Procedure StackInit;

Begin

Top:=Nil;

End;

{Np phn t vo Stack nh danh sch}

Procedure SPUSH(V: );

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Var P:PNode;

Begin

New(P);

P^.Info:= V;

P^.Link:= top;

Top := p;

End;

{Ly phn t ra khi stack nh danh sch}

Procedure SPOP: ;

Var P:PNode;

Begin

If Top=Nil then Writeln(Stack is empty)

Else

Begin

SPOP:=Top^.Info;

P:=Top^.Next;

Dispose(Top);

Top:=P;

End;

End;

BEGIN

StackInit;

;

END.

6. Biu din hng i (Queue) bng danh sch ni n kiu FIFO:

6.1. Khi nim:

Hng i l mt cu trc d liu gn ging vi ngn xp, nhng khc vi ngn

xp nguyn tc chn phn t cn ly ra khi tp phn t. Tri ngc vi ngn xp,

phn t c ly ra khi hng i khng phi l phn t mi nht c a vo m l

phn t c lu trong hng i lu nht.

iu ny nghe c v hp vi quy lut thc t hn l ngn xp ! Quy lut ny

ca hng i cn c gi l Vo trc ra trc (FIFO - First In First Out). V d v

hng i c rt nhiu trong thc t. Mt dng ngi xp hng ch ct tc 1 tim ht

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tc, ch vo rp chiu phim, hay siu th l nhng v d v hng i. Trong lnh vc

my tnh cng c rt nhiu v d v hng i. Mt tp cc tc v ch phc v bi h

iu hnh my tnh cng tun theo nguyn tc hng i.

Hng i cn khc vi ngn xp ch: phn t mi c a vo hng i s

nm pha cui hng, trong khi phn t mi a vo ngn xp li nm nh ngn

xp.

Nh vy, ta c th nh ngha hng i l mt dng c bit ca danh sch m

vic ly ra mt phn t, get, c thc hin 1 u (gi l u hng), cn vic b

sung 1 phn t, put, c thc hin u cn li (gi l cui hng).

- Li vo l pha bn phi Queue c qun l bi nt L.

- Li ra l pha bn tri Queue c qun l bi nt R.

- Khng xt trng hp trn Queue bi n cn ph thuc vo nhiu th khc.

- Queue rng khi nt L v R u trng.

6.2. Code

Type

Pnode = ^Node;

Node = Record

Info: ;

Link: PNode;

End;

Var L,R: PNode;

Procedure QueueInit;

Begin

L := Nil;

End;

{Ly gi tr ca phn t v tr u danh sch}

Function Get: ;

Begin

If (L=R) and (R=Nil) then Writeln(Queue is empty)

Else Get := L^.info;

End;

{Np phn t vo Queue v tr cui cng}

Procedure QPUSH(V: );

Var P:PNode;

Begin

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New(P);

P^.Info := V;

P^.Link := Nil;

If L=Nil then L := P

Else R^.link := P;

R := P;

End;

{Ly phn t ra khi Queue u danh sch}

Procedure QPOP: ;

Var P:PNode;

Begin

If (L=R) and (R=Nil) then Writeln(Queue is empty)

Else Begin

QPOP:=L^.Info;

P:=L^.Link;

L^.Link:=Nil;

Dispose(L);

L:=P;

End;

End;

BEGIN

QueueInit;

;

END.

7. Bi tp ng dng

7.1. Bi tp minh ha

Vit chng trnh Dslk.pas minh ho cc cch lm vic vi danh sch lin kt

thun. Phn d liu ca mt phn t sl cc thng tin v mt sinh vin.

Type SVienPtr = ^SVien;

SVien = record

maso: string[6];

hoten: string[23];

next : SvienPtr;

end;

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var L, R: SVienPtr; chon: byte; traloi: char;

Procedure Bosung;

var p: SVienPtr; ans: integer;

Begin

while true do begin

new(p);

with p^ do begin

write('Ma sinh vien : ');

readln(maso);

write('Ho va ten : ');

readln(Hoten);

write('Diem trung binh: ');

readln(dtb);

end;

p^.next:=NIL;

if L=NIL then begin L:= p; R:= p end

else begin

R^.next:= p; R:= p

end;

write('Co tiep tuc khong 1/0 ? ');

readln(ans);

if ans=0 then break;

end;

end;

procedure DuyetXuoi;

var p: SVienPtr;

begin

if L = NIL then begin

writeln('D.sach rong'); exit;

end;

p := L;

while p NIL do

begin

with p^ do writeln(maso:5,' ',Hoten:25,'

',dtb:5:2);

p := p^.Next;

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end;

End;

procedure ChenSau;

var q,p: SVienPtr; found: boolean; masv: string[6];

begin

if L NIL then begin

write('Ma so SV can tim de chen :

');

readln(masv);

p:= L; found:= false;

while (pNIL) and (not found) do

if p^.maso=masv then found :=

true

else p:=p^.next;

if found then begin

new(q);

with q^ do

begin

write('Ma so : ');

readln(maso);

write('Ho ten : ');

readln(Hoten);

write('Diem TB :');

readln(dtb);

end;

q^.next:= p^.next;

p^.next:= q;

end

else begin

write('Khong tim thay...');

readln;

end;

end;

end;

Procedure TimXoa;

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var masv: string[6]; found: boolean; p,q: SVienPtr;

begin

write('Ma so SV can loai khoi danh sach : ');

readln(masv);

p:= L;

if pNIL then begin

found:= false;

while (pNIL) and (not found) do

if p^.maso=masv then found := true

else begin

q:=p; p:=p^.next

end;

if found then

begin

if p=L then L :=p^.next

else q^.next:=p^.next;

if p^.next=NIL then R:=q;

dispose(p)

end

else begin

write('Khong tim thay...');

readln;

end;

end;

End;

BEGIN

L := NIL;

repeat

writeln; writeln('1. Bo sung mot sinh vien');

writeln('2. Duyet danh sach sinh vien');

writeln('3. Tim kiem mot phan tu va chen vao sau');

writeln('4. Tim kiem mot phan tu va xoa');

writeln('5. Ket thuc chuong trinh');

writeln; write('Chon chuc nang: '); readln(chon);

writeln;

case chon of

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1: Bosung;

2: DuyetXuoi;

3: ChenSau;

4: TimXoa;

End;

Until chon=5;

while LNIL do Begin

R:= L; L:= L^.next;

Dispose(R);

End;

End.

7.2. Bi tp t gii

Bi tp 1: Vit mt hm xc nh xem mt danh sch lin kt cho c th t tng

dn hay khng theo 2 cch: Khng qui v qui.

Bi tp 2: Cho 2 danh sch lin kt n i din cho 2 tp hp c tr bi L1 v L2.

Vit chng trnh hin th:

1. Phn giao ca 2 danh sch trn.

2. Phn hp ca 2 danh sch trn.

3. Phn hiu ca 2 danh sch trn.

Bi tp 3: Cho 2 danh sch lin kt L1 v L2.

1. Sp xp li 2 danh sch theo th t tng dn.

Trn 2 danh sch li thnh danh sch L3 sao cho L3 vn c th t tng dn.

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