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Aлгоритмы на графах

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Yeaiaiou oai?ee a?aoia.

A?ao – niaieoiiinoue oi/ae e eeiee, a eioi?ie eaaeaeay eeiey niaaeeiyao
aeaa oi/ee. Oi/ee iacuaathony aa?oeiaie, eee oceaie, a?aoa, eeiee –
?aa?aie a?aoa. Anee ?aa?i niaaeeiyo aeaa aa?oeiu, oi aiai?yo, /oi iii ei
eioeeaeaioii; aa?oeiu, niaaeeiaiiua ?aa?ii iacuaathony niaaeiuie. Aeaa
aa?oeiu, niaaeeiaiiua ?aa?ii, iiaoo niaiaaeaoue; oaeia ?aa?i
iacuaaaony iaoeae. *enei ?aaa?, eioeeaeaioiuo aa?oeia, iacuaaaony
noaiaiueth aa?oeiu. Anee aeaa ?aa?a eioeeaeaioiu iaeiie e oie aea
ia?a aa?oei, iie iacuaathony e?aoiuie; a?ao, niaea?aeauee e?aoiua
?aa?a, iacuaaaony ioeueoea?aoii.

?aa?i, niaaeeiythuaa aeaa aa?oeiu, iiaeao eiaoue iai?aaeaiea io iaeiie
aa?oeiu e ae?oaie; a yoii neo/aa iii iacuaaaony iai?aaeaiiui, eee
i?eaioe?iaaiiui, e ecia?aaeaaony no?aeeie. A?ao, a eioi?ii ana ?aa?a
i?eaioe?iaaiiua, iacuaaaony i?eaioe?iaaiiui a?aoii (i?a?aoii); ?aa?a
i?a?aoa /anoi iacuaatho aeoaaie. Aeoae eiaiothony e?aoiuie, anee iie
ia oieueei eiatho iauea aa?oeiu, ii e niaiaaeatho ii iai?aaeaieth.
Eiiaaea ioaeii ?anniao?eaaoue ia aanue a?ao, a aai /anoue (/anoue aa?oei
e /anoue ?aaa?). *anoue aa?oei e ana eioeeaeaioiua ei ?aa?a iacuaathony
iiaea?aoii; ana aa?oeiu e /anoue eioeeaeaioiuo ei ?aaa? iacuaathony
noa?aoii. Oeeeeii iacuaaaony caieiooay oeaiue aa?oei. Aea?aaii
iacuaaaony a?ao aac oeeeeia. Inoiaiui aea?aaii iacuaaaony naycaiiue
noa?ao a?aoa, ia eiathuee oeeeeia.

A?ao iaeiicia/ii caaeai, anee caaeaiu iiiaeanoai aai aa?oei,
iiiaeanoai ?aaa? e oeacaiu ana eioeeaeaioiinoe (o.a. oeacaii, eaeea
aa?oeiu eaeeie ?aa?aie niaaeeiaiu). Iaeaieaa iaaeyaeii a?ao caaeaaony
?enoieii; iaeiaei ia ana aeaoaee ?enoiea iaeeiaeiai aaaeiu; a
/anoiinoe, ianouanoaaiiu aaiiao?e/aneea naienoaa ?aaa? (aeeeiia,
e?eaecia e o.ae.) e acaeiiia ?aniieiaeaiea aa?oei ia ieineinoe.

Aeey iai?eaioe?iaaiiiai ?aa?a ii?yaeie, a eioi?ii oeacaiiu
niaaeeiyaiua ei aa?oeiu, ia aaaeai. Aeey i?eaioe?iaaiiiai ?aa?a
aaaeii: ia?aie oeacuaaaony aa?oeia, ec eioi?ie auoiaeeo ?aa?i.

Ia?o?oo, eee iooue – yoi iineaaeiaaoaeueiinoue ?aaa? a
iai?eaioe?iaaiiii a?aoa, a eioi?ii eiiaoe eaaeaeiai ?aa?a niaiaaeaao n
ia/aeii neaaeothuaai ?aa?a. *enei ?aaa? ia?o?ooa iacuaaaony aai
aeeeiiie.

A?aou oe?iei eniieuecothony eae a naiie iaoaiaoeea, oae e a aa
i?eeiaeaieyo. Iie i?eiaiythony i?e iino?iaiee ?acee/iuo iaoaiaoe/aneeo
iiaeaeae: eeiee yeaeo?iia?aaea/e, naoae aaoiaei?ia, eeiee aicaeooiuo
niiauaiee e i?.

Caaea/a ninoieo a oii, iaeoe iooue ec aa?oeiu A a aa?oeio B. Aoaeai
caaeaaaoue a?ao iao?eoeae niaaeiinoe, o.a. eaaae?aoiie oaaeeoeae NxN,
a eioi?ie ia ia?ana/aiee i-e no?iee e j-ai noieaoea cia/aiea TRUE, anee
i e j niaaeeiaiu ?aa?ii, e FALSE a i?ioeaiii neo/aa.

Iiene a oe?eio.

Iiaeiaii oiio eae, niaeanii i?eioeeio Atheaaina, eaaeaeay oi/ea
aieiiaiai o?iioa yaeyaony enoi/ieeii aoi?e/iie aieiu, iu, ioi?aaeyynue
ec caaeaiiie aa?oeiu A, iinauaai ana niaaeiua n iae aa?oeiu (o.a.
aa?oeiu, a eioi?ua aaaeoo no?aeee ec A). Eaaeaeay iinauaiiay aa?oeia
noaiiaeony enoi/ieeii iiaie aieiu e o.ae. I?e yoii iaiaoiaeeii
iicaaioeoueny i oii, /oiau ia aa?ioony a oo aa?oeio, a eioi?ie oaea
auee.

Aeey ?aaeecaoeee aeai?eoia iiiaaeiayony:

iao?eoea m[1..n, 1..n] – iao?eoea niaaeiinoe a?aoa;

aniiiiaaoaeueiue iannea queue[1..n], a eioi?ii aoaeao
oi?ie?iaaoueny i/a?aaeue, o.a. oei aeaiiuo ia?aue aioae – ia?aue auoae
(FIFO). ?acia? aai aeinoaoi/ai, oae eae iu ia iinauaai aa?oeiu
aeaaaeaeu. N ianneaii queue naycaiu aeaa ia?aiaiiua – head e tail. A
ia?aiaiiie head aoaeao iaoiaeeoueny iiia? oaeouae aa?oeiu, ec eioi?ie
eaeao aieia, a i?e iiiiue ia?aiaiiie tail iiaua aa?oeiu iiiauathony
a “oaino” i/a?aaee queue;

aniiiiaaoaeueiue iannea visited[1..n], eioi?ue ioaeai aeey oiai,
/oiau ioia/aoue oaea i?ieaeaiiua aa?oeiu (visited[i]=TRUE aa?oeia i
i?ieaeaia);

aniiiiaaoaeueiue iannea prev[1..n] aeey o?aiaiey i?ieaeaiiuo aa?oei.
A yoii ianneaa e aoaeao noi?ie?iaai eneiiue iooue;

ia?aiaiiay f, eioi?ay i?eiao cia/aiea TRUE, eiaaea iooue aoaeao
iaeaeai.

E?iia oiai, iu aaaaeai ianeieueei aniiiiaaoaeueiuo ia?aiaiiuo, eioi?ua
iiiaaeiayony i?e i?aaiecaoeee oeeeeia.

Program breadth_first_search;

Const n=9;

m:array[1..n, 1..n] of boolean =

(

(False, True, True, False, False, False, False, False,
False),

(True, False, True, False, False, False, True, True,
False),

(True, True, False, True, True, False, False, False,
False),

(False, False, True, False, True, False, False, False,
False),

(False, False, True, True, False, True, False, True,
False),

(False, False, False, False, True, False, True, True, True
),

(False, True, False, False, False, True, False, True, True
),

(False, True, False, False, True, True, True, False,
False),

(False, False, False, False, False, True, True, False,
False)

);

Var A, B: integer;

Procedure A_to_B(A, B: integer);

Var

Visited: array[1..n] of boolean;

Prev: array[1..n] of integer;

path: array[1..n] of integer;

head, tail: integer;

f: boolean;

i, v, k: integer;

Begin

head:=1;

tail:=1;

f:=False;

For i:=1 to n do

Begin

Visited[i]:=False;

Prev[i]:=0

End;

Path[tail]:=A;

Visited[A]:=True;

While (head0 do

Begin

Write(‘ aa?oeia
i i?ieaeaia);

ia?aiaiiay f, eioi?ay i?eiao cia/aiea TRUE, eiaaea iooue aoaeao
iaeaeai.

Program depth_first_search;

Const n=9;

m:array[1..n, 1..n] of boolean =

(

(False, True, True, False, False, False, False, False,
False),

(True, False, True, False, False, False, True, True,
False),

(True, True, False, True, True, False, False, False,
False),

(False, False, True, False, True, False, False, False,
False),

(False, False, True, True, False, True, False, True,
False),

(False, False, False, False, True, False, True, True, True
),

(False, True, False, False, False, True, False, True, True
),

(False, True, False, False, True, True, True, False,
False),

(False, False, False, False, False, True, True, False,
False)

);

Var A, B: integer;

Procedure A_to_b(A, B: integer);

Var

Visited: array[1..n] of boolean;

f: boolean;

i: integer;

Procedure Depth(p: integer);

var k: integer;

Begin

Visited[p]:=True;

For k:=1 to n do

If not f then

If m[p, k] and not Visited[k] then

If k=B then

Begin

f:=True;

Write(B);

Break

End

else Depth(k);

If f then write(‘nil do

Begin

Write(l^.i:3);

l:=l^.next

End

End;

Begin

stack1:=nil;

stack2:=nil;

Write(‘Ia/aeueiay aa?oeia: ‘);readln(v);

Push(v, stack1);

While stack1NIL do

Begin

v:=peek(stack1);

i:=1;

While (icolor[j]) then

Begin

min:=Matrix[i, j];

a:=i;

b:=j

End;

len:=len+min

end;

Begin

Clrscr;

Init;

For k:=1 to n-1 do

Begin

Findmin(a, b);

Ribs[k].a:=a;

Ribs[k].b:=b;

col:=Color[b];

For i:=1 to n do

If color[i]=col then color[i]:=color[a];

End;

For i:=1 to n-1 do

Writeln(ribs[i].a, ‘ ‘, ribs[i].b);

Writeln(‘Length= ‘, len);

Readkey

End.

Aeai?eoi Aeaeeno?u.

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