0\0\ 600 --
0′?4????UY??
l ò,Xn
l ò,X,|4§X
l ò,XF! Z?0
l ò,X′tL
_K?Nl
E??E??
6.1 ò,Xn
6.2 ò,X,|4§X
6.3 ò,XF! Z
6.4 ??*ó??K?Nl
6.5 §%fcK?Nl
6.1 ò,Xnò,Xn
6.1.1 n
ò +4§&?,XY0KL? ü V
`E?,XL? ü E4???J
èZa?64§Xt1 ?èüò4§Xú4§
&?/? NJ&? è E? NJ&?,XYcJíè81?tNJ&?Kè
,ü?5E?è></E-?tNJ&?KY,ìF?G2??
ò 6-1
(a) (b)
üTM6?tò4§Xè?t Y ?ò è G!£5
E?F?Y? ?è o?t ′ ?ò è G!£5E?F?"uY?
??
üY ?òèE?úE?/?0 ? è ?1?,X?0?
/? ? è o?0?/? ? èA?0 <vi,vj>èW></
¢NJ&? viNJ&? vjY?5E??
81Y ?òY ntNJ&?èí??Y n(n-1)5?è
?à ?úKY n(n-1)5?,XY ?ò/?0 Y ?`<
ò ?
1NJ&? v?,X?,XD,?/?0NJ&? v,X ?z è
1NJ&? v?,X?,XD,?/?0NJ&? v,X 9z ?
ü′ ?òèE?A?0 (vi,vj)èW;H#?-,ü <
vi,vj>
` <vj,vi>?5??81′ ?òY ntNJ&?èí
??Y n(n-1)/25E?è?à ?úKY n(n-1)/25E?,X
′ ?ò/?0 ′ ?`<ò ?
aNJ&? v,ìG,XE?,X5D/?0NJ&? v,X z ?
C?XKSz ?C?XTE?ê?,XD,??
811 ?tNJ&?
`? a?tNJ&?,ì àèíE-5C?
X?5 2C? ?
81C?XNJ&?"uYG?á?)?èí/?E-5C?X
1T )C?X ?
ü′ ?òèVp¢NJ&? viNJ&? vjYC?Xè
í/? vi
` vjE2E??Vpò???tNJ&?KèF?E2E?è
í/?A1ò E2E?ò è úíèúJ,XU?E2E?$ò/?
E2E?úG£ ?
üY ?òèVpíb!£?íNJ&? vi
` vjè¢ vi
vj
`¢ vj viF?YC?Xèí/?A1ò E2E?ò × ú
íèúJ,XU?E2E?$ò/? E2E?úG£ ?
6.1.2 ò,X
? ?0
? ?0?
? 1????tò4§X CreateGraph(G)
? 2??2?4-nNJ&? LocateVex(G,item)
? 3?9? aò¤tNJ&? GetVex(G,v)
? 4?òNJ&?C PutVex(G,v,value)
? 5?E¨21 ?tF?y&? FirstAdjVex(G,v)
? 6?E¨2??tF?y&? NextAdjVex(G,v,w)
? 7?|9?tNJ&? InsertVex(G,v)
? 8??L8?tNJ&? DeleteVex(G,v)
? 9?|9?5E? InsertEdge(G,v,w)
? 10??L8?5E? DeleteEdge(G,v,w)
? 11?F! Zò Traverse(G,v)
6.2 ò,X,|4§Xò,X,|4§X
6.2.1 F?y-?L
1. Y ?ò,XF?y-?L
KY ntNJ&?,XY ?ò ?1*ü?t n×n,X?6-?L
></?A?A1-?L ,X á/? Mèí' <vi,vj>A1Y ?ò
,X?5?êè M[i,j]=1× úí M[i,j]=0?1 itNJ&?,X
?z-?L 1 i> 3 ′,XtD×9z1 i? 3 ′,X
tDèJèY ?ò?,X5D1b-?L 3 ′,XtD?
ê 2 ′ ?ò,XF?y-?L
KY ntNJ&?,X′ ?ò3 ?1*ü?t n×n,X?6-?
L ></?A?A1-?L ,X á/? Mèí'? vi,vj?A1′
?ò,X?5E?êè M[i,j]=M[j,i]=1× úíè
M[i,j]=M[j,j]=0?1 itNJ&?,Xz-?L 1 i> 3 ′
,XtDê1 i? 3 ′,XtD?òE?,XD,?1b-?L
3 ′,XtD,X? èE-′!£5E?ü-?L £E?Z
? ??
ò 6-4
ò 6-5
ü CAá??èr)?F?y-?L ></"?,X2O
_nV?
/?
#define MAX_VERTEX_NUM 20
typedef struct graph{
EntryType
item[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
int n;
}Graph;
6.2.2 F?y><
E?4§&?,X4§X?
adjvex next
adjvexA1E?ê?qL,XNJ&?üD4?,X??è
next? ???5E?ê?4§&?,X?J\?
ò 6-6
itemNJ&?Y?è firstedge? ?1 ?5E?ê?4§&?,X?
J\?
ü CAá??èr)?F?y><></"?,X2O
_nV?/?
#define MAX_VERTEX_NUM 30 //??NJ&?tD
type struct EdgeNode{ //E?4§&?
X??4èD4?,XNJ&?4§X?
item firstedge
int adjvex;
struct EdgeNode *next;
}EdgeNode;
typedef struct VexNode{ //NJ&?4§&?
EntryType item;
EdgeNode *firstedge;
}VexNode,AdjList[MAX_VERTEX_NUM];
??Y ?ò
`′ ?òF?y><,X1k"?r)??
(1)??Y ?òF?y><
void Create_adj(AdjList adj, int n)
{
for (i=0;i<n;i++){ //??êNJ&?D4?
scanf(&adj[i].item);
adj[i].firstedge=NULL;
}
scanf(&i,&j); //Eg9?
while (i) {
s=(EdgeNode*)malloc(sizeof(EdgeNode));
//???,X?4§&?
s->adgvex=j-1;
s->next=adj[i-1].firstedge;
//ú?,X?4§&?|9,ìh,X!5B
adj[i-1].firstegde=s;
scanf(&i,&j); //Eg9??5?
}
}
? 2???′ ?ò,XF?y><
void Create_adj(AdjList adj, int n)
{
for (i=0;i<n;i++){ //??êF?y><
scanf(&adj[i].item);
adj[i].firstedge=NULL;
}
scanf(&i,&j); //Eg9E?
while (i) {
s1=(EdgeNode*)malloc(sizeof(EdgeNode));
s1->adgvex=j-1;
s2=(EdgeNode*)malloc(sizeof(EdgeNode));
s2->adgvex=i-1;
s1->next=adj[i-1].firstedge;
adj[i-1].firstegde=s1;
s2->next=adj[j-1].firstedge;
adj[j-1].firstegde=s2;
scanf(&i,&j);
}
}
6.3 ò,XF! Zò,XF! Z
??,XòF! Z??Y?/??#?zìF! Z
`Sz
ìF! ZèE-?/?F! Z??íY ?ò
`′ ?ò
E?
*ü?
6.3.1 #?zìF! Z
#?zìF! Z,X??2Ob?,XcF! Z?JF!
ZE?/? ?1£E??¢ò¤tNJ&? v? ¥èA?K?A1NJ
&?è'
aq ?¢ v,Xt>A?K?,XF?y&?? ¥4?4á#?zì
F! Zò,XJ-NJ&?è,è7?òYa vYC?X,ìE?
,XNJ&?F?>A?K?`!6?
?M6?àA|A???V)r)?#?zì1k"??
Z?bü1k"? úNJ&? ú?>A?K?E?èL?
?U???t?4èD4? visited[0..n-1]? nòNJ&?,XD
,??è*ü9A?5BA?K???èJ?? visited[i]
? 00 i0 n-1? 3 ′è></F?y><?? i,XNJ&?
"uY>A?K?E?è?oA1NJ&?>A?K?èú visited[i]5B?
3 ′?
int visited[0..n-1]={0,0,...0};
void DFS(AdjList adj,int v)
{//vF! ZCK?&?,XüF?y><,X??èJ??
¢ 0??
visited[v]=1; visite(adj[v].item);
for (w=adj[v].firstedge;w;w=w->next)
if (!visited[w->adjvex]) DFS(adj,w->adjvex);
}
íb′ ?òèE-t1k"? ?1F! Z vNJ&?ü,XE2
E?úG£,XYNJ&?è5àa vNJ&?áü?tE2E?úG£
,XYNJ&?F! Zá×5àíbY ?ò ?1F! ZCK?
NJ&? v6?óE?,XYNJ&??81à?F! Zò,XY
NJ&?èL??UüTE?#?zìF! Z1k"?,X
?.Tèr
tí!£tNJ&?A?K?(??,X?#?
int visited[0..n-1]={0,0,...0};
void DFSTraverse(AdjList adj)
{
for (v=0;v<n;v++) if (!visited[v]) DFS(adj,v);
}
6.3.2 SzìF! Z
íò,XSzìF! Z?"?£E??¢ò¤tNJ
&? v? ¥èüA?K?A1NJ&? v aèq ?A?K? v,XYt>
A?K?E?,XF?y&?è'
aaA?K?!£tF?y&?,XF?y&?è
èA?K?NNch±?>A?K?,XNJ&?JF?y&?3ì>
A?K?è,èò,XYNJ&?F?>A?K?!6??M6í
?t′ ?òEˉ> SzìF! Z,XE?/??
?M6?àA|A???r)?SzìF! Z1k"?L??U5×
<%,X′tK?Nl?
? 1?üSzìF! Zè?U">A?K?,XNJ&?J
F?y&?3>ìA?K?è′!8è?NOí!£tNJ&?,XA?K?
NNcEˉ> A?)è1? aM6Y!8NNcA?K? ?NJ&?,XF?y
&??hy*ü?tKó?4§XA?)NJ&?A?K?NNcè ?1
y*üKó?4§X,X?0(M&?èúA?K?,X!£tNJ&?9Kóè
'
aèaq ??KóèJA?K?Wà,XA?1j
? 2?üSzìF! ZE?/? à#?zìF! Z?
èZFS!G?áA?K?¤tNJ&?è3L??U???t?
4èD4? visited[0..n-1]? nòNJ&?,XD,??è*ü9A?
)!£tNJ&? ú?4£>A?K?E??
int visited[0..n-1]={0,0,...0};
void BFS(AdjList adj,int v)
{//vF! ZCK?&?üF?y><,X??èF?y><??¢ 0
??
InitQueue(Q); //QKó?
visited[v]=1; visite(adj[v].item); EnQueue(Q,v);
while (!QueueEmpty(Q)) {
DeQueue(Q,v);
for (w=adj[v].firstedge;w;w=w->next)
if (!visited[w->adjvex]) {
visited[w->adjvex]=1;
visite(adj[w->adjvex].item);
EnQueue(Q,w->adjvex); }
}
}
6.4 ??*ó??K?Nl??*ó??K?Nl
6.4.1 ò,X*ó??
`?k
íb?t1Y ntNJ&?,X′ ?E2E?òèW,XE?D?
n?- n-15?81¢EY? n-15E?èSk′ ?ò?'
E2E?èí+ ntNJ&? ?E- n-15E????4??,Xò>/?
s′ ?ò,X *ó?? ?/Z?t′ ?E2E?ò,X*ó?
?è ?4?ü></,XNJ&?*ó??,X
4§&??
ò 6-10
ò 6-11
ò 6-12
ò 6-13
6.4.2 ??*ó??
ü?tòè!£5E?ê? ?11Y?ta,ìG
,XDè?àúW/? ?E-o ?1KY?n,X ?
è!¨Vè></?tNJ&?E? o?tNJ&?,XC±/??
8?C
,XêKè?4?C?,XE??11?E-/?ú,XòE?>
/?0 5% ?
òê5%,X*ó??á?,Xè¢á à,XNJ&?? ¥
?1*ó?á à,X*ó??è nt4§&?,X*ó???nY n-
15E??
ò 6-14
ò 6-15
?M6?àAu1k??TM6?é*ó??,X
`?
1 ?é*ó??,X
`? 16+11+5+6+18=56×1
`é*ó??,X? 16+19+33+18+6=92?E??à
ú
`??,X*ó??/? ??*ó?? ?
XE???*ó??,X?"????*ó??0Nè G"u
Y?t4§&?
`?5E?èOjEY??tNJ&?0*ó??
,X
è'
a!£ ?¢áü*ó??,XE?EY??5
?6??,XE?èZ±A?t9*ó??,XE?á?E?
?2C?èaA1E?F?y,X?tNJ&??NO?t?4£ü*ó?
?è
?tíáü*ó??è815%Y ntNJ&??E-G?5×<%,X
5%?tE2E?′ ?ò?èíYE-/?5êEY? n-1E? ?
1kE-t5%,X??*ó??Z?Ao4?,XE?/? ?1£E?
?A?5B 2tL? üè UL? ü,X2?ü*ó??,X4§
&?è V-UL? ü,X2?áü*ó??,XNJ&??Oj
EY??t0*ó??
4§&?,XNJ&?èJúW9 UL?
üè'
aüFwo?0?NJ&?ü UL? üè5à o?0?NJ&?ü
V-UL? ü,XE?R?5??,XE?èJ^E-5E?
`
Fwtáü UL? ü,XNJ&?t9*ó??è GEg?E-5
E?è'
aúJNJ&?#?t UL? üèG?áE-t?0 n-1
??
?M6?à5×<%??V)r)?E-t?0E?/?,X1k
"??
úd?? 1?W?UY?NM?0?Y5êEY??
5E?
`úNJ&?t9 UL? ü×? 2?5%,X!£tNJ&?
áü UL? üèü V-UL? ü?Z¤P?1k"?,X
êKè?0NKè)[è?àúE-t1k"?A?Au?tEY}D
4? closedgeè*ü9A?)¢L? ü UL? ü V-UKY??
,XE??í!£t2b V-UL? ü,XNJ&?èüEY}D4?
,ü?t,ìh,XúG£ closedge[i-1]èWùà?t
3è?
t
3*ü9></üA1NJ&?a V-UL? ü¤oNJ&?X?,X
E???,XFw5E?,Xè81A1NJ&?Eˉ9 UL? üèí
0× o?t
3></E-5??,XE?íh,Xü V-U
L? ü,XNJ&????J2O
_nV?/?
#define MAX_NUM 10
struct {
int adjvex;
float lowcist;
}closedge[MAX_NUM];
Ht1k"?,X;> E?/? ?1£E??
{??ê closedgeD4?,XY?×
EY?¤tNJ&? k0*ó??,X
4§&?èJúWt9 UL?
ü×
G?á???0 n-1 ??
l EY??5$μC?5ê,XE?×
l Eg?E-5E?,X?t0?&?×
l ?
V-UL? ü,XNJ&?μCè Ga UL? üX???
,XE??
}
A?A15%1F?y-?L ,X6?4-?èí`H,X1k"??
void Mini_SpanTree(Graph G,int k,int n)
{//G5%,XF?y-?L è k*ó??
4§&?,Xc ?è n5%,X
NJ&?D,?
for (j=0;j<n;j++)
if (j!=k) closedge[j]={k,G[k][j]};
closedge[k].lowcost=0;
for (i=1;i<n;i++)
{
k=minmun(closedge);
printf(k,closedge[k].adjvex);
closedge[k].lowcost=0; //úNJ&?t9 UL? ü
for (j=0;j<n;j++)
if (closedge[i]&&G[k][j]<closedge[j].lowcost)
closedge[j]={k,G[k][j]};
}
}
6.5 §%fcK?Nl§%fcK?Nl
§%fcY ?ò,X?tG??U?0?ü4-n,XY
?ò Gè81NJ&?c? vi1,vi2,...,vin$μC???5ê?81ü
Y ?ò G¢NJ&? viNJ&? vjY?5C?Xèíüc?
NJ&? vi?üNJ&? vj!è?/?E-tc??t §%c
? ?"?tY ?ò§%c?,XE?/?/? §%fc ?
_?Au1k??,X:*óhA1:4,XF?úAò/? ?
J!£K?Aò/?L??U,X?Aò/??
Aò/?·
?
Aò/? á/? ?Aò/?
c1 P?1D:
c2 Au1k
?.
c3 /?7D: c1,c2
c4 DB4§X c2,c3
c5 /?cA?Au c2
c6 4êA¥ s)ú c4,c5
c7 ?02?43 c4,c9
c8 BE?(=)ú c1
c9 Au1k s)ú c8
ò 6-16
§%fc,X?"??
? 1?¢òEY??t9z 0,XNJ&?èEg?×
? 2?¢ò?]A1NJ&? ?JY1A1NJ&??
,X?×
?á;> E-?t!9Pxè,èY,XNJ&?F?>Eg
?èEg?,Xc?E-t′)?Y ?ò,X§%c??4?
?,XA?5ù ?6?? ¥)??ü!£?êè ?6? àê,ü?
t9z 0,XNJ&?èEY?"??>< c1~c9?></,X!£
tNJ&?,X9z?
?M6?àA|A???V)r)?§%fc,X1k"??
A?Y ?ò1F?y><,X6?,|?
?M64-?1k"?r)?,X
? E?/??
{ úY9z 0,XNJ&?9ü×
'üM20NêG?á;> ???0?
¢üE??NJ&? k×
? 1?ú kNJ&?,XμCEg?×
? 2?úa kF?y,XYNJ&?,X9z£ 1?
}
#define MAX_VERTEX_NUM 30 //??NJ&?tD
type struct EdgeNode{ //E?4§&?
int adjvex;
struct EdgeNode *next;
}EdgeNode;
typedef struct VexNode{ //NJ&?4§&?
EntryType item;
int indegree; //A?)NJ&?,X9z
EdgeNode *firstedge;
}VexNode,AdjList[MAX_VERTEX_NUM];
?M6§%fc,X`H1k"??
Status TopologicalSort(AdjList adj)
{
InitStack(s);
for (i=0;i<MAX_VERTEX_NUM-1;i++)
if (adj[i].indegree==0) Push(s,i);
while (!StackEmpty(s)) {
Pop(s,i); printf(i);
for (p=adj[i].firstedge;p;p=p->next) {
adj[i].indegree-=1;
if (adj[i].indegree==0) Push(s,i);
}
}
}