-
1 2 3
-
7.1 GG= VEG1=V={v0 ,v1,v2,v3,v4
}E={(v0,v1),(v0,v3),(v1,v2),(v1,v4),(v2,v3)(v2,v4)}G1(vi,vj)vivj
-
G2 vivjvivjGGGGGGG2=V={v0 v1,v2,v3}E={ , , ,}
-
1 2 3 4
-
1 ,vu e= (v, u), vu e 2 V = V V=V V=V V = V+V Gne = 2*e 2 e
-
n(n-1)n~ n(n-1)/2 n~ ~ ~
- 4 V={Vi0,Vi1,Vin} (Vij-1,Vij)E E,(1
-
5 , G1V0,V1,V2,V3 G2 V0,V2,V3,V0G1G2
-
6 G=< V, E > vu v u G
-
7 G=VEG1=V1E1V1 VE1 E G1G (b)(c) (a) (a)(b)(c)
-
8 G G G G
-
D D DD
-
G1G1T1G1n-19
-
G1V(G1)={1,2,3,4,5,6} E(G1)={, , , , , ,
}G2V(G2)={1,2,3,4,5,6,7} E(G1)={(1,2), (1,3), (2,3), (2,4),(2,5),
(5,6), (5,7)}
-
341310
-
123563 1235631 3563125765237 12576521512356125761231
-
7.2
-
G=(V,E)n1GAn
-
nn(n+1)/2nnViTD(Vi)Ai(i)ViAiViAi A0 00
-
#define n 6 /**/#define e 8 /**/typedef char vextype;
/**/typedef float adjtype; /**/typedef struct{ vextype vexs[n];
adjtype arcs[n][n];} graph;
-
21435
-
BADCE
-
21534000000000000000000000000=807080705040503040203020arcs6203050407080
-
CREATEGRAPH(graph *ga){ int i,j,k; float w; for
(i=0;ivexs[i]getchar(); /**/ for (i=0;iarcs[j][i]w; }}
-
iVi
Vi Vj,2Vj
-
^^^^
-
ViiViiViiv,uvuGm(mn), eGm+2*eGG
-
Vi
-
^^^^^^^^
-
^^^^^
-
7.3 1)v 2)vv3)
-
v 1v 2v 1 V0,V1,V3,V7,V4,V2,V5,V6,
1GV0 2 V0,V1,V4,V7,V3,V2,V5,V6
-
V1V3 V7 V6 V2 V5 V8 V4
-
V1V3 V7 V6 V2 V4 V8 V5
- ,visited[Max]vivisited[i]falsevivisited[i]true void DFSTraverse
(Graph G, Status( *Visit) (int v )){ VisitFunc=Visit; for ( v=0;
v
-
n e v w 2e O(e)1O(n+e)O(n)O(n2)
-
V1 V2 V4 V8 V5 V6 V3 V7V1 V2 V4 V8 V5 V6 V3 V7
-
V1 V2 V4 V8 V3 V6 V7 V5
-
1)v 2)V034)
-
vi1vi 2 vi w1 ,w2 , wk 3; 1
G V0 V0,V1,V2,V3,V4,V5,V6,V7
-
V0V1V2V3V4V5V6V7V1V2V3V0V4V5V6V7 3(2Q1v 2vw1 ,w2 , wk 3;
-
V1 V2 V3 V4 V5 V6 V7 V8V1 V2 V3 V4 V6 V7 V8 V5
- 1,visited[Max]2 void BFSTraverse (Graph G, Status( *Visit) (int
v )){ for (v=0;v
-
d0 + d1 + + dn-1 = O(e) di i n O(n2)
-
V1 V2 V3 V4 V5 V6 V7 V8V1 V2 V3 V4 V5 V6 V7 V8V1 V2 V4 V8 V5 V6
V3 V7V1 V2 V4 V8 V5 V6 V3 V7
-
V1 V2 V3 V4 V6 V7 V8 V5V1 V2 V4 V8 V3 V6 V7 V5
-
nn-1nn-17.4
-
V1 V2 V4 V8 V5 V3 V6 V7V1 V2 V3 V4 V5 V6 V7 V8
-
nnn(n-1)/2nn-1n-1
-
(Prim)N=(V,{E})TENU={u0},(u0V),
TE=uU,vV-U(u,v)E(u0,v0)(u0,v0)TEv0UU=VT=(V,{TE})N
: 6?
-
U={ V1 }U={ V1,V3 }U={ V1,V3,V6}U={ V1,V3,V6,V4 }U={
V1,V3,V6,V4,V2 }U={ V1,V3,V6,V4,V2,V5 }
-
: G : closedge[ ]U V-UviV-U
,closedge[i-1],Closedge[i-1].lowcost=Min{cost(u,vi)| uU}
Closedge[i-1].adjvexU :u,v) (u,v)TEuUvj
-
1 1 1 1 1 1 0 6 1 5 max max 1 3 1 1 3 3 0 5 0 5 6 4U={ v1}U={
v1,v3}UUviV-U ,closedge[i-1],Closedge[i-1].lowcost=Min{cost(u,vi)|
uU} Closedge[i-1].adjvexUV-U={ v2,V3,V4,V5,V6 }V-U={ v2, V4,V5,V6
}
-
0 v1 v1 v1 0 0 0 6 1 5 max max lowcost{v1}iadjvex 0 1 2 3 4 5
Uclosedge v1 v2 v3 v4 v5 v6
- T(n)=O(n)Void MiniSpanTree_Prim(MGrph G, VertexType u)
{k=LocateVex(G, u); for (j=0; j
-
(Kruskal)N=(V,{E})nT=(V,{})ETTT
-
ijAOV(Activity On Vertex network)AOVvivjvjviAOV 7.5
-
AOV~AOVAOV
-
C1--C2--C3--C4--C5--C7--C9--C10--C11--C6--C12--C8
C9--C10--C11--C6--C1--C12--C4--C2--C3--C5--C7--C8AOV
-
0VjVjVkVk1Vk0ntypedef struct node{ int vex; // struct node
*next; //}JD;typedef struct tnode{ int vexdata; int in; // struct
node *link; //}TD;TD g[M]; //g[0]
- Status Topologicalsort(ALGraph G){ FindInDegree(G, indegree);
//indegree InitStack(S); for (i=0; inextarc) { k=p->adjvex; //i1
if(! (--indegree[k])) Push(S, k); } //0 } if(count
-
16
-
6
-
6
-
6
-
6
-
6
-
6
-
6 1
-
6 1
-
6 14
-
6 14
-
6 14
-
6 143
-
6 143
-
6 143
-
6 143
-
6 143
-
6 1 343
-
6 1 34
-
6 1 34
-
6 1 34
-
6 1 342
-
6 1 342
-
6 1 342
-
6 1 3 242
-
6 1 3 24
-
6 1 3 2 44
-
6 1 3 2 4
-
6 1 3 2 45
-
6 1 3 2 45
-
6 1 3 2 4 55
-
6 1 3 2 4 5
-
T(n)=O(e)0T(n)=O(n)T(n)=O(n+e)
-
7.6 119 V1V91 2
-
AOE(Activity On Edge)AOE~Ve(j)VjVl(j) Vje(i) ail(i)
ail(i)-e(i)ai~l(i)=e(i)
-
e(i)=l(i)aidut()1e(i)=Ve(j) 2l(i)=Vl(k)-dut()Ve(j)Vl(j)
-
Ve(i)Vl(j)e(i)l(i)l(i)-e(i)V1V2V3V4V5V6V7V8V90645771614180668710161418a1a2a3a4a5a6a7a8a9a10a11
-
V1Ve[1]=0,Ve[i]VnVl[n]=Ve[n],Vl[i]VeVle[i]l[i],e[i]=l[i]typedef
struct node{ int vex; // int length; struct node *next;
//}JD;typedef struct tnode{ int vexdata; int in; // struct node
*link; //}TD;TD g[M]; //g[0]
-
Ve[i]Vl[i]e[i]l[i],e[i]=l[i]
- Status TopologicalOrder(ALGraph G, Stack &T){
FindInDegree(G, indegree); InitStack(T); count=0;
ve[0..G.vexnum-1]=0; while (! StackEmpty(S)) { Pop(S, j); Push(T,
j); ++count; for (p=G.vertices[j].firstarc; p; p=p->nextarc) {
k=p->adjvex; if (--indegree[k]==0) Push(S, k); if
(ve[j]+*(p->info)>ve[k]) ve[k]=ve[j]+*(p->info); } } if
(count
-
2 Status CriticalPath(ALGraph G){ if (! ToplogicalOrder(G, T))
return ERROR vl[0..G.vexnum-1]=ve[G.vexnum-1]; while (!
StackEmpty(T)) for (Pop(T, j), p=G.vextices[j].firstarc; p;
p=p->nextarc) { k=p->adjvex; dut=*(p->info); if
(vl[k]-dutadjvex; dut=*(p->info); ee=ve[j]; el=vl[k]-dut; tag=
(ee==el) ? '*:; printf(j,k,dut,ee,el, tag ); } }
-
7.7 13
813192120
-
(Dijkstra)V1S2V-S=TTS1V0S V0T 2 SV0 TV0S V0TVkV0Vk V0SVk
-
S={V0},T={}TTWSTWV0ViWSS=V
-
13
8
30
32
V2:8
13
-------13
30
32
V1:13
-------
-------13
30
22
20
V3:13
-------
-------
-------19
22
20
V4:19
--------
--------
--------
--------21
20
V6:20
-
ad[ ][ ]dist[ ]V0pre[ ]V0V00
- Void ShortestPath_DIJ(Mgraph G,int v0,PathMatrix &p,
shortPathTable &D){ for (v=0; v
-
13
8
13
19
21
20
T(n)=O(n)
-
Dijkstran T(n)=O(n)(Floyd)n0
- length[][]path[i][j]ViVjVjVoid ShortFloyd(Mgraph G, PathMatrix
&P[], DistancMatrix &D) { for (v=0; v
-
T(n)=O(n)
-
01(vi,vj)A[i,j]A[j,i]
