-
7.1 7.2 7.3 7.4 7.5 7.6
1
7 *
(1)(2)ADT(3)(4)(5)(6)DijkstraFloyedDijkstraFloyed
1
7 *
7.1 7.2 7.3 7.4 7.5 7.6
1
7 *
7.1 GG= VE G1=V1={v0 ,v1,v2,v3,v4 }E1={ (v0,v1),(v0,v3),(v1,v2),
(v1,v4),(v2,v3)(v2,v4) }
1
7 *
(Undigraph) GG(Digraph) GG(Arc) 7.1 G1 V0 V4 V3 V1 V2V0 V1 V2
V3G2
1
7 *
(Undirected Complete Graph)n(n-1)/2(Directed Complete
Graph)n(n-1) 7.1 e= (v, u), vu e
1
7 *
vD(v)vv, ID(v); vv, OD(v) 7.1 eDv
1
7 *
7.1 : D=VEv1,v2, ,vk, E (i=1,2,k-1), v =v1, u =vk,
vuv=u:G=VEv1,v2, ,vk,(vi,vi+1)E( i=1,2,k-1), v =v1, u =vk,
vuv=u
1
7 *
1V0,V1,V2,V3 V0V3V0,V1,V2,V3,V02V0,V2,V3 V0V3 V0,V2,V3,V0G1G2 V0
V4 V3 V1 V2V0 V1 V2 V37.1
1
7 *
7.1 : ,,,
1
7 *
1V0,V1,V2,V3 V0,V1,V2,V4,V12 V0,V2,V3,V0G1G2 V0 V4 V3 V1 V2V0 V1
V2 V37.1
1
7 *
7.1 : ()G=< V, E > vu v u G
1
7 *
7.1 : G=VEG1=V1E1V1 VE1 EE1V1 G1G: ,
1
7 *
7.1 :GG TG T TG TG T
1
7 *
ADT Graph { V
R
} ADT Graph 7.1 V , R={VR}VR={v,wVP(v,w)
1
7 *
CreatGraph(&G) //DestroyGraph(&G) // 7.1
InsertVEx(&G, v) //DeleteVEx(&G, v) //InsertArc(&G, v,
w) //DeleteArc(&G, v, w) //DFSTraVErse(G, v, Visit())
//BFSTraVErse(G, v, Visit()) //
1
-
7.1 7.2 7.3 7.4 7.5 7.6
1
7 *
7.2.17.2.27.2
1
7 *
(1)(2): G=, V={v0,v1,v2, vn-1 },
7.2
1
7 *
(Adjacency Matrix)7.2.1 Gn A[i][j]=1 (vi,vi+1)E E0
1
7 *
0 1 2 30 0 1 1 11 1 0 0 12 1 0 0 13 1 1 1 0(1)i(2),(3)?7.2.1 V0
V2 V1 V3
1
7 *
0 1 2 30 0 1 1 11 1 0 0 12 1 0 0 13 1 1 1 0(1)i(i)(2)(3)7.2.1 V0
V2 V1 V3
1
7 *
0 1 2 3 401234 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0
0v0v4v2v1v3i7.2.1
1
7 *
0 1 2 3 401234 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0
0v0v4v2v1v3ii7.2.1
1
7 *
7.2.1 n A[i][j]=Wij (vi,vi+1)E E0
1
7 *
() 0 1 2 3 401234 2 4 2 2 2 v0v4v2v1v3224227.2.1
1
7 *
#define INFINITY INT_MAX //#define MAX_VERTEX_NUM //Typedef enum
{DG,DN,UDG,UDN} GraphKind;typedef struct ArcCell { // VRType adj;
// VRType InfoType *info; // } ArcCell, AdjMatrix[MAX_VERTEX_NUM]
[MAX_VERTEX_NUM];7.2.1
1
7 *
7.2.1 typedef struct { // VErtexType // vexs[MAX_VERTEX_NUM];
AdjMatrix arcs; // int vexnum, arcnum; // GraphKind kind; // }
MGraph;
MGraph G;
1
7 *
2153462030504070807.2.1
1
7 *
()G7.2.1 G.VExnumG.arcnumG.kind1G.vexs[i];2
G.arcs[i][j].adj=INFINITY; i,j,w,G.arcs[i][j].adj=W;
G.arcs[j][i].adj=W
1
7 *
void Creatgraph(MGraph &G){int i,j,k;float w;
scanf(%d,%d,%d,G.VExnum,G.arcnum,G.kind);for(i=1;i
-
7.1 7.2 7.3 7.4 7.5 7.6
1
7 *
7.3.17.3.2 7.3
1
7 *
v1v6v3v2v4v5v7v8v9v1v6v3v2v4v5v7v8v9Visited[9]1111111117.3.1
000000000
123456789
1
7 *
7.3.1 (1)Vi(2)ViVjVj;(3)VjVi
1
7 *
:1v;23vwwv(v)7.3.1
1
7 *
void DFS(Graph G, int v) { // v G visited[v] = TRUE;
VisitFunc(v); for(w=FirstAdjVEx(G, v);w!=0; w=NextAdjVEx(G,v,w)) if
(!visited[w]) DFS(G, w); // vw // DFS} // DFS7.3.1
1
7 *
FALSE, 7.3.1
1
7 *
void DFSTraVErse(Graph G, Status (*Visit)(int v)) { // G
VisitFunc = Visit; for (v=0; v
-
7.1 7.2 7.3 7.4 7.5 7.6
1
7 *
7.4.1 **7.4.2 7.4.3 **7.4.4 7.4
1
7 *
7.4.1
1
7 *
7.4.1 ()()
1
7 *
MSTabcdefg18181915208209315167.4.1 G=(V,E)UV(u,v)(),uUvV-U(u,v)
(f,e), (f,d),(g,d),(c,d)(f,e),
1
7 *
7.4.1 G=(V,E)TG (1)U={1|1V}()T={ }
(2)min{weight(u,v)|uUvV-U}(ui,vi)TviU (3)bU=V --(Prim)
1
7 *
v2v5v6v4v1v36515536642v2v5v6v4v1v3651100100lowcost0 1 2 3 4
5adjVExclosedge[n]7.4.1 (Prim)
0615100100
v1v1v1v1v1
1
7 *
v1-v3:lowcostclosedge[n]0 1 2 3 4 55v306 v3v34 adjVEx7.4.1
(Prim)v2v5v6v4v1v36515536642v2v5v6v4v1v3651100100
0615100100
v1v1v1v1v1
1
7 *
v1-v3v3-v6v2v5v6v4v1v351465lowcostclosedge[n]0 1 2 3 4
520v6adjVEx7.4.1 (Prim)v2v5v6v4v1v36515536642
050564
v3v1v1v3v3
1
7 *
v1-v3v3-v6v6-v4v2v5v6v4v1v321465v3-v2v2-v5lowcostclosedge[n]0 1
2 3 4 500v23adjVEx7.4.1 (Prim)v2v5v6v4v1v36515536642
050260
v3v1v6v3v3
1
7 *
void MiniSpanTree_P(MGraph G, VErtexType u) { k = LocateVEx (G,
u ); for ( j=0; j
-
7.1 7.2 7.3 7.4 7.5 7.6
1
7 *
7.5 7.5.1 7.5.2
1
7 *
DAG DAG(project) 7.5
1
7 *
1
2
7.5
1
7 *
7.5.1
1
7 *
1 8 2 4,5 3 4,5 4 5 4,6 6 9 7 6 8 9 9 10 17.5.1
1
7 *
94652381710 1 82 4,53 4,54 5 4,66 97 68 99 10 17.5.1 DAG
1
7 *
(AOV) AOVAOVvivjvivj 7.5.1 AOV
1
7 *
(1);(2);(3);(4)AOV 7.5.1
1
7 *
7.5.1 (1)0(2)(3)ab0()
1
7 *
123897564123897564 7.5.1
1
7 *
indegree[]v1v6v4v32 1 1 0 0 7.5.1
4
5
2^
5
5^
v1v2^V3V4V5^V6
3
4^
2^
021230
1
7 *
indegree[](1)indegree[],;(2)while() { vi; vi,vj1, vj0,vj;
}(3)n,7.5.1
1
7 *
void FindInDegree(ALGraph G, int indegree[]){int i; ArcNode *p;
for (i=0;iadjvex]++; p=p->next; } }}7.5.1
1
7 *
Status TopologicalSort(ALGraph G) { SqStack S; int count,k,i;
ArcNode *p; int indegree[MAX_VERTEX_NUM]; FindInDegree(G,
indegree); // InitStack(S); for (i=0; inextarc) { k = p->adjVEx;
if (!(--indegree[k])) Push(S, k); } } if (countinfo > ve[k])
ve[k] = ve[j]+p->info;} } if (countadjvex; dut=p->info; //dut
if (vl[k]-dut < vl[j]) vl[j] = vl[k]-dut; }7.5.2
1
7 *
for (j=0; jnextarc) { k=p->adjvex;dut=p->info; ee = ve[j];
el = vl[k]-dut; tag = (ee==el) ? '*' : ' '; printf(j, k, dut, ee,
el, tag); // } return OK;} // CriticalPath7.5.2
1
7 *
7.5.2 Ve[i]Vl[i], O(n+e) e[k]l[k]O(e) O(n+e)
1
-
7.1 7.2 7.3 7.4 7.5 7.6
1
-
A B Email,AB 7.6
1
7 *
7.6 7.6.1 7.6.2
1
7 *
7.6.1 GviviG
1
7 *
v0v2v4v1v33262534 Dijkstrav7.6.1
1
7 *
D[5]P[5] 1 5 2 6 2 7 2 0 1 2 3 4final[5]7.6.1
v0v2v4v1v33262534
0636060
-100-1-1
10000
1
7 *
D[5]P[5] 1 1 1 0 1 2 3 4final[5]7.6.1 v0v2v4v1v33262534
05367
-12022
10100
1
7 *
DviS={vi}DvviD[i]viS7.6.1
1
7 *
(1)arcsarcs[i][j]S={vi}DvviD[i](2)vjvjvjS7.6.1
1
7 *
(3)vV-SvkD[j]+arcs[j][k]
