7.1 7.2 7.3 7.4 7.5 7.6

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(1)(2)ADT(3)(4)(5)(6)DijkstraFloyedDijkstraFloyed

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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

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(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

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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

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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]