Data structure--painting--minimum spanning tree (prim algorithm)

Source: Internet
Author: User
Tags array definition

Minimum spanning tree configuration for a communication network, which is to make the build tree value on the right and minimize it. Prim and Kruskal algorithms are often used. Look at the prim algorithm: just in case n={v,{e}} It is the smallest spanning tree in the communication network, TE it is n set edge. From Algorithm u={u0} (UO belongs to V). te={} start, re-run the following operations: in all u belongs to U. V belongs to the v-u Edge (u,v) belongs to the least expensive edge found in E (u0,v0) into the set TE, at the same time V0 incorporates U, until u=v. At this point the TE must have N-1, t={v,{te}} as the smallest spanning tree of N.

To implement this algorithm, a second auxiliary array, Closedge, is required to record the edge with the minimum weight from u to v-u. Each time a new vertex is merged into U, the Closedge is updated.

Detailed code such as the following:

#include <iostream> #include <queue> #include <limits.h> #include ".  /header.h "using namespace std;//Primm algorithm constructs a minimum spanning tree const int max_vertex_num=20; Maximum vertex number typedef enum {DG,DN,UDG,UDN} graphkind;//(a map. Have to the net.    No direction graph, no net) typedef int VRTYPE;TYPEDEF Char infotype;typedef char vertextype; #define INFINITY int_maxtypedef struct arccell{  Vrtype adj; Vrtype is a vertex relationship type, for an unauthorized graph. Use 1 or 0 to indicate whether the vertices are adjacent or not. For the right graph.        The value type InfoType info;//the ARC-related information pointer Arccell () {adj=0;    info=0; }}arccell,adjmatrix[max_vertex_num][max_vertex_num];typedef struct mgraph{vertextype Vexs[MAX_VERTEX_NUM];//vertex vector A  Djmatrix arcs;  adjacency Matrix int vexnum,arcnum;  Figure current vertex number and arc number Graphkind kind;    The kind of graph flag}mgraph;//records from the vertex set U to v-u the least-cost edge of the auxiliary array definition typedef struct minedge{vertextype Adjvex; Vrtype Lowcost;}    Minedge,closedge[max_vertex_num];int minimum (mgraph g,closedge closedge) {int min=1;                for (int i=1;i<g.vexnum;++i) {if (closedge[i].lowcost!=0) {min=i;            Break }    } for (int i=min+1;i<g.vexnum;++i) {if (CLOSEDGE[I].LOWCOST&LT;CLOSEDGE[MIN].LOWCOST&AMP;&AMP;CLOSEDGE[I].L    owcost>0) min=i; } return min;}    int Locatevex (mgraph G,vertextype v1) {for (int i=0;i<max_vertex_num;++i) {if (G.VEXS[I]==V1) return i; } return max_vertex_num+1;} Status Createudn (mgraph &g) {//used array (adjacency matrix) notation.  Constructing the G.KIND=UDN network;    The manual assignment is an vexnumber=0,arcnumber=0 int;    char info;    cout<< "Please input the Vexnumber arcnumber and info:";    cin>>vexnumber>>arcnumber>>info;    G.vexnum=vexnumber;    G.arcnum=arcnumber; for (int i=0;i<g.vexnum;++i) {//construct vertex vector cout<< "Please input the vertex of number" <<i<< "(Type ch        AR) ";    cin>>g.vexs[i]; } for (int i=0;i<g.vexnum;++i)//Initialize adjacency matrix for (int j=0;j<g.vexnum;++j) {g.arcs[i][j].adj=infinity            ;        g.arcs[i][j].info=0;    } char V1,v2;    int weight=0,i=0,j=0; Char infOmation; for (int k=0;k<g.arcnum;++k) {//Initialize adjacency matrix cout<< "Please input the Vertexs of the arc and it ' s weight" &l        t;<k+1<< "";        cin>>v1>>v2>>weight;  I=locatevex (G,V1);        J=locatevex (G,V2);        G.arcs[i][j].adj=weight;        G.arcs[j][i].adj=weight;            if (info!=48) {//0 ASCII code is cout<< "please input infomation:";            cin>>infomation;            G.arcs[i][j].info=infomation;        G.arcs[j][i].info=infomation; }} return OK; void Dismgraph (mgraph m) {for (int. i=0;i<m.vexnum;++i) {for (int j=0;j<m.vexnum;++j) {cout<&lt        ;m.arcs[i][j].adj<< "";    } cout<<endl;    }}//Primm algorithm void Minispantree_prim (mgraph g,vertextype u) {int P=locatevex (G,U);    Closedge Closedge;            for (int j=0;j<g.vexnum;++j) {//auxiliary array initialization if (j!=p) closedge[j].adjvex=u;    Closedge[j].lowcost=g.arcs[p][j].adj; } Closedge[p].lowcost=0;    Closedge[p].adjvex=u;    int k=0;        for (int i=1;i<g.vexnum;++i) {k=minimum (G,closedge);        cout<<closedge[k].adjvex<< "--" <<G.vexs[k]<<endl;        closedge[k].lowcost=0; for (int j=0;j<g.vexnum;++j) {//update Closedge array if (G.arcs[k][j].adj<closedge[j].lowcost&&g.arcs[k][j]                . adj!=0) {closedge[j].adjvex=g.vexs[k];            Closedge[j].lowcost=g.arcs[k][j].adj;    }}}}int Main () {mgraph m;    CREATEUDN (m);    Dismgraph (m);    Minispantree_prim (M, ' a '); return 0;}

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Data structure--painting--minimum spanning tree (prim algorithm)

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