Data structure (c implementation)-------Graph's breadth-first traversal

[This is my own study notes, welcome reprint, but please specify the source:http://blog.csdn.net/jesson20121020]

Algorithm Description:

The initial state of Figure g is that all vertices have not been accessed, and in g any selected vertex VI is the initial starting point, then the breadth-first traversal can be defined as follows: first, access to the initial starting point VI, and then go to all the adjacency points of VI w1,w2,..., wk; Then, go to W1,W2, ..., all the unreachable vertices of the adjacency of the WK, and so on, until all the vertices in the diagram with the initial point vi have been accessed.

Algorithm implementation:

(1) Accessing the initial vertex VI

(2) Set vertex v visited tag

(3) Vertex v queue

(4) while (team not empty) {

Take out the first vertex of the team I;

Search all the adjacency points of vertex i in turn;

If it is not accessed, the adjacency point is accessed and enqueued.

｝

The source code for the breadth-first traversal of graphs using adjacency matrices is as follows:

/** * Breadth Traverse graph **/void bfs_mg (mgraph mg,int s) {//clear Access flag init_visit ();//define a queue to hold the adjacency vertex of the current node int q[max_vex_num];int front = 0; int rear = 0;int i,j,k;printf ("%c\t", Mg.vexs[s]); visit[s] = 1; q[rear++] = s;//traversal queue while (front < rear) {i = q[front++];for (j = 1; J <= mg.vexnum;j++) {if (visit[j] = = 0 && MG.ARCS[I][J] = = 1) {printf ("%c\t", Mg.vexs[j]); visit[j] = 1; q[rear++] = j;}}}

The source code for the breadth-first traversal of graphs using adjacency tables is as follows:

/** * Breadth Traverse graph **/void Bfs_ag (algraph ag,int s) {arcptr p;//empty access flag init_visit ();//define a queue to hold the adjacency vertex of the current node int q[max_vertex_num]; int front = 0;int Rear = 0;int i,j,k;printf ("%c\t", Ag.vertices[s]); visit[s] = 1; q[rear++] = s;//traversal queue while (front < rear) {i = q[front++];for (P = ag.vertices[i].firstarc;p;p=p->nextarc) {j = P->a Djvex;if (visit[j] = = 0) {printf ("%c\t", ag.vertices[j].vexdata); visit[j] = 1; q[rear++] = j;}}}

Algorithm Description:

For a connected graph with n vertices and e edges, because each base point needs to be enqueued once, the while statement needs to execute n times, and for the adjacency matrix, it is also necessary to execute n times for the neighboring matrices, so the time complexity of the BFS_MG is O (n^2), and for the adjacency table, The number of internal loops depends on the total number of Benzi nodes of each vertex, so the time complexity of Bfs_ag is O (n+e).

As you can see, the breadth-first traversal requires a secondary queue, and an array of flags, so the spatial complexity is O (n).

Full code:

complete code for breadth-first traversal with adjacency matrices:

/* ============================================================================ name:graph.c Author:jesson 20121020 version:1.0 description:create Graph using adjacency Matrix, Ansi-style ================================= =========================================== * * #include <stdio.h> #include <stdlib.h> #define Max_vex_num 50typedef Char vertextype;typedef enum {DG, UDG} graphtype;typedef struct {vertextype vexs[max_vex_num];int Arcs[max_vex _num][max_vex_num];int Vexnum, Arcnum; Graphtype type;} mgraph;//set vertex access flag int visit[max_vex_num];/** * To get the specified vertex subscript in the vertex collection by name * VEX Vertex * return if found, returns subscript, otherwise, 0 */int GETINDEXOFV Exs (char Vex, mgraph *mg) {int i;for (i = 1; I <= mg->vexnum; i++) {if (mg->vexs[i] = = vex) {return i;}} return 0;} /** * Create adjacency Matrix */void create_mg (mgraph *mg) {int I, J, K;int v1, v2, Type;char C1, c2;printf ("Please input graph type DG (0) or UDG (1): "), scanf ("%d ", &type), if (type = = 0) Mg->type = Dg;else if (type = = 1) mg->type= udg;else {printf ("Please input correct graph type DG (0) or UDG (1)!"); return;} printf ("Please input Vexmun:"); scanf ("%d", &mg->vexnum);p rintf ("Please input arcnum:"); scanf ("%d", &mg-& Gt;arcnum); GetChar (); for (i = 1; I <= mg->vexnum; i++) {printf ("Please input%dth vex (char):", I); scanf ("%c", &m G->vexs[i]); GetChar ();} Initialize the adjacency matrix for (i = 1; I <= mg->vexnum; i++) {for (j = 1; J <= mg->vexnum; J + +) {Mg->arcs[i][j] = 0;}} Enter the information for the edge, establish the adjacency matrix for (k = 1; k <= mg->arcnum; k++) {printf ("Please input%dth Arc v1 (char) v2 (char):", k); scanf ("%c %c ", &AMP;C1, &c2); v1 = Getindexofvexs (c1, mg); v2 = Getindexofvexs (c2, MG); if (Mg->type = = 1) mg->arcs[v1][v2] = MG-&GT;ARCS[V2][V1] = 1;elsemg->arcs[v1][v2] = 1;getchar ();}} /** * Print adjacency matrix and vertex information */void print_mg (mgraph MG) {int I, j;if (mg.type = = DG) {printf ("Graph type:direct graph\n");} else{printf ("Graph type:undirect graph\n");} printf ("Graph vertex number:%d\n", Mg.vexnum);p rintf ("graph arc Number:%d\n ", Mg.arcnum);p rintf (" Vertex set:\n "); for (i = 1; I <= mg.vexnum; i++) printf ("%c\t", Mg.vexs[i]);p rintf ("\nadjacency matrix:\n"); for (i = 1; I <= mg.vexnum; i++) {j = 1;for (; J < MG . Vexnum; J + +) {printf ("%d\t", Mg.arcs[i][j]);} printf ("%d\n", Mg.arcs[i][j]);}} /** * Initialize vertex access flag **/void init_visit () {int i;for (i = 0;i < max_vex_num;i++) Visit[i] = 0;} /** * Breadth Traverse graph **/void bfs_mg (mgraph mg,int s) {//clear Access flag init_visit ();//define a queue to hold the adjacency vertex of the current node int q[max_vex_num];int front = 0; int rear = 0;int i,j,k;printf ("%c\t", Mg.vexs[s]); visit[s] = 1; q[rear++] = s;//traversal queue while (front < rear) {i = q[front++];for (j = 1; J <= mg.vexnum;j++) {if (visit[j] = = 0 && MG.ARCS[I][J] = = 1) {printf ("%c\t", Mg.vexs[j]); visit[j] = 1; q[rear++] = j;}}} /** * Main function */int main (void) {mgraph mg;create_mg (&mg);p rint_mg (MG);p rintf ("\nthe result of bfs:\n"); BFS_MG (mg,1); return exit_success;}

complete code for breadth-first traversal with adjacency table:

/* ============================================================================ name:algraph.c author:jess on20121020 Version:Copyright:Your Copyright Notice description:graph using linklist, Ansi-style ============== ============================================================== * * #include <stdio.h> #include <stdlib.h > #include <stdio.h> #define max_vertex_num 50typedef enum {DG, UDG} graphtype;typedef char vertextype;// Table node typedef struct ARCNODE {int adjvex;//adjacency node int weight;//edge weight struct arcnode *nextarc;//Next node pointer} arcnode, *arcptr;//head node Ty pedef struct {vertextype vexdata;int id; Arcptr Firstarc;} vnode;//head node array typedef struct {Vnode vertices[max_vertex_num];int vexnum, Arcnum; Graphtype type;}  Algraph;int visit[max_vertex_num];/** * gets subscript */int getindexofvexs (char vex, algraph *ag) in the vertex array based on the vertex character {int i;for (i = 1; i <= ag->vexnum; i++) {if (Ag->vertices[i].vexdata = = vex) {return i;}} return 0;} /** * Create adjacency table */void Create_ag (algraph *ag) {ARCPTR P,q;int I, J, K, type; Vertextype v1, v2;printf ("Please input graph type UG (0) or UDG (1):"); scanf ("%d", &type); if (type = = 0) Ag->type = d G;else if (type = = 1) Ag->type = udg;else {printf ("Please input correct graph type UG (0) or UDG (1)!"); return;} printf ("Please input vexnum:"); scanf ("%d", &ag->vexnum);p rintf ("Please input arcnum:"); scanf ("%d", &ag-  >arcnum); GetChar (); for (i = 1; I <= ag->vexnum; i++) {printf ("Please input the%dth vex (char):", I); scanf ("%c", &ag->vertices[i].vexdata); GetChar (); Ag->vertices[i].firstarc = NULL;} for (k = 1; k <= ag->arcnum; k++) {printf ("Please input the%dth Arc v1 (char) v2 (char):", k); scanf ("%c%c", &v1 , &v2); i = Getindexofvexs (v1, ag); j = Getindexofvexs (v2, AG);//create adjacency table according to the type of diagram//Method 1, insert into the link header/*if (ag->type = DG) {//Map p = (arcptr) malloc (sizeof (Arcnode));p->adjvex = J;p->nextarc = ag->vertices[i].firstarc; Ag->vertices[i].firstarc = P;} else {//no graph P = (arcptr) malloc (sizeof (Arcnode));P->adjvex = J;p->nextarc = ag->vertices[i].firstarc; Ag->vertices[i].firstarc = P;p = (arcptr) malloc (sizeof (Arcnode));p->adjvex = I;p->nextarc = Ag->vertices[j ].firstarc; Ag->vertices[j].firstarc = P;} *///Method 2, insert to the end of the list if (Ag->type = = DG) {//P = (arcptr) malloc (sizeof (Arcnode));p->adjvex = j;//table is empty if (ag-> Vertices[i].firstarc = = NULL) {Ag->vertices[i].firstarc = P;} else{//find the last table node q = ag->vertices[i].firstarc;while (Q->nextarc! = NULL) {q = Q->nextarc;} Q->nextarc = P;} P->nextarc = NULL;} else {//no graph P = (arcptr) malloc (sizeof (Arcnode));p->adjvex = j;//table is empty if (Ag->vertices[i].firstarc = = null) {ag-> Vertices[i].firstarc = P;} else{//find the last table node q = ag->vertices[i].firstarc;while (Q->nextarc! = NULL) {q = Q->nextarc;} Q->nextarc = P;} P->nextarc = Null;p = (arcptr) malloc (sizeof (Arcnode));p->adjvex = i;//table is empty if (Ag->vertices[j].firstarc = = null) {Ag->vertices[j].firstarc = p;} else{//find the last table node q = ag->vertices[j].firstarc;while(Q->nextarc! = NULL) {q = Q->nextarc;} Q->nextarc = P;} P->nextarc = NULL;} GetChar ();}}  /** * Output Graph related information */void print_ag (algraph AG) {arcptr p;int i;if (ag.type = DG) {printf ("Graph type:direct graph\n");} else {printf ("Graph type:undirect graph\n");} printf ("Graph vertex number:%d\n", Ag.vexnum);p rintf ("graph arc Number:%d\n", Ag.arcnum);p rintf ("vertex set: \ n"); for ( i = 1; I <= ag.vexnum; i++) printf ("%c\t", Ag.vertices[i].vexdata);p rintf ("\nadjacency list:\n"); for (i = 1; I <= ag.vexnum; i++) {printf ("%d ", i);p = Ag.vertices[i].firstarc;while (P! = NULL) {printf ("-->%d ", P->adjvex);p = P->nextarc;} printf ("\ n");}} /** * Initialize vertex access flag **/void init_visit () {int i;for (i = 0;i < max_vertex_num;i++) Visit[i] = 0;} /** * Breadth Traverse graph **/void Bfs_ag (algraph ag,int s) {arcptr p;//empty access flag init_visit ();//define a queue to hold the adjacency vertex of the current node int q[max_vertex_num]; int front = 0;int Rear = 0;int i,j,k;printf ("%c\t", Ag.vertices[s]); visit[s] = 1; q[rear++] = s;//traversal queue while (front < rear) {i = Q[front++];for (p = ag.vertices[i].firstarc;p;p=p->nextarc) {j = p->adjvex;if (visit[j] = = 0) {printf ("%c\t", Ag.vertices[j]. Vexdata); visit[j] = 1; q[rear++] = j;}}} int main (void) {algraph ag;create_ag (&ag);p Rint_ag (AG);p rintf ("\nthe result of bfs:\n"); Bfs_ag (ag,1); return exit_success;}

Data structure (c implementation)-------Graph's breadth-first traversal