连通图的遍历(深度遍历/广度遍历)
概念：图中的所有节点都要遍历到，并且只能遍历一次。
深度遍历
广度遍历
深度遍历
概念：从一个给定的顶点开始，找到一条边，沿着这条边一直遍历。
广度遍历
概念：从一个给定的顶点开始，找到这个顶点下的所有子顶点后，再找下一层的子顶点。
深度遍历的实现思路
1，创建一个bool数组，用来识别哪个顶点已经被遍历过了。
2，递归
3，递归找给定顶点是否有下一个顶点（方法：get_first_neighbor），都找完后，
4，再递归找给定顶点之后的在3处找到的顶点后的下一个顶点（方法：get_next_neighbor）
光度遍历的实现思路
1，用队列实现，先入队给定顶点
2，出队
3，入队：与在2处出队的顶点有相连的顶点
代码
graph_link.h
#ifndef __graph_link__#define __graph_link__#include <stdio.h>#include <malloc.h>#include <assert.h>#include <memory.h>#include <stdbool.h>#define default_vertex_size 10#define T char//边的结构typedef struct Edge{
//顶点的下标
int idx; //指向下一个边的指针
struct Edge* link;}Edge;//顶点的结构typedef struct Vertex{
//顶点的值
T data; //边
Edge* adj;
}Vertex;//图的结构typedef struct GraphLink{
int MaxVertices; int NumVertices; int NumEdges;
Vertex* nodeTable;
}GraphLink;//初始化图void init_graph_link(GraphLink* g);//显示图void show_graph_link(GraphLink* g);//插入顶点void insert_vertex(GraphLink* g, T v);//插入边尾插void insert_edge_tail(GraphLink* g, T v1, T v2);//插入边头插void insert_edge_head(GraphLink* g, T v1, T v2);//删除边void remove_edge(GraphLink* g, T v1, T v2);//删除顶点void remove_vertex(GraphLink* g, T v);//销毁图void destroy_graph_link(GraphLink* g);//取得指定顶点的第一个后序顶点int get_first_neighbor(GraphLink* g, T v);//取得指定顶点v1的临街顶点v2的第一个后序顶点int get_next_neighbor(GraphLink* g, T v1, T v2);//深度遍历void dfs_graph(GraphLink* g, T v);//取得顶点的data值T getVertexValue(GraphLink* g, int i);//广度遍历void cfs_graph(GraphLink* g, T v);#endifgraph_link.c
#include "graph_link.h"#include "nodequeue.h"//初始化图void init_graph_link(GraphLink* g){
g->MaxVertices = default_vertex_size;
g->NumVertices = g->NumEdges = 0;
g->nodeTable = (Vertex*)malloc(sizeof(Vertex) * g->MaxVertices);
assert(NULL != g->nodeTable); for(int i = 0; i < g->MaxVertices; ++i){
g->nodeTable[i].adj = NULL;
}
}//显示图void show_graph_link(GraphLink* g){
if(NULL == g)return;
for(int i = 0; i < g->NumVertices; ++i){
printf("%d %c->", i, g->nodeTable[i].data);
Edge* p = g->nodeTable[i].adj;
while(NULL != p){
printf("%d->", p->idx);
p = p->link;
} printf(" NULL\n");
}
}//插入顶点void insert_vertex(GraphLink* g, T v){
if(g->NumVertices >= g->MaxVertices)return;
g->nodeTable[g->NumVertices++].data = v;
}//查找顶点的indexint getVertexIndex(GraphLink* g, T v){
for(int i = 0; i < g->NumVertices; ++i){
if(v == g->nodeTable[i].data)return i;
} return -1;
}//插入边(头插）void insert_edge_head(GraphLink* g, T v1, T v2){
int p1 = getVertexIndex(g, v1); int p2 = getVertexIndex(g, v2);
if(p1 == -1 || p2 == -1)return;
Edge* p = (Edge*)malloc(sizeof(Edge));
p->idx = p2;
p->link = g->nodeTable[p1].adj;
g->nodeTable[p1].adj = p;
p = (Edge*)malloc(sizeof(Edge));
p->idx = p1;
p->link = g->nodeTable[p2].adj;
g->nodeTable[p2].adj = p;
}//取得指定顶点的第一个后序顶点int get_first_neighbor(GraphLink* g, T v){
int i = getVertexIndex(g, v);
if (-1 == i)return -1;
Edge* p = g->nodeTable[i].adj;
if(NULL != p)
return p->idx;
else
return -1;
}//取得指定顶点v1的临街顶点v2的第一个后序顶点int get_next_neighbor(GraphLink* g, T ve1, T ve2){ int v1 = getVertexIndex(g, ve1); int v2 = getVertexIndex(g, ve2); if(v1 == -1 || v2 == -1)return -1;
Edge* t = g->nodeTable[v1].adj;
while(t != NULL && t->idx != v2){
t = t->link;
} if(NULL != t && t->link != NULL){
return t->link->idx;
} return -1;
}//取得顶点的data值T getVertexValue(GraphLink* g, int i){
if(i == -1)return 0; return g->nodeTable[i].data;
}//深度遍历void dfs_graph_v(GraphLink* g, int v, bool* visited){
printf("%c->", getVertexValue(g,v));
visited[v] = true; //取得相邻顶点的下标
int w = get_first_neighbor(g, getVertexValue(g, v));
while(w != -1){
if(!visited[w]){
dfs_graph_v(g, w, visited);
}
w = get_next_neighbor(g, getVertexValue(g, v), getVertexValue(g,w));
}
}void dfs_graph(GraphLink* g, T v){
int cnt = g->NumVertices;
bool* visited = (bool*)malloc(sizeof(bool) * cnt);
assert(NULL != visited);
for(int i = 0; i < cnt; ++i){
visited[i] = false;
}
int index = getVertexIndex(g, v);
dfs_graph_v(g, index, visited); free(visited);
}//广度遍历void cfs_graph(GraphLink* g, T v){ //创建一个辅助的bool数组，用来识别哪个顶点已经被遍历过了
int cnt = g->NumVertices;
bool* visited = (bool*)malloc(sizeof(bool) * cnt);
assert(NULL != visited);
for(int i = 0; i < cnt; ++i){
visited[i] = false;
} //创建队列
NodeQueue q;
init(&q); //入队
int tar = getVertexIndex(g, v);
enQueue(&q, tar); //队列不为空就执行
while(length(&q) != 0){ //取得队列的第一个元素
int ve = getHead(&q)->data;
printf("%c->", getVertexValue(g, ve));
visited[ve] = true; //出队
deQueue(&q);
Edge* e = g->nodeTable[ve].adj;
while(NULL != e){ //如果这个顶点没有被遍历过,入队
if(!visited[e->idx]){
visited[e->idx] = true;
enQueue(&q, e->idx);
}
e = e->link;
}
}
}graph_linkmain.c
#include "graph_link.h"int main(){
GraphLink gl; //初始化图
init_graph_link(&gl); //插入节点
insert_vertex(&gl, 'A');
insert_vertex(&gl, 'B');
insert_vertex(&gl, 'C');
insert_vertex(&gl, 'D');
insert_vertex(&gl, 'E');
insert_vertex(&gl, 'F');
insert_vertex(&gl, 'G');
insert_vertex(&gl, 'H');
insert_edge_head(&gl, 'A', 'B');
insert_edge_head(&gl, 'A', 'C');
insert_edge_head(&gl, 'B', 'D');
insert_edge_head(&gl, 'B', 'E');
insert_edge_head(&gl, 'C', 'F');
insert_edge_head(&gl, 'C', 'G');
insert_edge_head(&gl, 'D', 'H');
insert_edge_head(&gl, 'E', 'H');
insert_edge_head(&gl, 'F', 'G'); //显示图
show_graph_link(&gl); //深度遍历
dfs_graph(&gl, 'E'); printf("null\n");
//广度遍历
cfs_graph(&gl, 'F'); printf("null\n");
}完整代码
编译方法：g++ -g nodequeue.c graph_link.c graph_linkmain.c
作者：小石王
原文链接：https://www.cnblogs.com/xiaoshiwang/p/9397645.html