图（Graph）广度优先遍历

定义：

图是一种网状数据结构，是由一个顶点的有穷非空集V(G)和一个弧（arc）的集合E(G)组成，通常记作G=（V,E），其中G表示一个图，V是图G中点的集合，E是图G中弧的集合。

存储结构：

1. 邻接矩阵，用一个一维数组来存储G的顶点，用一个相对应的二维数组来存储G的弧。

queue<char> q;
#define MVNum 100
bool Visited[MVNum];

typedef struct AMGraph {
	char vexs[MVNum];   //顶点表
	int arcs[MVNum][MVNum];   //邻接矩阵
	int vexnum, arcnum;   //当前的顶点数和边数
}AMGraph;

int LocateVex(AMGraph& G, char v) {  //找到顶点v的对应下标
	for (int i = 0; i < G.vexnum; i++) {
		if (G.vexs[i] == v) return i;
	}
}

int CreateUDG_1(AMGraph& G) {  //邻接矩阵创建无向图
	char v1, v2;
	cin >> G.vexnum >> G.arcnum;
	getchar();
	for (int i = 0; i < G.vexnum; i++) {
		cin >> G.vexs[i];
	}
	for (int i = 0; i < G.vexnum; i++) {
		for (int j = 0; j < G.vexnum; j++) {
			G.arcs[i][j] = 0;
		}
	}
	for (int k = 0; k < G.arcnum; k++) {
		getchar();
		cin >> v1 >> v2;
		int i = LocateVex(G, v1);
		int j = LocateVex(G, v2);
		G.arcs[i][j] = G.arcs[j][i] = 1;
	}
	return 1;
}


void BFS_AM(AMGraph& G, char v0) {    //广度优先遍历
	int u, i, v, w;
	v = LocateVex(G, v0);
	cout << v0;
	Visited[v] = 1;
	q.push(v0);

	while (!q.empty()) {
		u = q.front();
		v = LocateVex(G, u);
		q.pop();

		for (int i = 0; i < G.vexnum; i++) {
			w = G.vexs[i];
			if (G.arcs[v][i] && !Visited[i]) {
				cout << w;
				q.push(w);
				Visited[i] = 1;
			}
		}
	}
}

3. 邻接表，为每一个顶点建立一个单链表存放与它相邻的边
   顶点表，顺序存储 ，每个数组元素存放顶点的数据和边表的头指针
   边表，链式存储，单链表中存放与一个顶点相邻的所有边，一个链表节点表示一条从该顶点到链表结点顶点的边

queue<char> q;
#define MVNum 100
bool Visited[MVNum];
typedef struct ArcNode {   //边结点
	int adjvex;
	ArcNode* nextarc;
	int info;
}ArcNode;
typedef struct VexNode {   //表头结点
	char data;
	ArcNode* firstarc;
}VexNode,AdjList[MVNum];
typedef struct ALGraph {
	AdjList vertices;
	int vexnum, arcnum;
}ALGraph;

int LocateVex(ALGraph& G, char v) {
	for (int i = 0; i < G.vexnum; i++) {
		if (v == G.vertices[i].data) return i;
	}
}

int CreateUDG_2(ALGraph& G) {   //邻接表创建无向图
	char v1, v2;
	cin >> G.vexnum >> G.arcnum;
	getchar();
	for (int i = 0; i < G. vexnum; i++) {
		cin >> G.vertices[i].data;
		G.vertices[i].firstarc = NULL;
	}
	for (int k = 0; k < G.arcnum; k++) {
		getchar();
		cin >> v1 >> v2;
		int i = LocateVex(G, v1);
		int j = LocateVex(G, v2);
		ArcNode* p1 = new ArcNode;
		p1->adjvex = j;
		p1->nextarc = G.vertices[i].firstarc;
		G.vertices[i].firstarc = p1;
		ArcNode* p2 = new ArcNode;
		p2->adjvex = i;
		p2->nextarc = G.vertices[j].firstarc;
		G.vertices[j].firstarc = p1;
	}
	return 1;
}

void BFS_AL(ALGraph& G, char v0) {
	int u, w, v;
	ArcNode* p;
	cout << v0;
	v = LocateVex(G, v0);
	Visited[v] = 1;
	q.push(v0);
	while (!q.empty()) {
		u = q.front();
		v = LocateVex(G, u);
		q.pop();
		for (p = G.vertices[v].firstarc; p; p = p->nextarc) {
			w = p->adjvex;
			if (!Visited[w]) {
				cout << G.vertices[w].data;
				Visited[w] = 1;
				q.push(G.vertices[w].data);
			}
		}
	}
}

• 非连通图的广度优先遍历

void BFS(AMGraph G) {
	int v;
	for (v = 0; v < G.vexnum; v++) Visited[v] = 0;

	for (v = 0; v < G.vexnum; v++)
		if (!Visited[v]) BFS_AM(G, G.vexs[v]);
}