图的表示、广度优先搜索、深度优先搜索

//用二维数组表示邻接矩阵
int G[|V|][|V|];
//初始化
for(int i=0;i<|V|;i++){
    for(int j=0;j<|V|;j++){
        if( (i,j) in E){
            G[i][j] = 1;//or G[i][j] = weight[i][j];
        }
        else if(i==j){
            G[i][j] = 0;
        }
        else{
            G[i][j] = MAX;
        }
    }
}

//邻接表的表示
class Node{
public:
    int index;//顶点索引
    Node* next=nullptr;//下一顶点
    Node(int i):index(i){}
};
class VNode{
public:
    char vertex;//顶点
    int index;//顶点索引
    int dist;//BFS:表示顶点到源点的距离,DFS:表示顶点第一次被发现的时间
    int finish;//BFS:无意义,DFS:表示顶点的邻接表扫描完成时的时间
    Color color;//顶点颜色
    int prev;//顶点的前驱
    Node* firstNode=nullptr;//第一条边的尾节点
    VNode(char c,int i):vertex(c),index(i){}
};
class Graph{
    vector<VNode> Adj;//所有顶点
};
//初始化
void AddEdge(Graph &G,int i,int j,int weight,int w[][|V|]){
    Node* p = new Node(j);
    p->next = G.Adj[i].firstNode;
    G.Adj[i].firstNode = p;
    w[i][j]=weight;
        //有向图只需上面部分代码即可
    Node* p2 = new Node(i);
    p2->next = G.Adj[j].firstNode;
    G.Adj[j].firstNode = p2;
    w[j][i] = weight;
}
//初始化顶点
for(int i=0;i<|V|;i++){
    G.Adj.push_back(VNode(V[i], i));
}
//初始化边、权重
int w[6][6];
for (int i = 0; i < 6; ++i){
    for (int j = 0; j < 6; ++j){
        if(i == j){
            w[i][j] = 0;
        }
        else{
            w[i][j] = MAX;
        }    
    }
}
for (i,j) in E:
    AddEdge(G,i,j,weight[i][j],w);

1.从队列Q中弹出一个元素u
2.访问与u相邻的每个顶点v,若v的颜色为白色(未被发现)
    则将v的颜色置为灰色
    v与源点的距离更新为u到源点距离加1
    v的前驱更新为u
    将v压入队列Q
3.u的邻接表扫描完成,将u的颜色置为黑色

BFS(G,s)
    for each vertex u in G.V
        u.color = white
        u.d = MAX
        u.p = NIL
    s.color = gray
    s.d = 0
    s.p = NIL
    Q = ∅
    ENQUEUE(Q,s)
    while Q ≠ ∅
        u = DEQUEUE(Q)
        for each v in G.Adj[u]
            if v.color == white
                v.color = gray
                v.d = u.d+1
                v.p = u
                ENQUEUE(Q,v)
        u.color = black

PrintPath(G,s,v)
    if v==s
        print s
    else if v.p == NIL
        print "No such path"
    else
        PrintPath(G,s,v.p)
        print v

1.全局时间戳time加1,u被发现的时间更新为time,u的颜色更新为灰色
2.访问与u相邻的每个顶点v,若v的颜色为白色(未被发现)
    v的前驱更新为u
    对v进行深度优先访问
3.u的邻接表扫描完成,u的颜色置位黑色,time加1,u的邻接表扫描完成时间更新为time

DFS(G)
    for each vertex u in G.V
        u.color = white
        u.p = NIL
    time  = 0
    for each vertex u in G.V
        if u.color == white
            DFS-VISIT(G,u)
DFS-VISIT(G,u)
    time = time +1//u has just been discovered
    u.d = time
    u.color = gray
    for each v in G.Adj[u]//explore edge(u,v)
        if v.color == white
            v.p = u
            DFS-VISIT(G,v)
    u.color = black//blacken u,it is finished
    time = time +1
    u.f = time