算法导论22（基本的图算法）

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1. 广度优先搜索（BFS）

#include<iostream> #include<queue>using namespace std;const int N=100;bool visited[N];int d[N],pred[N];struct Node{    int v;    Node *next;    Node(int x):v(x),next(0){}};struct Graph    {    int VNum,ENum;        Node *Adj[N]; };    //无向图，图的顶点的编号为0..VNum-1void createGraph(Graph &G)    {        cin>>G.VNum>>G.ENum;       for(int i=0;i<G.VNum;++i)G.Adj[i]=0;      for(int i=0;i<G.ENum;++i)        {        int u,v;            cin>>u>>v;            Node *p=new Node(v);        p->next=G.Adj[u];          G.Adj[u]=p;        p=new Node(u);          p->next=G.Adj[v];          G.Adj[v]=p;    }    }    void BFS(Graph G,int s){    for(int i=0;i<G.VNum;++i)    {        visited[i]=false;        d[i]=INT_MAX;        pred[i]=-1;    }    visited[s]=true;    d[s]=0;    queue<int> q;    q.push(s);    while(!q.empty())    {        int u=q.front();        q.pop();        for(Node *p=G.Adj[u];p;p=p->next)        {            int v=p->v;            if(!visited[v])            {                visited[v]=true;                d[v]=d[u]+1;                pred[v]=u;                q.push(v);            }        }    }}void printPath(Graph G,int s,int v){    if(v==s)cout<<s<<' ';    else     {        printPath(G,s,pred[v]);        cout<<v<<' ';    }}//输入//8 10//0 1//0 4//1 5//2 3//2 5//2 6//3 6//3 7//5 6//6 7////输出//1 0//1 //1 5 2//1 5 2 3//1 0 4//1 5//1 5 6//1 5 6 7int main()      {      Graph G;      createGraph(G);    int s=1;    BFS(G,s);    for(int i=0;i<G.VNum;++i)    {        printPath(G,s,i);        cout<<endl;    }    return 0;      }

2. 深度优先搜索（DFS）

#include<iostream>using namespace std;const int N=100;   bool visited[N];int d[N],pred[N],f[N],time;  struct Node    {        int v;      Node *next;    Node(int x):v(x),next(0){}  };struct Graph    {           int VNum,ENum;    Node *Adj[N];     };    //有向图，图的顶点的编号为0..VNum-1void createGraph(Graph &G)    {        cin>>G.VNum>>G.ENum;       for(int i=0;i<G.VNum;++i)G.Adj[i]=0;        for(int i=0;i<G.ENum;++i)        {        int u,v;            cin>>u>>v;            Node *p=new Node(v);        p->next=G.Adj[u];          G.Adj[u]=p;    }    }    void DFSVisit(Graph G,int u)  {      d[u]=++time;      visited[u]=true;      for(Node *p=G.Adj[u];p;p=p->next)      {        int v=p->v;        if(!visited[v])          {              pred[v]=u;              DFSVisit(G,v);          }       }      f[u]=++time;  }  void DFS(Graph G)  {      for(int i=0;i<G.VNum;++i)      {          visited[i]=false;          pred[i]=-1;      }    time=0;    for(int i=0;i<G.VNum;++i)      {          if(!visited[i])DFSVisit(G,i);      }  }  //输入//6 8//0 1//0 3//1 4//2 4//2 5//3 1//4 3//5 5////输出//1 8//3 6//9 12//2 7//4 5//10 11int main()      {      Graph G;      createGraph(G);      DFS(G);    for(int i=0;i<G.VNum;++i)    {        cout<<d[i]<<' '<<f[i]<<endl;    }    return 0;      }

3. 拓扑排序

#include<iostream>#include<vector>#include<stack>using namespace std;struct Node{    int v,w;    Node *next;    Node(int x,int y):v(x),w(y),next(0){}};struct Graph{    int VNum,ENum;    vector<Node *> Adj;};void createGraph(Graph &G){    cin>>G.VNum<<G.ENum;    for(int i=0;i<G.VNum;++i)Adj.push_back(0);    for(int i=0;i<G.ENum;++i)    {        int u,v,w;        cin>>u>>v>>w;        Node *p=new Node(v,w);        p->next=G.Adj[u];        G.Adj[u]=p;    }}vector<int> GetIndegree(Graph G){    vector<int> indegree(G.VNum,0);    for(int i=0;i<G.VNum;++i)    {        for(Node *p=G.Adj[i];p;p=p->next)        {            int v=p->v;            ++indegree[v];        }    }    return indegree;}vector<int> TopoSort(Graph G){    vector<int> res;    vector<int> indegree=GetIndegree(G);    stack<int> S;    for(int i=0;i<G.VNum;++i)    {        if(indegree[i]==0)S.push(i);    }    while(!S.empty())    {        int u=S.top();        S.pop();        res.push_back(u);        for(Node *p=G.Adj[u];p;p=p->next)        {            int v=p->v;            if(--indegree[v]==0)S.push(v);        }    }    return res;}int main(){    Graph G;    createGraph(G);    vector<int> res=TopoSort(G);    for(int i=0;i<res.size();++i)cout<<res[i]<<' ';    cout<<endl;    return 0;}

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