Graph-004-DFS-and-Components

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最新推荐文章于 2024-07-21 11:20:45 发布

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本文介绍了一种使用深度优先搜索算法来分析图的连通组件的方法，通过构建稠密图和稀疏图的数据结构，实现图的遍历和连通性判断。通过读取图文件并构建图模型，最后运用组件类进行连通组件计数。

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DenseGraph.h

#ifndef INC_05_DFS_AND_COMPONENTS_DENSEGRAPH_H
#define INC_05_DFS_AND_COMPONENTS_DENSEGRAPH_H

#include <iostream>
#include <vector>
#include <cassert>

using namespace std;

// 稠密图 - 邻接矩阵
class DenseGraph{

private:
    int n, m;
    bool directed;
    vector<vector<bool>> g;

public:
    DenseGraph( int n , bool directed ){
        this->n = n;
        this->m = 0;
        this->directed = directed;
        for( int i = 0 ; i < n ; i ++ )
            g.push_back( vector<bool>(n, false) );
    }

    ~DenseGraph(){

    }

    int V(){ return n;}
    int E(){ return m;}

    void addEdge( int v , int w ){

        assert( v >= 0 && v < n );
        assert( w >= 0 && w < n );

        if( hasEdge( v , w ) )
            return;

        g[v][w] = true;
        if( !directed )
            g[w][v] = true;

        m ++;
    }

    bool hasEdge( int v , int w ){
        assert( v >= 0 && v < n );
        assert( w >= 0 && w < n );
        return g[v][w];
    }

    void show(){

        for( int i = 0 ; i < n ; i ++ ){
            for( int j = 0 ; j < n ; j ++ )
                cout<<g[i][j]<<"\t";
            cout<<endl;
        }
    }

    class adjIterator{
    private:
        DenseGraph &G;
        int v;
        int index;
    public:
        adjIterator(DenseGraph &graph, int v): G(graph){
            this->v = v;
            this->index = -1;
        }

        int begin(){

            index = -1;
            return next();
        }

        int next(){
            for( index += 1 ; index < G.V() ; index ++ )
                if( G.g[v][index] )
                    return index;
            return -1;
        }

        bool end(){
            return index >= G.V();
        }
    };
};
#endif

SparseGraph.h

#ifndef INC_05_DFS_AND_COMPONENTS_SPARSEGRAPH_H
#define INC_05_DFS_AND_COMPONENTS_SPARSEGRAPH_H

#include <iostream>
#include <vector>
#include <cassert>

using namespace std;

// 稀疏图 - 邻接表
class SparseGraph{

private:
    int n, m;
    bool directed;
    vector<vector<int>> g;

public:
    SparseGraph( int n , bool directed ){
        this->n = n;
        this->m = 0;
        this->directed = directed;
        for( int i = 0 ; i < n ; i ++ )
            g.push_back( vector<int>() );
    }

    ~SparseGraph(){

    }

    int V(){ return n;}
    int E(){ return m;}

    void addEdge( int v, int w ){

        assert( v >= 0 && v < n );
        assert( w >= 0 && w < n );

        g[v].push_back(w);
        if( v != w && !directed )
            g[w].push_back(v);

        m ++;
    }

    bool hasEdge( int v , int w ){

        assert( v >= 0 && v < n );
        assert( w >= 0 && w < n );

        for( int i = 0 ; i < g[v].size() ; i ++ )
            if( g[v][i] == w )
                return true;
        return false;
    }

    void show(){

        for( int i = 0 ; i < n ; i ++ ){
            cout<<"vertex "<<i<<":\t";
            for( int j = 0 ; j < g[i].size() ; j ++ )
                cout<<g[i][j]<<"\t";
            cout<<endl;
        }
    }

    class adjIterator{
    private:
        SparseGraph &G;
        int v;
        int index;
    public:
        adjIterator(SparseGraph &graph, int v): G(graph){
            this->v = v;
            this->index = 0;
        }

        int begin(){
            index = 0;
            if( G.g[v].size() )
                return G.g[v][index];
            return -1;
        }

        int next(){
            index ++;
            if( index < G.g[v].size() )
                return G.g[v][index];
            return -1;
        }

        bool end(){
            return index >= G.g[v].size();
        }
    };
};

#endif

Components.h

#ifndef INC_05_DFS_AND_COMPONENTS_COMPONENTS_H
#define INC_05_DFS_AND_COMPONENTS_COMPONENTS_H

#include <iostream>
#include <cassert>
using namespace std;


template <typename Graph>
class Component{

private:
    Graph &G;
    bool *visited;
    int ccount;
    int *id;

    void dfs( int v ){

        visited[v] = true;
        id[v] = ccount;
        typename Graph::adjIterator adj(G, v);
        for( int i = adj.begin() ; !adj.end() ; i = adj.next() ){
            if( !visited[i] )
                dfs(i);
        }
    }

public:
    Component(Graph &graph): G(graph){

        visited = new bool[G.V()];
        id = new int[G.V()];
        ccount = 0;
        for( int i = 0 ; i < G.V() ; i ++ ){
            visited[i] = false;
            id[i] = -1;
        }

        for( int i = 0 ; i < G.V() ; i ++ )
            if( !visited[i] ){
                dfs(i);
                ccount ++;
            }
    }

    ~Component(){
        delete[] visited;
        delete[] id;
    }

    int count(){
        return ccount;
    }

    bool isConnected( int v , int w ){
        assert( v >= 0 && v < G.V() );
        assert( w >= 0 && w < G.V() );
        return id[v] == id[w];
    }
};

#endif

ReadGraph.h

#ifndef INC_05_DFS_AND_COMPONENTS_READGRAPH_H
#define INC_05_DFS_AND_COMPONENTS_READGRAPH_H

#include <iostream>
#include <string>
#include <fstream>
#include <sstream>
#include <cassert>

using namespace std;

template <typename Graph>
class ReadGraph{

public:
    ReadGraph(Graph &graph, const string &filename){

        ifstream file(filename);
        string line;
        int V, E;

        assert( file.is_open() );

        assert( getline(file, line) );
        stringstream ss(line);
        ss>>V>>E;

        assert( V == graph.V() );

        for( int i = 0 ; i < E ; i ++ ){

            assert( getline(file, line) );
            stringstream ss(line);

            int a,b;
            ss>>a>>b;
            assert( a >= 0 && a < V );
            assert( b >= 0 && b < V );
            graph.addEdge( a , b );
        }
    }
};
#endif

testG1.txt

testG2.txt

main.cpp

#include <iostream>
#include "SparseGraph.h"
#include "DenseGraph.h"
#include "ReadGraph.h"
#include "Components.h"

using namespace std;


int main() {

    // TestG1.txt
    string filename1 = "testG1.txt";
    SparseGraph g1 = SparseGraph(13, false);
    ReadGraph<SparseGraph> readGraph1(g1, filename1);
    Component<SparseGraph> component1(g1);
    cout<<"TestG1.txt, Component Count: "<<component1.count()<<endl;

    cout<<endl;

    // TestG2.txt
    string filename2 = "testG2.txt";
    SparseGraph g2 = SparseGraph(7, false);
    ReadGraph<SparseGraph> readGraph2(g2, filename2);
    Component<SparseGraph> component2(g2);
    cout<<"TestG2.txt, Component Count: "<<component2.count()<<endl;

    return 0;
}