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图论(Graph Theory)

矩阵矩阵:适合表示稠密图(完全图)

邻接表:适合表示稀疏图

深度优先遍历

======= 图 ============

稀疏图 - 邻接表

// 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();
        }
    };
};

稠密图 - 邻接矩阵

// 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();
        }
    };
};

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