Graph-002-Vertex Adjacent Iterator

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本文深入探讨了图数据结构的两种实现方式：邻接矩阵和邻接表，通过DenseGraph和SparseGraph类的定义，详细解释了稠密图和稀疏图的特性及操作方法，包括节点数量、边的数量、添加边、检查边的存在性以及遍历相邻节点等关键功能。

DenseGraph.h

#ifndef INC_03_VERTEX_ADJACENT_ITERATOR_DENSEGRAPH_H
#define INC_03_VERTEX_ADJACENT_ITERATOR_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];
    }

    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_03_VERTEX_ADJACENT_ITERATOR_SPARSEGRAPH_H
#define INC_03_VERTEX_ADJACENT_ITERATOR_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;
    }

    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

main.cpp

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

using namespace std;


int main() {

    int N = 20;
    int M = 100;

    srand( time(NULL) );


    // Sparse Graph
    SparseGraph g1(N , false);
    for( int i = 0 ; i < M ; i ++ ){
        int a = rand()%N;
        int b = rand()%N;
        g1.addEdge( a , b );
    }

    // O(E)
    for( int v = 0 ; v < N ; v ++ ){
        cout<<v<<" : ";
        SparseGraph::adjIterator adj( g1 , v );
        for( int w = adj.begin() ; !adj.end() ; w = adj.next() )
            cout<<w<<" ";
        cout<<endl;
    }

    cout<<endl;


    // Dense Graph
    DenseGraph g2(N , false);
    for( int i = 0 ; i < M ; i ++ ){
        int a = rand()%N;
        int b = rand()%N;
        g2.addEdge( a , b );
    }

    // O(V^2)
    for( int v = 0 ; v < N ; v ++ ){
        cout<<v<<" : ";
        DenseGraph::adjIterator adj( g2 , v );
        for( int w = adj.begin() ; !adj.end() ; w = adj.next() )
            cout<<w<<" ";
        cout<<endl;
    }

    return 0;
}