数据结构与算法C++之单源最短路径算法 Bellman-Ford

实现程序如下

#include 
#include "SparseGraph.h"
#include "ReadGraph.h"
#include "BellmanFord.h"

using namespace std;

int main() {

    string filename = "testG2.txt";
    //string filename = "testG_negative_circle.txt";
    int V = 5;

    SparseGraph<int> g = SparseGraph<int>(V, true);
    ReadGraph<SparseGraph<int>, int> readGraph(g, filename);

    cout<<"Test Bellman-Ford:"<<endl<<endl;
    BellmanFord<SparseGraph<int>, int> bellmanFord(g,0);
    if( bellmanFord.negativeCycle() )
        cout<<"The graph contain negative cycle!"<<endl;
    else
        for( int i = 1 ; i < V ; i ++ ){
            cout<<"Shortest Path to "<<i<<" : "<<bellmanFord.shortestPathTo(i)<<endl;
            bellmanFord.showPath(i);
            cout<<"----------"<<endl;
        }

    return 0;
}

BellmanFord.h定义为

#include 
#include 

#ifndef _EDGE_H_
#define _EDGE_H_
#include "Edge.h"
#endif

using namespace std;

template <typename Graph, typename Weight>
class BellmanFord{

private:
    Graph &G;
    int s;
    Weight* distTo;
    vector<Edge<Weight>*> from;
    bool hasNegativeCycle;

    bool detectNegativeCycle(){

        for( int i = 0 ; i < G.V() ; i ++ ){
            typename Graph::adjIterator adj(G,i);
            for( Edge<Weight>* e = adj.begin() ; !adj.end() ; e = adj.next() )
                if( !from[e->w()] || distTo[e->v()] + e->wt() < distTo[e->w()] )
                    return true;
        }

        return false;
    }

public:
    BellmanFord(Graph &graph, int s):G(graph){

        this->s = s;
        distTo = new Weight[G.V()];
        for( int i = 0 ; i < G.V() ; i ++ ){
            from.push_back(NULL);
        }

        // Bellman-Ford
        distTo[s] = Weight();

        for( int pass = 1 ; pass < G.V() ; pass ++ ){

            // Relaxation
            for( int i = 0 ; i < G.V() ; i ++ ){
                typename Graph::adjIterator adj(G,i);
                for( Edge<Weight>* e = adj.begin() ; !adj.end() ; e = adj.next() )
                    if( !from[e->w()] || distTo[e->v()] + e->wt() < distTo[e->w()] ){
                        distTo[e->w()] = distTo[e->v()] + e->wt();
                        from[e->w()] = e;
                    }
            }
        }

        hasNegativeCycle = detectNegativeCycle();
    }

    ~BellmanFord(){

        delete[] distTo;
    }

    bool negativeCycle(){
        return hasNegativeCycle;
    }

    Weight shortestPathTo( int w ){
        assert( w >= 0 && w < G.V() );
        assert( !hasNegativeCycle );
        return distTo[w];
    }

    bool hasPathTo( int w ){
        assert( w >= 0 && w < G.V() );
        return from[w] != NULL;
    }

    void shortestPath( int w, vector< Edge<Weight> > &vec ){

        assert( w >= 0 && w < G.V() );
        assert( !hasNegativeCycle );

        stack<Edge<Weight>*> s;
        Edge<Weight> *e = from[w];
        while( e->v() != this->s ){
            s.push(e);
            e = from[e->v()];
        }
        s.push(e);

        while( !s.empty() ){
            e = s.top();
            vec.push_back( *e );
            s.pop();
        }
    }

    void showPath(int w){

        assert( w >= 0 && w < G.V() );
        assert( !hasNegativeCycle );

        vector< Edge<Weight> > vec;
        shortestPath(w, vec);
        for( int i = 0 ; i < vec.size() ; i ++ ){
            cout<<vec[i].v()<<" -> ";
            if( i == vec.size()-1 )
                cout<<vec[i].w()<<endl;
        }
    }
};

“testG2.txt”

5 8
0 1 5
0 2 2
0 3 6
1 2 -4
1 4 2
2 4 5
2 3 3
4 3 -3

输出为

当输入有负权环的图时

5 9
0 1 5
0 2 2
0 3 6
1 2 -4
2 1 1
1 4 2
2 4 5
2 3 3
4 3 -3

输出为