프림(Prim) 알고리즘, 최소신장 트리, 탐욕(Greedy) 알고리즘 [C++ 소스]

프림(Prim) 알고리즘, 최소신장 트리

탐욕(Greedy) 알고리즘 [C++ 소스]

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프림 알고리즘.zip

"본문 내용"은 언제나 휴일 본 사이트에 있습니다.

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//Edge.h

#pragma once

#include <string>

using namespace std;

class Edge

{

    string vt1;

    string vt2;

    int weight;

public:

    Edge(string vt1,string vt2,int height);

    bool Exist(string vt)const;

    bool Exist(string vt1, string vt2)const;

    string Other(string vt)const;

    void View()const;

    int GetWeight()const;

    string GetVt1()const;

    string GetVt2()const;

};

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//Edge.cpp

#include "Edge.h"

#include <iostream>

using namespace std;

 

Edge::Edge(string vt1,string vt2,int weight)

{

    this->vt1 = vt1;

    this->vt2 = vt2;

    this->weight = weight;

}

bool Edge::Exist(string vt)const

{

    return (vt1 == vt)||(vt2==vt);

}

bool Edge::Exist(string vt1, string vt2)const

{

    return Exist(vt1) && Exist(vt2);

}

string Edge::Other(string vt)const

{

    if(vt1 == vt)

    {

        return vt2;

    }

    if(vt2 == vt)

    {

        return vt1;

    }

    return "";

}

void Edge::View()const

{

    cout<<"("<<vt1<<","<<vt2<<","<<weight<<")";

}

int Edge::GetWeight()const

{

    return weight;

}

 

string Edge::GetVt1()const

{

    return vt1;

}

string Edge::GetVt2()const

{

    return vt2;

}

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//Graph.h

#pragma once

#include "Edge.h"

#include <iostream>

#include <vector>

using namespace std;

typedef vector<string> Vertexs;

typedef Vertexs::iterator VIter;

typedef Vertexs::const_iterator CVIter;

typedef vector<Edge *> Edges;

typedef Edges::iterator EIter;

typedef Edges::const_iterator CEIter;

 

class Graph

{

    Vertexs vertexs;

    Edges edges;

public:

    ~Graph(void);   

    bool AddVertex(string vt);

    bool Exist(string vt)const;

    bool AddEdge(string vt1, string vt2,int weight);//간선 추가

    bool Exist(string vt1,string vt2)const;

    void ViewNeighbors()const;

    void ViewNeighbor(string vt)const;   

    int GetVertexCount()const;

    Edges GetEdges()const;

    string GetFirstVertex()const;

};

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//Graph.cpp

#include "Graph.h"

#include <string.h>

#include <algorithm>

 

Graph::~Graph(void)

{

    EIter seek = edges.begin();

    EIter last = edges.end();

    for(  ;seek != last; ++seek)

    {

        delete (*seek);//간선 소멸       

    }   

}

 

bool Graph::AddVertex(string vt)

{

    if(Exist(vt))

    {

        return false;

    }

    vertexs.push_back(vt);

    return true;

}

 

bool Graph::Exist(string vt)const

{

    return find(vertexs.begin(),vertexs.end(),vt) != vertexs.end();

}

 

bool Graph::AddEdge(string vt1, string vt2,int weight)//간선 추가

{

    if(Exist(vt1)&&Exist(vt2))

    {

        if(Exist(vt1,vt2))

        {

            return false;

        }

 

        CEIter seek = edges.begin();

        CEIter last = edges.end();

        for(  ;seek != last; ++seek)

        {

            if((*seek)->GetWeight()>=weight)

            {

                break;

            }

        }   

        edges.insert(seek,new Edge(vt1,vt2,weight));

        return true;

    }

    return false;

}

 

bool Graph::Exist(string vt1,string vt2)const

{

    CEIter seek = edges.begin();

    CEIter last = edges.end();

    for(  ;seek != last; ++seek)

    {

        if((*seek)->Exist(vt1,vt2))

        {

            return true;

        }

    }   

    return false;

}

 

void Graph::ViewNeighbors()const

{

    cout<<"=== 이웃 정점 ==="<<endl;

    CVIter seek = vertexs.begin();

    CVIter last = vertexs.end();

    for(   ;seek != last; ++seek)

    {

        cout<<(*seek)<<"의 이웃: ";

        ViewNeighbor(*seek);//i정점의 이웃 보여주기

    }

    cout<<endl;

}

 

void Graph::ViewNeighbor(string vt)const

{

    CEIter seek = edges.begin();

    CEIter last = edges.end();

    for(  ;seek != last; ++seek)

    {

        if((*seek)->Exist(vt))

        {

            cout<<(*seek)->Other(vt)<<" ";

        }

    }

    cout<<endl;

}

int Graph::GetVertexCount()const

{

    return vertexs.size();

}

Edges Graph::GetEdges()const

{

    return edges;

}

string Graph::GetFirstVertex()const

{

    if(vertexs.size()==0)

    {

        return "";

    }

    return vertexs[0];

}

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//Prim.h

#pragma once

#include "Graph.h"

class Prim

{

    Graph *graph;   

    Edges edges;

public:

    Prim(Graph *graph);

    Graph * MakeMSTree();

private:

    bool SelectVertex(Graph *mstree);

    string IsGreedyVertex(Edge *edge,Graph *mstree)const;

};

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//Prim.cpp

#include "Prim.h"

Prim::Prim(Graph *graph)

{

    this->graph = graph;

}

Graph *Prim::MakeMSTree()

{

    cout<<"프림 알고리즘 시작"<<endl;

    Graph *mstree = new Graph();

    string start = graph->GetFirstVertex();

    cout<<start<<endl;

    mstree->AddVertex(graph->GetFirstVertex());

    edges = graph->GetEdges();

    int vcnt = graph->GetVertexCount();

    while(mstree->GetVertexCount() < vcnt)

    {

        if(SelectVertex(mstree) == false)

        {

            break;

        }

    }

    if(mstree->GetVertexCount() <vcnt)

    {

        delete mstree;

        cout<<"고립 상태의 영역이 있어서 최소 신장 트리를 만들 수 없습니다."<<endl;

        return 0;       

    }   

    return mstree;

}

 

bool Prim::SelectVertex(Graph *mstree)

{

    EIter seek = edges.begin();

    EIter last = edges.end();

    for(   ;seek != last; ++seek)

    {

        string next_vtx = IsGreedyVertex(*seek,mstree);

        if(next_vtx != "")

        {

            string other =(*seek)->Other(next_vtx);

            int weight = (*seek)->GetWeight();

            cout<<"("<<other<<","<<next_vtx<<":"<<weight<<")"<<endl;

            mstree->AddVertex(next_vtx);

            mstree->AddEdge(next_vtx, other,weight);

            return true;

        }

    }

    return false;

}

 

string Prim::IsGreedyVertex(Edge *edge,Graph *mstree)const

{

    string vtx1 = edge->GetVt1();

    string vtx2 = edge->GetVt2();

    if(mstree->Exist(vtx1))

    {

        if(mstree->Exist(vtx2))

        {

            return "";

        }

        return vtx2;

    }

    if(mstree->Exist(vtx2))

    {

        return vtx1;

    }

    return "";

}

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//Program.cpp

#include "Prim.h"

 

int main()

{

    Graph *graph = new Graph();//그래프 동적 생성

    graph->AddVertex("A");

    graph->AddVertex("B");

    graph->AddVertex("C");

    graph->AddVertex("D");

    graph->AddVertex("E");

    graph->AddVertex("F");

    graph->AddVertex("G");

    graph->AddVertex("H");

 

    graph->AddEdge("A","B",5);

    graph->AddEdge("A","D",3);

    graph->AddEdge("A","E",4);

    graph->AddEdge("B","D",3);

    graph->AddEdge("B","H",2);

    graph->AddEdge("C","D",3);

    graph->AddEdge("C","G",4);

    graph->AddEdge("D","H",5);

    graph->AddEdge("D","E",3);

    graph->AddEdge("D","F",3);

    graph->AddEdge("E","F",2);

    graph->AddEdge("F","G",6);

    graph->AddEdge("G","H",3);

    graph->ViewNeighbors();

   

    Prim *prim = new Prim(graph);

    Graph *mstree = prim->MakeMSTree();

    if(mstree)

    {

        cout<<"최소 신장 트리 만들기 성공"<<endl;

        mstree->ViewNeighbors();

        delete mstree;

    }

    delete prim;

    delete graph;

    return 0;

}

 

 

▷ 실행 결과

=== 이웃 정점 ===

A의 이웃: D E B

B의 이웃: H D A

C의 이웃: D G

D의 이웃: F E C B A H

E의 이웃: F D A

F의 이웃: E D G

G의 이웃: H C F

H의 이웃: B G D

 

프림 알고리즘 시작

A

(A,D:3)

(D,F:3)

(F,E:2)

(D,C:3)

(D,B:3)

(B,H:2)

(H,G:3)

최소 신장 트리 만들기 성공

=== 이웃 정점 ===

A의 이웃: D

D의 이웃: B C F A

F의 이웃: E D

E의 이웃: F

C의 이웃: D

B의 이웃: H D

H의 이웃: B G

G의 이웃: H 

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