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无向图个数最少且元素间不相连的子集

问题

设给定一个任意的无向图,将图划分若干的子集,子集集合中任意俩个节点不相连,使用贪心算法使子集个数最少。

算法步骤或流程:

  • 构造一个向量A按结点度大小加入。
  • 构建向量B为空,B存储最后的结果,其元素为子集
  • 取向量A的第一个元素m(即度最大)加入向量B,遍历B中的元素,如果m与B中元素(子集)中的元素都不相连,则加入到当前子集,如果相连则创建新子集。
  • 将向量A中m除去,重新对向量A按度大小排序,重复3

undirectGraph

C++代码

#include

#include
using namespace std;

#include
vector < vector < int >>vec;
const int size = 5 ;
char undirectedGraph[size][size];
vector<vector > sortvector;
vector < vector < int >>\getGreedySet(vector < vector < int >*>_vec, int n)
{
cout<<(char)(65 + n)<<endl;
vector < vector < int >
>::iterator it1;
vector < int >::iterator it2;
bool linkext = false;
for (it1 = _vec->begin(); it1 != _vec->end(); it1++) //外集合
{
vector < int >*temp1 = *it1;
int link = 0;
for (it2 = temp1->begin(); it2 != temp1->end(); it2++)
{
if (undirectedGraph[n][it2] == ‘1’)
{
link++;
break;
}
// cout<<”(“<<
it2<<”,”<<n<<”)”;
}
if (link == 0)
{
temp1->push_back(n);
linkext = true;
break;

    }


}

if (!linkext)
{
    vector < int >*nodeset = new vector < int >();
    nodeset->push_back(n);
    \_vec->push\_back(nodeset);

}
return _vec;

};
int charToInt(char cr)
{
if(cr==’1’)
return 1;
else
return 0;
}

int getDegreeOfNode(int i)
{
int result=0;
for(int j=i+1; j<sortvector.size(); j++)
{
int x=sortvector[i][1];
int y=sortvector[j][1];
result+=charToInt(undirectedGraph[x][y]);
}

for(int m=0; m<i; m++)
{
    int x=sortvector\[m\]\[1\];
    int y=sortvector\[i\]\[1\];
    result+=charToInt(undirectedGraph\[x\]\[y\]);
}

return result;

}

int getinitDegreeOfNode(int i)
{
int result=0;
for(int j=i+1; j<size; j++) result+=charToInt(undirectedGraph[i][j]);
for(int m=0; m<i; m++) result+=charToInt(undirectedGraph[m][i]);
return result;
}
bool greaterMark(vector a,vector b)
{
return a[0]> b[0];
}

int main()
{
vec = new vector < vector < int >>();
vector < int >
nodeset = new vector < int >();
vector < vector < int >*>::iterator it1;
vector < int >::iterator it2;
cout <<
“请输入无向图顶点连接情况:\n(1表示连通,0表示未连通)”
<< endl;
cout << “ >”;
for (int i = 0; i < size; i++) cout << (char)(65 + i);
cout << endl;
for (int i = 0; i < size; i++)
{
cout << (char)(65 + i) << “>”;
cin >> undirectedGraph[i];

}


for (int i = 0; i < size; i++)
{
    vector<int> temp;
    temp.push_back(getinitDegreeOfNode(i));
    temp.push_back(i);
    sortvector.push_back(temp);
}
while(sortvector.size()>0)
{
    std::sort(sortvector.begin(),sortvector.end(),greaterMark);//对无向图进行按照度大小排序

    vec = getGreedySet(vec, sortvector\[0\]\[1\]);
    sortvector.erase(sortvector.begin());
    int i=sortvector.size();
    for(int j=0; j<i; j++) sortvector\[j\]\[0\]=getDegreeOfNode(j);
}

cout << "\\n个数最少且元素间不相连的子集有:" << endl;
for (it1 = vec->begin(); it1 != vec->end(); it1++)
{
    vector < int >\*temp1 = \*it1;

    for (it2 = temp1->begin(); it2 != temp1->end(); it2++) cout << (char)(65 + *it2);
    cout << "  ";
}

}