//程序下载自:http://download.csdn.net/source/1930594
//头文件Minheap.h
template <class Type>
class MinHeap //最小堆类;
{
public:
MinHeap(Type a[], int n); //带两参数的构造函数,在此程序中没有应用;
MinHeap(int ms); //构造函数重载,只初始化堆的大小,对堆中结点不初始化;另外,堆元素的存储是以数组
~MinHeap(); //形式,且无父、子指针,访问父亲结点,利用数组标号进行;
bool Insert(const Type &x); //插入堆中一个元素;
bool RemoveMin(Type &x); //删除堆顶最小结点;
void MakeEmpty(); //使堆为空
bool IsEmpty();
bool IsFull();
int Size();
protected:
void FilterDown(const int start, const int endOfHeap); / /自顶向下构造堆
void FilterUp(const int start); //自底向上构造堆
private:
Type *heap;
int maxSize;
const int defaultSize;
int currentSize; //堆当前结点个数大小
};
template <class Type>
MinHeap<Type>::MinHeap(int ms):defaultSize(100)
{
maxSize=ms>defaultSize ? ms : defaultSize;
heap=new Type[maxSize];
currentSize=0;
}
template <class Type>
MinHeap<Type>::MinHeap(Type a[], int n):defaultSize(100)
{
maxSize=n>defaultSize ? n : defaultSize;
heap=new Type[maxSize];
currentSize=n;
for (int i=0; i<n; i++) heap[i]=a[i];
int curPos=(currentSize-2)/2;
while (curPos>=0)
{
FilterDown(curPos, currentSize-1);
curPos–;
}
}
template <class Type>
MinHeap<Type>::~MinHeap()
{
delete []heap;
}
template <class Type>
void MinHeap<Type>::FilterDown(const int start, const int endOfHeap)
{
int i=start, j=i*2+1;
Type temp=heap[i];
while (j<=endOfHeap)
{
if (j<endOfHeap&&heap[j]>heap[j+1]) j++;
if (temp<heap[j]) break;
else
{
heap[i]=heap[j];
i=j;
j=2*i+1;
}
}
heap[i]=temp;
}
template <class Type>
void MinHeap<Type>::FilterUp(const int start)
{
int i=start, j=(i-1)/2;
Type temp=heap[i];
while (i>0)
{
if (temp>=heap[j]) break;
else
{
heap[i]=heap[j];
i=j;
j=(i-1)/2;
}
}
heap[i]=temp;
}
template <class Type>
bool MinHeap<Type>::RemoveMin(Type &x)
{
if (IsEmpty())
{
cerr<<“Heap empty!”<<endl;
return false;
}
x=heap[0];
heap[0]=heap[currentSize-1];
currentSize–;
FilterDown(0, currentSize-1);
return true;
}
template <class Type>
bool MinHeap<Type>::Insert(const Type &x)
{
if (IsFull())
{
cerr<<“Heap Full!”<<endl;
return false;
}
heap[currentSize]=x;
FilterUp(currentSize);
currentSize++;
return true;
}
template <class Type>
bool MinHeap<Type>::IsEmpty()
{
return currentSize==0;
}
template <class Type>
bool MinHeap<Type>::IsFull()
{
return currentSize==maxSize;
}
template <class Type>
void MinHeap<Type>::MakeEmpty()
{
currentSize=0;
}
template <class Type>
int MinHeap<Type>::Size()
{
return currentSize;
}
//MinCover.cpp #include<iostream.h> #include<fstream.h> #include”MinHeap.h” int *p; //最小堆结点 class HeapNode //堆结点类; { friend class VC; public: operator int()const{return cn;} //重载运算符,比较两个结点; private: int i,cn,*x,*c; //i标示堆中结点号,cn标示当前加入的覆盖顶点中权重之和,x数组标示那些 //顶点加入了覆盖顶点的行列,c数组标示X中的覆盖顶点中所有的邻接 // 顶点; }; class VC // VC类用来对堆中结点内部的的操作, { friend MinCover(int **,int [],int); private: void BBVC(); bool cover(HeapNode E); void AddLiveNode(MinHeap<HeapNode>&H,HeapNode E,int cn,int i,bool ch); int **a,n,*w,*bestx,bestn; }; void VC::BBVC() { MinHeap<HeapNode>H(100000); //建立初始空堆; HeapNode E; E.x=new int[n+1]; E.c=new int[n+1]; for(int j=1;j<=n;j++) { E.x[j]=E.c[j]=0; } int i=1,cn=0; //开始时; while(true) { if(i>n) { if(cover(E)) { for(int j=1;j<=n;j++) bestx[j]=E.x[j]; bestn=cn; break; } } else { if(!cover(E)) AddLiveNode(H,E,cn,i,true); //加入结点标号为i 的结点到顶点覆盖集中,并把更新后的结点再插入堆中; AddLiveNode(H,E,cn,i,false); //不把结点标号为 i 的结点加入到顶点覆盖集中,并把更新后的结点插入堆中; } if(H.IsEmpty())break; H.RemoveMin(E); //把 堆顶点先移除给E; cn=E.cn; i=E.i+1; } } //cover bool VC::cover(HeapNode E) { for(int j=1;j<=n;j++) { if(E.x[j]==0&&E.c[j]==0) return false; //存在任意一条边的两个顶点都为0的情况下,为未覆盖情况;X[j]记录覆盖顶点,c[j]记录与覆盖顶点相连的顶点; } //0表征未覆盖,1表征已覆盖; return true; } void VC::AddLiveNode(MinHeap<HeapNode> &H,HeapNode E,int cn,int i,bool ch) { HeapNode N; N.x=new int[n+1]; N.c=new int[n+1]; for(int j=1;j<=n;j++) { N.x[j]=E.x[j]; N.c[j]=E.c[j]; } N.x[i]=ch?1:0; if(ch) { N.cn=cn+w[i]; / /记录I顶点是否加入覆盖的行列中; for(int j=1;j<=n;j++) if(a[i][j]>0) //如果i,j相邻,刚把j顶点加入覆盖邻接顶点集中; N.c[j]++; } else { N.cn=cn; } N.i=i; H.Insert(N); } int MinCover(int **a,int v[],int n) { VC Y; Y.w=new int[n+1]; for(int j=1;j<=n;j++) { Y.w[j]=v[j]; //初始化VC类对象Y; } Y.a=a; Y.n=n; Y.bestx=v; //将地址赋予bestx, Y.BBVC(); return Y.bestn; //bestn是最后的最小顶点覆盖集权重; } int main() { int u,v; int n,c; ifstream infile(“input.txt”); if(!infile) { cout<<“Can’t open input.txt”<<endl; return 0; } ofstream outfile(“output.txt”); if(!outfile) { cout<<“Can’t open output.txt”<<endl; return 0; } infile>>n>>c; //Make2DArray(a,n+1,n+1); int **a; a=new int *[n+1]; for(int k=0;k<=n;k++) a[k]=new int[n+1]; for(int i=0;i<=n;i++) for(int j=0;j<=n;j++) a[i][i]=0; p=new int[n+1]; for(i=1;i<=n;i++) infile>>p[i]; for(i=1;i<=c;i++) { infile>>u>>v; a[u][v]=1; a[v][u]=1; } cout<<MinCover(a,p,n)<<endl; for(i=1;i<=n;i++) cout<<p[i]<<” “; cout<<endl; return 0; } ‘input.txt’ 7 7 1 100 1 1 1 100 10 1 6 2 4 2 5 3 6 4 5 4 6 6 7 说明:在文章中,顶点与结点是两个不同的概念,结点中有记录当前加入顶点覆盖集的 i,有加入顶点覆盖集中的x[],有加入与顶点覆盖集邻接的c[]顶点集; 此程序的运行流程:首先是初始建最小堆过程,把每个顶点插入到堆中,在每个顶点的内部,X[]数组就是记录此时的顶点覆盖集,然后选取此结点内部顶点覆盖集权重之和cn最小的顶点做为扩展结点,然后以比此顶点标号大1的结点为参考(i = E.i + 1),分别插入两个结点到堆中,一个是 i 顶点加入顶点覆盖集后的结点,一个是 i顶点没有加入顶点覆盖集后的结点,然后重新建堆,再重新移出堆结点,重复如此,直到所有顶点都被标记进x[]或c[]中()。