小根堆+Kruskal算法

小根堆头文件：

#include "stdafx.h"#include <vector>#include <iostream>#include <iomanip>using namespace std;template<typename DataType>class MinHeap{public:MinHeap();MinHeap(int);MinHeap( DataType[], int);MinHeap( vector<DataType> );bool removeTop();DataType getTop();bool insert( DataType );bool empty() const;void display() const;private:int capacity;int size;DataType * topPointer;void displayAux( int, int ) const;};template<typename DataType>MinHeap<DataType>::MinHeap(){size = 0;capacity = 10;topPointer = new DataType[capacity + 1];}template<typename DataType>MinHeap<DataType>::MinHeap(int capacity){size = 0;this.capacity = capacity;topPointer = new DataType[capacity + 1];}template<typename DataType>MinHeap<DataType>::MinHeap(DataType arr[], int num){size = 0;capacity = num;topPointer = new DataType[capacity + 1];for(int i = 0; i < num; i++)insert( arr[i] );}template<typename DataType>MinHeap<DataType>::MinHeap( vector<DataType> vec ){size = 0;capacity = vec.size();topPointer = new DataType[capacity + 1];for(int i = 0; i < capacity; i++)insert( vec.at(i) );}template<typename DataType>DataType MinHeap<DataType>::getTop(){return *(topPointer + 1);}template<typename DataType>bool MinHeap<DataType>::removeTop(){*(topPointer + 1) = *(topPointer + size);int start = 1;int end = size;int next = 2*start;while( next <= end ){if( next < end ){if( *(topPointer + next) > *(topPointer + next + 1) )next = next + 1;}if( *(topPointer + start) > *(topPointer + next ) ){DataType tmp = *(topPointer + start);*(topPointer + start) = *(topPointer + next);*(topPointer + next) = tmp;}start = next;next = 2*start; } size--; return true;}template<typename DataType>bool MinHeap<DataType>::insert(DataType item){if( ++size <= capacity )*(topPointer + size) = item;elsereturn false;int start = size;int next = size/2;while( next > 0 && *(topPointer + start) < *(topPointer + next) ){DataType tmp = *(topPointer + next);*(topPointer + next) = *(topPointer + start);*(topPointer + start) = tmp;start = next;next = start/2;}return true;}template<typename DataType>bool MinHeap<DataType>::empty() const{return(0 == size);}template<typename DataType>void MinHeap<DataType>::display() const{displayAux(1,0);}template<typename DataType>void MinHeap<DataType>::displayAux(int index, int indent) const{if( index <= size ){ displayAux( index * 2 , indent + 20 ); cout << setw(indent) << *( topPointer + index) << endl; displayAux( index * 2 + 1, indent + 20 );}elsereturn;}

Kruskal头文件：

#include <iostream>using namespace std;class NodeEdge{public:NodeEdge():startNode(0),endNode(0),distance(0){}NodeEdge(int start, int end):startNode(start),endNode(end){}NodeEdge(int start, int end, int dis):startNode(start),endNode(end),distance(dis){}const NodeEdge & operator = ( const NodeEdge & );void display( ostream & out ) const;public:int startNode;int endNode;int distance;};bool operator < ( const NodeEdge & left, const NodeEdge & right ) {if( left.distance < right.distance )return true;elsereturn false;}bool operator > ( const NodeEdge & left, const NodeEdge & right ) {if( left.distance > right.distance )return true;elsereturn false;}const NodeEdge & NodeEdge::operator = ( const NodeEdge & rightSide ){if( this != & rightSide ){this->startNode = rightSide.startNode;this->endNode = rightSide.endNode;this->distance = rightSide.distance;}return *this;}void NodeEdge::display( ostream & out ) const{out << startNode <<"<---> " << endNode <<"(" << distance <<")";}ostream & operator << ( ostream & out, const NodeEdge & nodeEdge ){nodeEdge.display( out );return out;}

Kruskal源文件：

// Kruskal.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include "MinHeap.h"#include "Kruskal.h"#include <vector>const int NUM = 7;int getNodeRoot(int index);int map[NUM][NUM] = { {0,  28,  INT_MAX,  INT_MAX,  INT_MAX,  10,  INT_MAX},                      {28,  0,  16,  INT_MAX,  INT_MAX,  INT_MAX,  14},  {0,  16,  0,  12,  INT_MAX,  INT_MAX,  INT_MAX},  {INT_MAX,  INT_MAX,  12,  0,  22,  INT_MAX,  18},  {INT_MAX,  INT_MAX,  INT_MAX,  22,  0,  25,  24},  {10,  INT_MAX,  INT_MAX,  INT_MAX,  25,  0,  INT_MAX},                      {INT_MAX,  14,  INT_MAX,  18,  24,  INT_MAX,  0} };bool nodeVisited[NUM + 1] = {false}; int nodeRank[NUM + 1] = {0};int nodeRoot[NUM + 1];int _tmain(int argc, _TCHAR* argv[]){//int a[10] = {4,2,6,9.1,23,54,32,95,23.3};//MinHeap<int> MinHeap(a,10);//MinHeap.display();vector<NodeEdge> nodeVec;for(int i = 0; i < NUM + 1; i++)nodeRoot[i] = i;for(int i = 0; i < NUM; i++){for(int j = i + 1; j < NUM; j++){if(map[i][j] != INT_MAX)nodeVec.push_back( NodeEdge(i+1,j+1,map[i][j]) );}}MinHeap<NodeEdge> nodeMinHeap( nodeVec );nodeVec.clear();nodeMinHeap.display();while( !nodeMinHeap.empty() ){NodeEdge tmp = nodeMinHeap.getTop();int root1 = getNodeRoot( tmp.startNode );int root2 = getNodeRoot( tmp.endNode );if( root1 != root2 ){nodeVec.push_back( tmp );if( nodeRank[root1] > nodeRank[root2] ){if( nodeRoot[tmp.startNode] != root1 && nodeRoot[ nodeRoot[tmp.startNode] ] == nodeRoot[tmp.startNode] )nodeRoot[ nodeRoot[tmp.startNode] ] = root1;if( nodeRoot[tmp.endNode] != root1 && nodeRoot[ nodeRoot[tmp.endNode] ] == nodeRoot[tmp.endNode] )nodeRoot[ nodeRoot[tmp.startNode] ] = root1;nodeRoot[ tmp.startNode ] = root1;nodeRoot[ tmp.endNode ] = root1;}else{if( nodeRoot[tmp.startNode] != root2 && nodeRoot[ nodeRoot[tmp.startNode] ] == nodeRoot[tmp.startNode] )nodeRoot[ nodeRoot[tmp.startNode] ] = root2;if( nodeRoot[tmp.endNode] != root1 && nodeRoot[ nodeRoot[tmp.endNode] ] == nodeRoot[tmp.endNode] )nodeRoot[ nodeRoot[tmp.startNode] ] = root2;nodeRoot[ tmp.startNode ] = root2;nodeRoot[ tmp.endNode ] = root2;if( nodeRank[root1] == nodeRank[root2] )nodeRank[root2]++;}}nodeMinHeap.removeTop();}for( vector<NodeEdge>::iterator it = nodeVec.begin(); it != nodeVec.end(); it++ )cout << *it << endl;return 0;}        int getNodeRoot( int index ){if( nodeRoot[index] != index )return getNodeRoot( nodeRoot[index] );elsereturn index;}

参考程序：

http://www.codeproject.com/Articles/163618/Kruskal-Algorithm