图——最小生成树

“test.cpp”

#include<iostream>using namespace std;#include<vector>#include<string>#include<assert.h>#include "Heap.h"#include "UnionFindFet.h"template<class V,class W>class GraphLink{public:struct Node{W _w;size_t _src;size_t _dst;Node* _next;Node(size_t src,size_t dst,const W& w):_src(src),_dst(dst),_w(w),_next(NULL){}};GraphLink(V* vertexs,size_t size,bool isDirected = false):_vertexs(vertexs,vertexs+size),_isDirected(isDirected){_table.resize(size);}GraphLink(bool isDirected):_isDirected(isDirected){}public:void AddEdge(const V& src,const V& dst,const W& w){size_t newsrc = _GetIndex(src);size_t newdst = _GetIndex(dst);if(_isDirected)_AddEdge(newsrc,newdst,w);else{_AddEdge(newsrc,newdst,w);_AddEdge(newdst,newsrc,w);}}void Display(){for(size_t i = 0;i < _vertexs.size();++i){cout<<_vertexs[i]<<"["<<i<<"]->";Node* cur = _table[i];while(cur){cout<<cur->_w<<"["<<cur->_dst<<"]->";cur = cur->_next;}cout<<"NULL"<<endl;}}//克鲁斯卡尔算法bool Kruskal(GraphLink<V,W>& mintree){assert(_isDirected == false);mintree._vertexs = _vertexs;mintree._isDirected = _isDirected;mintree._table.resize(_vertexs.size());//仿函数，用权值来对堆进行建小堆struct Compare{bool operator()(Node* L,Node* R){return L->_w < R->_w;}};Heap<Node*,Compare> minheap;for (size_t i = 0;i < _table.size();i++){Node* cur = _table[i];while (cur){//对无向图进行过滤，不让相同的边重复进入if (cur->_src < cur->_dst){minheap.Push(cur);}cur = cur->_next;}}size_t n = 0;//使用并查集高效的判断是否成环UnionSet ufs(_vertexs.size());while (n < (_vertexs.size() - 1)){if(minheap.Empty())return false;Node* edge = minheap.Top();minheap.Pop();int root1 = ufs.FindRoot(edge->_src);int root2 = ufs.FindRoot(edge->_dst);if (root1 != root2){ufs.UnionSetFrient(root1,root2);mintree._AddEdge(edge->_src,edge->_dst,edge->_w);++n;}}//打印最小生成树的顶点之间的边mintree._KruskalDisplay();return true;}private:void _KruskalDisplay(){for (size_t i = 0;i < _table.size();++i){Node* cur = _table[i];while (cur){cout<<cur->_src<<"--"<<cur->_dst<<",";cur = cur->_next;}}}void _AddEdge(size_t src,size_t dst,const W& w){Node* tmp = new Node(src,dst,w);tmp->_next = _table[src];_table[src] = tmp;}size_t _GetIndex(const V& v){for(size_t i = 0;i < _vertexs.size();++i)if(_vertexs[i] == v)return i;assert(false);}private:vector<V> _vertexs;vector<Node*> _table;bool _isDirected;};void test(){string arr[] = {"A","B","C","D","E"};int size = sizeof(arr)/sizeof(arr[0]);GraphLink<string,int> gl(arr,size);gl.AddEdge("A","D",10);gl.AddEdge("D","B",20);gl.AddEdge("B","C",10);gl.AddEdge("C","E",40);gl.AddEdge("E","B",30);gl.AddEdge("E","A",20);gl.Display();GraphLink<string,int> g2(false);//最小生成树gl.Kruskal(g2);}int main(){test();system("pause");return 0;}

“Heap.h”

#pragma once  #include <vector>  #include <assert.h>  template<class T>  struct Less  {  bool operator()(const T& left,const T& Right)  {  return left < Right;  }  };  template<class T>  struct Greater  {  bool operator()(const T& left,const T& Right)  {  return left > Right;  }  };  template<class T,class Compare = Greater<T>>//缺省值给大堆  class Heap  {  public:  Heap(){}Heap(const T* arr,const size_t size)  {  for (int i = 0;i < size;i++)  {  _arr.push_back(arr[i]);  }  //建堆  for (int i = (_arr.size() - 2) / 2;i >= 0;i--)  {  //寻找非叶子结点，向下调整；  AdjustDown(i);  }  }  void Push(const T& data)  {  _arr.push_back(data);  AdjustUp(_arr.size()-1);  }  void Pop()  {  assert(_arr.empty() != true);  swap(_arr[0],_arr[_arr.size()-1]);  _arr.pop_back();  AdjustDown(0);  }  T Top()  {  return _arr[0];  }  bool Empty()  {  return _arr.empty();  }  int Size()  {  return _arr.size();  }  void Cout()  {  for (int i = 0; i < _arr.size();i++)  {  cout<<_arr[i]<<" ";  }  cout<<endl;  }  private:  void AdjustDown(int parent)  {  int child = 2 * parent + 1;//左孩子  Compare com;  while (child < _arr.size())  {  if (((child+1) < _arr.size())&&(com(_arr[child + 1],_arr[child])))  {  ++child;  }  if (com(_arr[child],_arr[parent]))  {  swap(_arr[child],_arr[parent]);  parent = child;  child = parent * 2 + 1;  }   else  {  break;  }  }  }  void AdjustUp(int child)  {  int parent = (child - 1) / 2;  Compare com;  while (child > 0)  {  if (com(_arr[child],_arr[parent]))  {  swap(_arr[child],_arr[parent]);  child = parent;  parent = (child - 1) / 2;  }   else  {  break;  }  }  }  private:  vector<T> _arr;  };  

“UnionFindSet.h”

#pragma once#include<vector>class UnionSet{public:UnionSet(int n):_n(n){_set.resize(n+1,-1);for(size_t i = 0;i < _set.size();++i){_set[i] = -1;}}void UnionSetFrient(int root1,int root2){int newroot1 = FindRoot(root1);int newroot2 = FindRoot(root2);if(newroot1 != newroot2){_set[newroot1] += _set[newroot2];_set[newroot2] = newroot1;}}int Count(){int count = 0;for(size_t i = 0;i < _set.size();++i){if(_set[i] < 0)++count;}//初始化时0位置的下标为-1，0位置下标不参与计算return (count - 1);}int FindRoot(int x){if(_set[x] >= 0)//不是根{x = _set[x];}return x;}private://int* _set;vector<int> _set;int _n;};