数据结构图的常用算法总结

本人在校期间写了一个win32应用程序，用于回顾算法导论图的常用算法（图中边的权值为两个圆心的像素点的距离）

1.dijkstra算法求两点之间最短路径：

贪心算法用优先队列实现，每次选择距离起点路径和最短的顶点弹出队列，此顶点最短路径就已经确定

初始图如下

选择起点如W

选择终点如下：

显示路线：

1）

2）

3）

4）

打开数据，第一行为W距离S点距离，剩下为边的距离一遍参考

470
A <-> D 120
D <-> C 71
C <-> E 93
E <-> G 107
G <-> B 129
B <-> A 83
F <-> C 125
C <-> A 122
C <-> G 118
X <-> O 85
O <-> Y 80
Y <-> D 113
D <-> P 101
P <-> H 112
H <-> Q 80
Q <-> R 86
R <-> I 67
I <-> E 75
E <-> H 74
H <-> I 108
I <-> Q 133
Q <-> Z 68
Z <-> P 83
P <-> C 161
C <-> H 86
E <-> J 101
J <-> S 87
S <-> R 119
I <-> S 68
I <-> J 105
G <-> J 112
J <-> T 70
T <-> K 84
K <-> G 63
G <-> T 83
F <-> K 96
G <-> U 141
U <-> F 82
F <-> B 59
B <-> L 87
L <-> U 53
L <-> V 74
V <-> B 114
B <-> M 101
M <-> W 79
W <-> N 68
N <-> A 76
A <-> M 96
M <-> N 91
M <-> V 61
N <-> X 83
X <-> A 115
A <-> O 99
O <-> D 85
Y <-> P 90
P <-> Q 86
U <-> K 103
B <-> D 147
A <-> L 157
X <-> C 211
O <-> P 137
D <-> H 89
B <-> C 104
C <-> J 181
W <-> A 130
W <-> X 143
N <-> O 128
O <-> B 169
M <-> L 113
L <-> F 65
F <-> G 89
F <-> E 172
H <-> G 167
Q <-> E 142
H <-> R 108
S <-> E 125
E <-> T 140
Q <-> D 137
D <-> E 141
E <-> B 180
O <-> C 142
Y <-> H 177
N <-> B 145
V <-> D 252

2.并查集思想求连通分量

对于原始图1：

结果为

对于实验室图2：

求出结果为：

3.贪心算法PRIM求MST

求MST用 KRUSKAL 算法如下：

主要CPP文件

// windowsDesign.cpp : 定义应用程序的入口点。
//

#include "stdafx.h"
#include "windowsDesign.h"
#include "class.h"
#include "function.h"
#include "globalVariable.h"
#include "dis_algo_graph.h"
#include "SS_algo_graph.h"
#include <string>
#include "MST_PRIM.h"
#include "MST_KRUSKAL.h"

#define MAX_LOADSTRING 100

// 全局变量:
HINSTANCE hInst;								// 当前实例
TCHAR szTitle[MAX_LOADSTRING];					// 标题栏文本
TCHAR szWindowClass[MAX_LOADSTRING];			// 主窗口类名

// 全局变量 我自己的
static int nowState = CommondState::emptyState ;
static WindowSize winsize ;
static DataSet graphData;

// 此代码模块中包含的函数的前向声明:
ATOM				MyRegisterClass(HINSTANCE hInstance);
BOOL				InitInstance(HINSTANCE, int);
LRESULT CALLBACK	WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK	About(HWND, UINT, WPARAM, LPARAM);

int APIENTRY _tWinMain(HINSTANCE hInstance,
                     HINSTANCE hPrevInstance,
                     LPTSTR    lpCmdLine,
                     int       nCmdShow)
{
	UNREFERENCED_PARAMETER(hPrevInstance);
	UNREFERENCED_PARAMETER(lpCmdLine);

 	// TODO: 在此放置代码。
	MSG msg;
	HACCEL hAccelTable;

	// 初始化全局字符串
	LoadString(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
	LoadString(hInstance, IDC_WINDOWSDESIGN, szWindowClass, MAX_LOADSTRING);
	MyRegisterClass(hInstance);

	// 执行应用程序初始化:
	if (!InitInstance (hInstance, nCmdShow))
	{
		return FALSE;
	}

	hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_WINDOWSDESIGN));

	// 主消息循环:
	while (GetMessage(&msg, NULL, 0, 0))
	{
		if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
		{
			TranslateMessage( &msg );
			DispatchMessage( &msg );
		}
	}

	return (int) msg.wParam;
}

//  函数: MyRegisterClass()
//  目的: 注册窗口类。
//  注释:
//    仅当希望
//    此代码与添加到 Windows 95 中的“RegisterClassEx”
//    函数之前的 Win32 系统兼容时，才需要此函数及其用法。调用此函数十分重要，
//    这样应用程序就可以获得关联的
//    “格式正确的”小图标。

ATOM MyRegisterClass(HINSTANCE hInstance)
{
	WNDCLASSEX wcex;

	wcex.cbSize = sizeof(WNDCLASSEX);

	wcex.style			= CS_HREDRAW | CS_VREDRAW;
	wcex.lpfnWndProc	= WndProc;
	wcex.cbClsExtra		= 0;
	wcex.cbWndExtra		= 0;
	wcex.hInstance		= hInstance;
	wcex.hIcon			= LoadIcon(hInstance, MAKEINTRESOURCE(IDI_WINDOWSDESIGN));
	wcex.hCursor		= LoadCursor(NULL, IDC_ARROW);
	wcex.hbrBackground	= (HBRUSH)(COLOR_WINDOW+1);
	wcex.lpszMenuName	= MAKEINTRESOURCE(IDC_WINDOWSDESIGN);
	wcex.lpszClassName	= szWindowClass;
	wcex.hIconSm		= LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

	return RegisterClassEx(&wcex);
}

//
//   函数: InitInstance(HINSTANCE, int)
//
//   目的: 保存实例句柄并创建主窗口
//
//   注释:
//
//        在此函数中，我们在全局变量中保存实例句柄并
//        创建和显示主程序窗口。
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
   HWND hWnd;

   hInst = hInstance; // 将实例句柄存储在全局变量中

   hWnd = CreateWindow(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, NULL, NULL, hInstance, NULL);

   if (!hWnd)
   {
      return FALSE;
   }

   long style = GetWindowLong(hWnd,GWL_STYLE);//获得窗口风格

   winsize.screenX = GetSystemMetrics(SM_CXSCREEN);//获取整个屏幕右下角X坐标
   winsize.screenY = GetSystemMetrics(SM_CYSCREEN)-40;//屏幕Y坐标

   SetWindowPos(hWnd, NULL,0,0,winsize.screenX,winsize.screenY,SWP_NOZORDER);//改变窗口位置、尺寸和Z序

   ShowWindow(hWnd, nCmdShow);
   UpdateWindow(hWnd);

   return TRUE;
}

//
//  函数: WndProc(HWND, UINT, WPARAM, LPARAM)
//
//  目的: 处理主窗口的消息。
//
//  WM_COMMAND	- 处理应用程序菜单
//  WM_PAINT	- 绘制主窗口
//  WM_DESTROY	- 发送退出消息并返回

LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
	static Point * myPoint = new Point();
	static TCHAR greet[] = TEXT("A");
	static Line * myline = new Line();
	static Point start,end;
	static list<Line> result;
	static list<Line> result_kruskal;

	int wmId, wmEvent;
	PAINTSTRUCT ps;
	HDC hdc;

	switch (message)
	{
	case WM_COMMAND:
		wmId    = LOWORD(wParam);
		wmEvent = HIWORD(wParam);
		// 分析菜单选择:
		switch ( wmId )
		{
		case IDM_GRAPH_CLEAR:
			{
				clearWindow( hWnd,winsize );
				graphData.lineList.clear();
				graphData.pointList.clear();
			}
			break;
		case IDM_MST_PRIM:
			{
				//1.得到所有边
				//2.显示所有边
				if(! result_kruskal.empty())
				{
					for( list<Line>::iterator it = result_kruskal.begin(); it != result_kruskal.end(); it++ )
					{
						it -> penColor = green ;
						drawLine( hWnd,*it ) ;
					}
					result_kruskal.clear();
				}
				result_kruskal = mstPrim( graphData, graphData.pointList.front() );
				if( ! result_kruskal.empty() )
				{
					for( list<Line>::iterator it = result_kruskal.begin(); it != result_kruskal.end(); it++ )
					{
						it -> penColor = red ;
						drawLine( hWnd,*it ) ;
						Sleep(1000);
					}
				}

			}
			break;

		case IDM_MST_KEUSKAL:
			{
				////1.得到所有边
				////2.显示所有边
				if(! result_kruskal.empty())
				{
					for( list<Line>::iterator it = result_kruskal.begin(); it != result_kruskal.end(); it++ )
					{
						it -> penColor = green ;
						drawLine( hWnd,*it ) ;
					}
					result_kruskal.clear();
				}
				result_kruskal = mstKruskal( graphData );
				if( ! result_kruskal.empty() )
				{
					for( list<Line>::iterator it = result_kruskal.begin(); it != result_kruskal.end(); it++ )
					{
						it -> penColor = red ;
						drawLine( hWnd,*it ) ;
						Sleep(1000);
					}
				}
			}
			break;

		case IDM_SET_SEARCH:
			{
				int* ssdata = setSsearchAlgorithm( graphData );
				int i=0;
				for( list<Point>::iterator it=graphData.pointList.begin(); it != graphData.pointList.end(); it++)
				{
					(*it).brushColor = RGB(255-ssdata[i]*70,ssdata[i]*70,100+ssdata[i]*70);
					i++;
					drawPoint(hWnd,*it);
				}
			}
			break;
		case IDM_ABOUT:
			DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
			break;
		case IDM_EXIT:
			DestroyWindow(hWnd);
			break;
		case IDM_FILE_SAVE:
			{
				saveGraph( graphData ) ;
			}
			break;
		case IDM_FILE_OPEN:
			{
				graphData.pointList.clear( );
				graphData.lineList.clear( );
				result_kruskal.clear( );
				clearWindow( hWnd,winsize );
				openGraph( graphData );
				drawGraph( hWnd,graphData );
			}
			break;
		case IDM_INSERT_NODE:
			nowState = CommondState::insertNodeState ;
			break ;
		case IDM_INSERT_OVER:
			nowState = CommondState::emptyState ;
			break ;
		case IDM_INSERT_LINE:
			nowState = CommondState::insertLineState ;
			break;
		case IDM_SEARCH_START :
			nowState = CommondState::selectStartState ;
			break;
		case IDM_SEARCH_END :
			nowState = CommondState::selectEndState ;
			break ;
		case IDM_SEARCH_OVER :
			nowState = CommondState::emptyState ;
			{
				if( ! result.empty() )
				{
					for( list<Line>::iterator it = result.begin(); it != result.end(); it++ )
					{
						it->penColor = green ;
						drawLine( hWnd,*it ) ;
					}
				}

				if( start.legal(winsize) && end.legal(winsize) )
				{
					result = singleDistance( graphData.pointList,graphData.lineList,start,end );
					if( ! result.empty() )
					for( list<Line>::iterator it = result.begin();it != result.end(); it++ )
					{
						Sleep(1000);
						it->penColor = red;
						drawLine( hWnd,*it );
					}

				}

			}
			break;
		case IDM_DATA_OPEN:
			{
				if( AllocConsole() )
				{
					freopen("CONOUT$","w",stdout);
					cout<<graph_data[start.key-'A'][end.key-'A']<<endl;
					for(list<Line>::iterator  it=graphData.lineList.begin(); it != graphData.lineList.end(); it++)
					{
						cout<<(*it).start.key<<" <-> "<<(*it).end.key<<" "<<(*it).weight<<endl;
					}
				}
				else
				{
					FreeConsole();
					AllocConsole() ;

					freopen("CONOUT$","w",stdout);
					cout<<graph_data[start.key-'A'][end.key-'A']<<endl;
					for(list<Line>::iterator  it=graphData.lineList.begin(); it != graphData.lineList.end(); it++)
					{
						cout<<(*it).start.key<<" <-> "<<(*it).end.key<<" "<<(*it).weight<<endl;
					}

				}
			}
			break;
		case IDM_DATA_CLOSE:
			{
				FreeConsole();
			}
			break;
		default:
			return DefWindowProc(hWnd, message, wParam, lParam) ;
		}
		break;
	case WM_PAINT:
		hdc = BeginPaint(hWnd, &ps);

		// TODO: 在此添加任意绘图代码...
		{
			//1.画出边界
			//2.画出所有节点
			//3.画出所有边
			//Line bianjie ;
			//bianjie.start.x = winsize.screenX / 4 * 3;
			//bianjie.start.y = 0;

			//bianjie.end.x = winsize.screenX / 4 * 3 ;
			//bianjie.end.y = winsize.screenY ;
			//drawLine( hWnd,bianjie );

			//drawGraph(hWnd,graphData);
		}

		EndPaint(hWnd, &ps);
		break;
	case WM_DESTROY:
		PostQuitMessage(0);
		break;

	case WM_LBUTTONDOWN:
		switch( nowState  )
		{
		// 插入节点
		case CommondState::insertNodeState:
			{
				// 获取位置
				myPoint->x = LOWORD(lParam);
				myPoint->y = HIWORD(lParam);
				if( myPoint->legal(winsize) )
				{
					drawPoint(hWnd,*myPoint);

					// 制作关键字
					if(! graphData.pointList.empty())
						greet[0] = TCHAR(graphData.pointList.back().key+1);
					myPoint->key = (char)greet[0];
					TextOut( GetDC(hWnd),myPoint->x - 5,myPoint->y - myPoint->r * 3,greet,1 ) ;

					//greet[0] ++;

					// 保存节点
					graphData.pointList.push_back(*myPoint);
				}

			}
			break;

		case CommondState::insertLineState:
			{
				if(myline->down == false)
				{
					// 获取位置
					Point point ;
					point.x = LOWORD(lParam) ;
					point.y = HIWORD(lParam) ;

					// 检查模糊节点
					bool  result = checkPointInList(point,graphData.pointList) ;

					if( result )
					{
						// 标记按下
						myline -> down = true ;
						myline -> start = point;
						myline -> end = point;
					}
				}
			}
			break ;	

		case CommondState::selectStartState:
			{
				//1.获取坐标
				//2.检查坐标
				//3.如果是节点：保存起点
				//4.否则继续寻找

				Point point ;
				point.x = LOWORD(lParam) ;
				point.y = HIWORD(lParam) ;

				bool result = checkPointInList( point,graphData.pointList );
				if( result )
				{
					if( start.legal(winsize) )
					{
						start.brushColor = green;
						drawPoint(hWnd,start);
					}

					start = point;
					start.brushColor = red;
					drawPoint(hWnd,start);
				}
			}
			break;

		case CommondState::selectEndState:
			{
				//1.获取坐标
				//2.检查坐标
				//3.如果是节点：保存起点
				//4.否则继续寻找

				Point point ;
				point.x = LOWORD( lParam ) ;
				point.y = HIWORD( lParam ) ;

				bool result = checkPointInList( point,graphData.pointList );
				if( result && checkTwoPoint( point,start ) == false )
				{
					if( end.legal( winsize ) )
					{
						end.brushColor = green ;
						drawPoint( hWnd,end ) ;
					}

					end = point;
					end.brushColor = blue ;
					drawPoint(hWnd,end) ;
				}
			}
			break;
		}

		break;

	case WM_MOUSEMOVE:
		{
			if( nowState == CommondState::insertLineState && myline->down == true )
			{
				drawLine(hWnd,*myline);
				Point point ;
				point.x = LOWORD(lParam) ;
				point.y = HIWORD(lParam) ;
				myline->end = point;
				drawLine( hWnd,*myline);
			}
		}

		break;

	case WM_LBUTTONUP:
		{
			if( nowState == CommondState::insertLineState && myline->down == true)
			{
				// 擦除上一条
				drawLine( hWnd,*myline) ;
				Point point ;
				point.x = LOWORD(lParam) ;
				point.y = HIWORD(lParam) ;

				// 检测节点
				bool result = checkPointInList(point,graphData.pointList);
				if( result && checkTwoPoint(point,myline->start) == false )
				{
					myline->end = point ;
					myline->down = false ;
					myline->realLine = true ;
					myline->weight = disTwoPoint(myline->start,myline->end);
					drawLine( hWnd,*myline ) ;
					graphData.lineList.push_back( *myline ) ;
					myline ->realLine = false ;

				}	

				// 错误抬起
				else if(result == false)
				{
					drawLine( hWnd,*myline);
				}
			}
		}
		break;

	default:
		return DefWindowProc(hWnd, message, wParam, lParam);
	}
	return 0;
}

// “关于”框的消息处理程序。
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
	UNREFERENCED_PARAMETER(lParam);
	switch (message)
	{
	case WM_INITDIALOG:
		return (INT_PTR)TRUE;

	case WM_COMMAND:
		if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
		{
			EndDialog(hDlg, LOWORD(wParam));
			return (INT_PTR)TRUE;
		}
		break;
	}
	return (INT_PTR)FALSE;
}

class.h

#ifndef class_h
#define class_h

#include <list>
#include <iostream>
using namespace std;

#define green RGB(50,205,50)
#define red RGB(255,0,0)
#define blue RGB(0,0,255)
#define white RGB(255,255,255)

#define al_red 1
#define al_white 2
#define al_black 3

class WindowSize
{
public:
	int screenX ;
	int screenY ;
	WindowSize()
	{
		screenX = screenY = 0;
	}

};

class Point
{
public:
	int x;
	int y;
	int r;
	char key;
	COLORREF brushColor;

	Point( )
	{
		x = 0;
		y = 0;
		r = 10;
		key = '*';
		brushColor =  green;
	}

	Point(const int & x,const int & y,const char &key )
	{
		this->x = x;
		this->y = y;
		r = 10;
		this->key = key ;
		brushColor =   green;

	}

	Point(const int &x,const int & y)
	{
		this->x = x;
		this->y = y;
		r = 10;
		this->key = '*' ;
		brushColor =   green;

	}

	Point(const Point & point)
	{
		this->x = point.x;
		this->y = point.y;
		r = 10;
		this->key = point.key;
		brushColor = point.brushColor;
	}

	bool legal(const WindowSize  &mywin)
	{
		bool result = true ;
		if(x <= 0 || x >= mywin.screenX || y <= 0 || y >= mywin.screenY)
		{
			result = false;
		}
		return result;
	}

};

class Line
{
public:
	Point start;
	Point end;
	int weight;
	bool down ;
	bool realLine;
	int penWidth;
	COLORREF penColor;
	Line()
	{
		realLine = false;
		penWidth = 2;
		penColor = green;
		down = false;
		weight = -1;
	}

};

class DataSet
{
public:
	list<Point>  pointList ;
	list<Line>  lineList ;
};

#endif

dijkstra算法

dis_algo_graph.h

#ifndef ALGO_H
#define ALGO_H

#include <iostream>
#include <list>
#include "class.h"
#include <utility>
#include <queue>
#include "function.h"
#include <string>
#include <map>
using namespace std;

static int ** graph_data ;
static char startkey;

class Node
{
public: 

	char key;

	Node( char key )
	{
		this -> key = key;
	}

	Node()
	{
		key = '*';
	}

};

bool operator< (const Node & a,const Node & b)
{
	return graph_data[startkey-'A'][a.key-'A'] > graph_data[startkey-'A'][b.key-'A'];
}
list<Line> findByMap( list<char> & road, list<Line>& linelist );

list<Line> singleDistance( list<Point> & pointlist,list<Line> & linelist,const Point & start,const Point & end)
{
	//disktra algorithm
	//1.利用邻接矩阵存储数据
	//2.利用优先队列：
	//	1)放入起点
	//	2)以此寻找终点

	int* color = new int[pointlist.size()];
	int* parent = new int[pointlist.size()];

	for(int i=0; i<pointlist.size(); i++)
	{
		color[i] = al_white;
		parent[i] = -1;
	}

	graph_data = new int*[ pointlist.size() ];
	for( int i=0; i<pointlist.size(); i++ )
		graph_data[i] = new int[ pointlist.size() ];

	for( int i=0; i<pointlist.size(); i++)
		for( int j=0; j<pointlist.size(); j++)
		{
			graph_data[i][j] = -1;
			if( i == j )
				graph_data[i][j] = 0;
		}

	for(list<Line>::iterator it = linelist.begin(); it != linelist.end(); it ++)
	{
		graph_data[(*it).start.key-'A'][(*it).end.key-'A'] = disTwoPoint((*it).start,(*it).end);
		graph_data[(*it).end.key-'A'][(*it).start.key-'A'] = disTwoPoint((*it).start,(*it).end);
	}

	priority_queue<Node,vector<Node>,less<vector<Node>::value_type>> Q;
	list<char> result ;

	Node first(start.key);
	color[start.key-'A'] = al_red;
	Q.push( first );
	Node now ;
	startkey = start.key;
	while(! Q.empty() )
	{
		now = Q.top();
		color[now.key-'A'] = al_black;
		Q.pop();

		if( now.key == end.key )
			break;
		for(int i=0; i<pointlist.size(); i++)
		{
			if(  now.key - 'A' != i && graph_data[now.key-'A'][i] != -1 )
			{
				if( color[i] == al_white )
				{
					parent[i] = now.key - 'A';

					graph_data[start.key-'A'][i] = graph_data[now.key-'A'][i] + graph_data[start.key-'A'][now.key-'A'] ;
					first.key = 'A' + i ;
					color[i] = al_red;
					Q.push( first ) ;
				}

				else if( color[i] = al_red )
				{

					if( graph_data[start.key-'A'][i] > graph_data[now.key-'A'][i] + graph_data[start.key-'A'][now.key-'A'] )
					{
						list<Node> zhongjian;
						while(! Q.empty() )
						{
							zhongjian.push_back(Q.top());
							Q.pop();
						}
						parent[i] = now.key - 'A';
						graph_data[start.key-'A'][i] = graph_data[now.key-'A'][i] + graph_data[start.key-'A'][now.key-'A'] ;
						while( ! zhongjian.empty() )
						{
							Q.push( zhongjian.front() );
							zhongjian.pop_front();
						}
					}

				}
			}
		}
	}

	char road = end.key;
	while( road != start.key )
	{
		if( parent[road-'A'] == -1)
			break;
		result.push_front( road );
		road = 'A'+ parent[road-'A'];
	}
	if(! result.empty())
	result.push_front(road);

	return findByMap(result,linelist);

}

list<Line> findByMap( list<char> & road,list<Line>& linelist )
{
	//1.实用map保存数据
	//2.搜素数据
	//3.返回结果

	string strnull;
	map<string,Line> mymap;
	for(list<Line>::iterator it=linelist.begin();it != linelist.end(); it++)
	{
		mymap.insert( make_pair(strnull +(*it).start.key + (*it).end.key,*it) );
		mymap.insert( make_pair(strnull +(*it).end.key + (*it).start.key,*it) );
	}

	list<Line> result;

	if(road.size() > 1)
		while(  road.size()>1 )
		{

			strnull = road.front();
			road.pop_front();
			strnull += road.front();

			result.push_back( mymap.find( strnull )->second );
		}
	return result;
}

#endif

function.h

#ifndef function_h
#define function_h

#include<iostream>
#include<math.h>
#include<fstream>
#include<list>
#include "class.h"
#include<map>
using namespace std;

void drawLine(HWND hwnd,Line  myline)
{
	HPEN pen,oldpen;
	pen = CreatePen(PS_SOLID,myline.penWidth,myline.penColor);
	HDC hdc = GetDC(hwnd);
	oldpen = (HPEN)SelectObject(hdc,pen);
	if(myline.realLine == false)
		SetROP2(hdc,R2_NOTXORPEN);
	else
		SetROP2(hdc,R2_COPYPEN);
	MoveToEx(hdc,myline.start.x,myline.start.y,NULL);
	LineTo(hdc,myline.end.x,myline.end.y);

	SelectObject(hdc,oldpen);
	DeleteObject(pen);
	ReleaseDC(hwnd,hdc);
}

void drawPoint(HWND hwnd,const Point & mypoint)
{

	HBRUSH brush ;
	HPEN hpen,oldpen;
	hpen = CreatePen(PS_SOLID,4,mypoint.brushColor);
	brush = CreateSolidBrush(mypoint.brushColor);
	HDC hdc = GetDC(hwnd);
	oldpen = (HPEN) SelectObject( hdc,hpen);
	SelectObject( hdc,brush );
	SetROP2( hdc,R2_COPYPEN );

	Ellipse( hdc,mypoint.x - mypoint.r , mypoint.y - mypoint.r , mypoint.x + mypoint.r , mypoint.y + mypoint.r );

	SelectObject(hdc,oldpen);
	DeleteObject(hpen);
	ReleaseDC(hwnd,hdc);
}

bool checkTwoPoint(const Point & a,const Point & b)
{
	bool result = false;
	int abx = abs(a.x - b.x);
	int aby = abs(a.y - b.y);

	if(abx*abx + aby*aby < a.r*a.r )
		result = true ;
	return result;
}

bool checkPointInList( Point &a, list<Point> mylist )
{
	bool result = false ;
	list<Point>::iterator it ;
	if(! mylist.empty())
		for( it = mylist.begin(); it != mylist.end(); it ++ )
		{
			if( checkTwoPoint(a,*it) == true )
			{
				result = true ;
				a = (*it) ;
				break ;
			}
		}
	return result;
}

int disTwoPoint(const Point & start,const Point & end)
{
	int x_w = abs(end.x - start.x);
	int y_w = abs(start.y - end.y);
	return (int)sqrt(float(x_w*x_w + y_w*y_w));
}

void drawGraph(HWND hWnd, DataSet & graphData)
{
	TCHAR greet[1] ;
	if(! graphData.pointList.empty())
	{
		for(list<Point>::iterator it = graphData.pointList.begin(); it != graphData.pointList.end(); it++)
		{
			greet[0] = (*it).key ;
			TextOut( GetDC(hWnd),(*it).x - 5,(*it).y - (*it).r*3,greet,1 ) ;
			drawPoint(hWnd,*it) ;
		}
	}

	if(! graphData.lineList.empty())
	{
		for(list<Line>::iterator it = graphData.lineList.begin(); it!=graphData.lineList.end(); it++)
		{
			drawLine(hWnd,*it);
		}
	}
}

void saveGraph( DataSet & graphData )
{
	//1.保存所有节点
	//2.保存所有边

	ofstream writer;
	writer.open("graph.txt");
	writer<<graphData.pointList.size()<<endl;
	for(list<Point>::iterator it = graphData.pointList.begin();it != graphData.pointList.end();it++)
	writer<<(*it).key<<" "<<(*it).x<<" "<<(*it).y<<endl;
	writer<<graphData.lineList.size()<<endl;
	for(list<Line>::iterator it = graphData.lineList.begin(); it != graphData.lineList.end(); it++)
	writer<<(*it).start.key<<" "<<(*it).end.key<<endl;
	writer.close();
}

void openGraph( DataSet & graphData )
{
	//1.读取所有节点
	//2.读取所有边

	ifstream reader;
	reader.open("graph.txt");
	map<char,Point> mymap;
	int i;
	Point point ;
	Line line ;
	for( reader>>i;i>0;i-- )
	{
		reader>>point.key;
		reader>>point.x;
		reader>>point.y;
		graphData.pointList.push_back( point );
		mymap.insert( make_pair( point.key,point ) );
	}

	for( reader>>i; i>0; i-- )
	{
		reader>>line.start.key ;
		line.start = ( mymap.find(line.start.key) )-> second ;
		reader>>line.end.key ;
		line.end = ( mymap.find(line.end.key) )-> second ;

		line.realLine = true ;
		line.weight = disTwoPoint( line.start,line.end ) ;
		graphData.lineList.push_back( line );

	}

	reader.close();
}

void clearWindow( HWND hwnd,const WindowSize & winsize )
{
	HBRUSH brush;
	brush = CreateSolidBrush( white );
	SelectObject( GetDC(hwnd),brush );
	Rectangle( GetDC(hwnd),0,0,winsize.screenX,winsize.screenY );
	DeleteObject( brush );
}

#endif

globalVariable.h

#ifndef globalVariable_h
#define globalVariable_h

#include <list>
#include "class.h"

class CommondState
{
public:
	static const int emptyState = 0;
	static const int insertNodeState = 1;
	static const int insertLineState = 2;
	static const int selectStartState = 3;
	static const int selectEndState = 4;

};

#endif

MST_KRUSKAL.h

#ifndef mst_kruskal
#define mst_kruskal

#include "class.h"
#include "function.h"
#include <iostream>
#include <list>
using namespace std;

int * mark;

bool linecom (const Line & a,const Line & b)
{
	return a.weight < b.weight;
}

void kruskal_union(const int & a,const int & b,const int & n);

list<Line> mstKruskal( DataSet dataset )
{
	/*
	1.对所有边排序
	2.依次找出最小的边，在保证不成环的情况下并连接
	3.返回边集合
	*/

	// 1
	const int n = dataset.pointList.size();
	mark = new int[n];
	for(int i=0;i<n;i++)
	{
		mark[i] = i;
	}
	dataset.lineList.sort( linecom );

	// 2
	list<Line> result;
	Line edge;
	while( ! dataset.lineList.empty() )
	{
		edge = dataset.lineList.front();
		dataset.lineList.pop_front();
		if( mark[ edge.start.key - 'A' ] != mark[ edge.end.key - 'A' ] )
		{
			result.push_back(edge);
			kruskal_union(mark[ edge.start.key - 'A' ],mark[ edge.end.key - 'A' ],n);
		}
	}

	// 3
	return result;
}

void kruskal_union( const int & a,const int & b,const int & n )
{
	int min_num = min(a,b);
	int max_num = max(a,b);
	for(int i=0;i<n;i++)
	{
		if( mark[i] == max_num )
			mark[i] = min_num;
	}
}

#endif

MST_PRIM.h

#ifndef MST_PRIM
#define MST_PRIM

#include <iostream>
#include <list>
#include "class.h"
#include <utility>
#include <queue>
#include "function.h"
#include <string>
#include <map>
using namespace std;

static int * mst_prior_queue_key;
static int ** mst_graph_data;
static int n;

class PriorNode
{
public:
	int data;
	PriorNode()
	{
		data = MAXINT;
	}

};

bool operator < ( const PriorNode & a , const PriorNode & b )
{
	return mst_prior_queue_key[a.data] > mst_prior_queue_key[b.data] ;
}

list<Line> findByMapWithMST( list<pair<char,char>> & road,list<Line>& linelist );

list<Line> mstPrim(DataSet & dataset ,const Point & start)
{
	//1.初始化优先队列和key值
	//2.以此取出最小的邻边，并不断更新key值
	//3.返回结果边集合

	// 1
	priority_queue<PriorNode,vector<PriorNode>,less<vector<PriorNode>::value_type>> Q;
	PriorNode node,innode;
	int num_node = dataset.pointList.size();
	n = num_node;
	int *al_color = new int[dataset.pointList.size()];

	mst_graph_data = new int*[num_node];
	for( int i=0; i<num_node; i++ )
	{
		mst_graph_data[i] = new int[num_node];
		for( int j=0;j<num_node;j++ )
		{
			mst_graph_data[i][j] = MAXINT;
			if( i == j )
				mst_graph_data[i][j] = 0;
		}
	}
	for(list<Line>::iterator it = dataset.lineList.begin(); it != dataset.lineList.end();  it ++)
	{
		mst_graph_data[(*it).start.key-'A'][(*it).end.key-'A'] = (*it).weight;
		mst_graph_data[(*it).end.key-'A'][(*it).start.key-'A'] = (*it).weight;
	}
	mst_prior_queue_key = new int[num_node];
	for(int i=0;i<num_node;i++)
		mst_prior_queue_key[i] = MAXINT;
	mst_prior_queue_key[start.key - 'A'] = 0;

	// 2
	list<pair<char,char>> result;
	int * parent = new int[num_node];
	for(int i=0;i<num_node;i++)
	{
		parent[i] = MAXINT;
		al_color[i] = al_white;
	}
	node.data = start.key-'A';
	al_color[node.data] = al_red;
	Q.push( node );
	while( ! Q.empty() )
	{
		node = Q.top();
		al_color[node.data] = al_black ;
		if( node.data != start.key - 'A' )
			result.push_back( make_pair( parent[node.data]+'A' , node.data+'A' ) );
		Q.pop();

		for( int i=0; i < num_node; i++ )
		{
			if( al_color[i] == al_red )
			{
				if( mst_graph_data[node.data][i] < mst_prior_queue_key[i] )
				{
					list<PriorNode> zhongjian ;
					while(! Q.empty() )
					{
						zhongjian.push_back(Q.top());
						Q.pop();
					}
					mst_prior_queue_key[ i ] = mst_graph_data[node.data][i] ;
					parent[i] = node.data ;
					while( ! zhongjian.empty() )
					{
						Q.push( zhongjian.front() );
						zhongjian.pop_front();
					}
				}
			}
			else if( al_color[i] == al_white )
			{
				if( mst_graph_data[node.data][i] < mst_prior_queue_key[i] )
				{
					mst_prior_queue_key[ i ] = mst_graph_data[node.data][i] ;
					parent[i] = node.data ;
					al_color[i] = al_red;
					innode.data =  i;
					Q.push( innode );
				}
			}
		}
	}

	return findByMapWithMST(result,dataset.lineList);
}

list<Line> findByMapWithMST( list<pair<char,char>> & road,list<Line>& linelist )
{
	//1.实用map保存数据
	//2.搜素数据
	//3.返回结果

	string strnull;
	map<string,Line> mymap;
	for(list<Line>::iterator it=linelist.begin();it != linelist.end(); it++)
	{
		mymap.insert( make_pair(strnull +(*it).start.key + (*it).end.key,*it) );
		mymap.insert( make_pair(strnull +(*it).end.key + (*it).start.key,*it) );
	}

	list<Line> result;

	while(  road.size()>0 )
	{

		strnull = road.front().first;
		strnull += road.front().second;
		road.pop_front();

		result.push_back( mymap.find( strnull )->second );
	}
	return result;
}

#endif

并查集算法

SS_algo_graph.h

#ifndef SS_H
#define SS_E

#include <iostream>
#include <list>
#include "class.h"
using namespace std;

//0.并查集
//1.给每个节点设置标志颜色位
//2.检查每一条边，是否可以合并
//3.合并边中的两个点所在的集合
//4.返回图的颜色集合

void set_union(const int & a,const int & b,const int & n);

int * pointset;
int * setSsearchAlgorithm( DataSet & graph )
{
	const int n = graph.pointList.size();
	const int m = graph.lineList.size();
	pointset = new int[ n ];
	bool ** edgeset = new bool*[ m ];
	for ( int i=0;i<n;i++ )
		pointset[i] = i;
	for( int i=0;i<m;i++ )
	{
		edgeset[i] = new bool[m];
		for (int j =0;j<m;j++)
		{
			edgeset[i][j] = true;
		}
	}

	for(list<Line>::iterator it = graph.lineList.begin();it != graph.lineList.end();it++)
	{
		if(edgeset[(*it).start.key-'A'][(*it).end.key-'A'] == true)
		{
			if(pointset[(*it).start.key-'A'] != pointset[(*it).end.key-'A'])
			{
				set_union(pointset[(*it).start.key-'A'] , pointset[(*it).end.key-'A'],n);
			}
			edgeset[(*it).start.key-'A'][(*it).end.key-'A'] = false;
		}
	}

	return pointset;
}

void set_union(const int & a,const int & b,const int & n)
{
	int min_num = min(a,b);
	int max_num = max(a,b);
	for(int i=0;i<n;i++)
	{
		if( pointset[i] == max_num )
			pointset[i] = min_num;
	}
}

#endif

源程序打包下载地址： http://pan.baidu.com/s/1kTxFiZl