最短路径实验报告

一、实验目的学习掌握图的存储结构利用最短路径算法，通过java编程实现最短路径输出。

二、实验环境Eclipse平台三、实验过程最短路径算法问题是计算机科学、运筹学、地理信息系统和交通诱导、导航系统等领域研究的一个热点。

传统的最短路径算法主要有Floyd算法和Dijkstra算法。

Floyd算法用于计算所有结点之间的最短路径。

Dijkstra算法则用于计算一个结点到其他所有结点的最短路径。

本程序利用Dijkstra算法用java语言实现最短路径的可视化。

流程: 画无向邻接矩阵邻接矩阵初始化求取最短路径Java文件如下M ain.java 文件：import java.awt.BorderLayout;import java.awt.Color;import java.awt.FlowLayout;import java.awt.event.ActionEvent;import java.awt.event.ActionListener;import java.awt.event.ItemEvent;import java.awt.event.ItemListener;import java.util.StringTokenizer;import javax.swing.JButton;import javax.swing.JComboBox;import javax.swing.JFrame;import javax.swing.JLabel;import javax.swing.JPanel;import javax.swing.border.TitledBorder;public class Main {public static void main(String args[]) {new UI("最短路径");}}@SuppressWarnings("serial")class UI extends JFrame implements ActionListener, ItemListener { JFrame frame;JButton button;JLabel label1, label2, label3;JComboBox list1, list2;JPanel panel1, panel2;ShortCanvas canvas;ShortInit inits;SetFont f;String circlename[];String circle1, circle2;String path[];int circlenum;int list2_index;int D[];int renum[];int num = 0;UI(String s) {super(s);canvas = new ShortCanvas();add(canvas,BorderLayout.CENTER);f=new SetFont();inits = new ShortInit();circlename = inits.getcirclename();circlenum =inits.getcirclenum();circle1 = circlename[0];circle2 = circlename[0];panel2 = new JPanel();panel2.setBorder(new TitledBorder("最短路径"));panel2.setBackground(Color.white);panel2.setLayout(new FlowLayout(FlowLayout.LEADING, 5, 5));label1 = new JLabel("起点", JLabel.LEFT);label1.setFont(f.setSysFontAndFace());panel2.add(label1);list1 = new JComboBox();list1.addItemListener(this);list1.setMaximumRowCount(5);// 设置 JComboBox 显示的最大行数panel2.add(list1);label2 = new JLabel("终点");label2.setFont(f.setSysFontAndFace());panel2.add(label2);list2 = new JComboBox();list2.addItemListener(this);panel2.add(list2);list2.setMaximumRowCount(5);// 设置 JComboBox 显示的最大行数for (int i = 0; i < circlenum; i++) {list1.addItem(circlename[i]);list2.addItem(circlename[i]);}button = new JButton("确定");button.addActionListener(this);button.setFont(f.setSysFontAndFace());panel2.add(button);label3 = new JLabel("");label3.setFont(f.setSysFontAndFace());panel2.add(label3);add(panel2,BorderLayout.SOUTH);setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);setBounds(100, 100, 530, 547);setVisible(true);validate();}public void itemStateChanged(ItemEvent e) {if (e.getSource() == list1)circle1 = (String) list1.getSelectedItem();if (e.getSource() == list2) {circle2 = (String) list2.getSelectedItem();list2_index = list2.getSelectedIndex();}}public void actionPerformed(ActionEvent e) {if (e.getSource() == button) {ShortPath sp = new ShortPath(circle1, circle2);path = sp.getpath();D = sp.getD();label3.setText("最短路径为:" + D[list2_index]);renum = new int[circlenum];StringTokenizer fenxi = newStringTokenizer(path[list2_index], "->");num = 0;while (fenxi.hasMoreTokens()) {String str = fenxi.nextToken();for (int i = 0; i < circlenum; i++) {if (str.equals(circlename[i])) {renum[num] = i;num++;}}}canvas.flag = 1;canvas.resultroad = renum;canvas.num = num;canvas.repaint();}}}SetFont.java文件import java.awt.Font;import javax.swing.JFrame;import javax.swing.UIManager;import javax.swing.UnsupportedLookAndFeelException;//系统外观处理@SuppressWarnings("serial")public class SetFont extends JFrame {public Font setSysFontAndFace() {try {// 根据类名称设置外观UIManager.setLookAndFeel("com.sun.java.swing.plaf.windows.WindowsLookAndFeel" );} catch (UnsupportedLookAndFeelException ex) {} catch (IllegalAccessException ex) {} catch (InstantiationException ex) {} catch (ClassNotFoundException ex) {}Font font = new Font("新宋体", Font.ITALIC + Font.BOLD, 17);return font;}}ShortCanvas.java文件://画无向邻接矩阵import java.awt.Canvas;import java.awt.Color;import java.awt.Graphics;@SuppressWarnings("serial")public class ShortCanvas extends Canvas {SetFont f;ShortInit init;String circlename[];int roadlength[];int arcs[][]; // 带权邻接矩阵int circlenum;int roadnum;int location[][]; // 各点坐标int flag = 0;int num;int resultroad[];// 结果线路ShortCanvas() {f = new SetFont();init = new ShortInit();circlename = init.getcirclename();roadlength = init.getroadlength();circlenum = init.getcirclenum();roadnum = init.getroadnum();arcs = new int[circlenum][circlenum];location = new int[circlenum][2];for (int i = 0; i < circlenum; i++)for (int j = 0; j < circlenum; j++)arcs[i][j] = 10000;set();}public void paint(Graphics g) {g.setFont(f.setSysFontAndFace());g.drawOval(60, 60, 25, 25); // ag.drawString(circlename[0], 70, 75);g.drawString(String.valueOf(roadlength[0]), 135, 135);g.drawOval(200, 180, 25, 25); // bg.drawString(circlename[1], 210, 195);g.drawLine(70, 85, 200, 192); // a--bg.drawOval(100, 300, 25, 25); // cg.drawString(circlename[2], 110, 315);g.drawString(String.valueOf(roadlength[1]), 90, 195);g.drawLine(70, 85, 112, 300); // a--cg.drawString(String.valueOf(roadlength[2]), 165, 250);g.drawLine(200, 192, 112, 300); // b--cg.drawOval(350, 180, 25, 25); // dg.drawString(circlename[3], 360, 195);g.drawString(String.valueOf(roadlength[3]), 285, 190);g.drawLine(225, 192, 350, 192); // b--dg.drawOval(250, 360, 25, 25); // gg.drawString(circlename[4], 260, 375);g.drawString(String.valueOf(roadlength[4]), 185, 345);g.drawLine(125, 315, 250, 375); // c--gg.drawString(String.valueOf(roadlength[5]), 305, 270);g.drawLine(275, 372, 350, 192); // g--dg.drawOval(450, 80, 25, 25); // eg.drawString(circlename[5], 460, 95);g.drawString(String.valueOf(roadlength[6]), 420, 150);g.drawLine(375, 192, 462, 105); // d--eg.drawOval(480, 300, 25, 25); // fg.drawString(circlename[6], 490, 315);g.drawString(String.valueOf(roadlength[7]), 465, 205);g.drawLine(462, 105, 492, 300); // e--fg.drawString(String.valueOf(roadlength[8]), 420, 280);g.drawLine(375, 192, 480, 312); // d--fg.drawString(String.valueOf(roadlength[9]), 370, 330);g.drawLine(275, 372, 480, 312); // g--fg.drawString(String.valueOf(roadlength[10]), 260, 85);g.drawLine(70, 85, 450, 92); // a--eint i, j;if (flag == 1) {g.setColor(Color.red);for (i = 0; i < num - 1; i++) {j = i + 1;g.drawLine(location[resultroad[i]][0] + 12,location[resultroad[i]][1] + 12,location[resultroad[j]][0] + 12,location[resultroad[j]][1] + 12);}}}public void set() {location[0][0] = 60;location[0][1] = 60;location[1][0] = 200;location[1][1] = 180;location[2][0] = 100;location[2][1] = 300;location[3][0] = 350;location[3][1] = 180;location[4][0] = 250;location[4][1] = 360;location[5][0] = 450;location[5][1] = 80;location[6][0] = 480;location[6][1] = 300;arcs[0][1] = arcs[1][0] = roadlength[0];arcs[0][2] = arcs[2][0] = roadlength[1];arcs[1][2] = arcs[2][1] = roadlength[2];arcs[1][3] = arcs[3][1] = roadlength[3];arcs[2][4] = arcs[4][2] = roadlength[4];arcs[4][3] = arcs[3][4] = roadlength[5];arcs[3][5] = arcs[5][3] = roadlength[6];arcs[5][6] = arcs[6][5] = roadlength[7];arcs[3][6] = arcs[6][3] = roadlength[8];arcs[4][6] = arcs[6][4] = roadlength[9];arcs[0][5] = arcs[5][0] = roadlength[10];}public int[][] getarcs() {return arcs;}}ShortInit.java文件：public class ShortInit {int circlenum=7;int roadnum=9;int num[];String circlename[];int roadlength[];ShortInit (){circlename=new String[10];roadlength=new int[15];circlename[0]="a";circlename[1]="b";circlename[2]="c";circlename[3]="d";circlename[4]="g";circlename[5]="e";circlename[6]="f";roadlength[0]=7;roadlength[1]=6;roadlength[2]=3;roadlength[3]=20;roadlength[4]=5;roadlength[5]=3;roadlength[6]=9;roadlength[7]=6;roadlength[8]=8;roadlength[9]=11;roadlength[10]=8;}public String[] getcirclename(){return circlename;}public int[] getroadlength(){return roadlength;}public int getcirclenum(){return circlenum;}public int getroadnum(){return roadnum;}}Shortpath.java 文件//求取最短路径public class ShortPath {int maxlength = 10000;int maxcirclenum = 30;ShortInit init;ShortCanvas canvas;String circlename[];String start, end;String path[];int arcs[][];int circlenum;int roadnum;int v0;int D[];ShortPath(String s1, String s2) {init = new ShortInit();canvas = new ShortCanvas();circlename = init.getcirclename();circlenum = init.getcirclenum();roadnum = init.getroadnum();start = s1;end = s2;arcs = canvas.getarcs();path = new String[circlenum];for (int p = 0; p < circlenum; p++)path[p] = start;for (int k = 0; k < circlenum; k++) {if (start.equals(circlename[k])) {v0 = k;}}shortestpath(v0);}public void shortestpath(int v0) {int v, i, w;int min;boolean finald[] = new boolean[maxcirclenum];D = new int[maxcirclenum];boolean p[][] = new boolean[maxcirclenum][maxcirclenum];for (v = 0; v < circlenum; v++) {finald[v] = false;D[v] = arcs[v0][v];for (w = 0; w < circlenum; ++w)p[v][w] = false;if (D[v] < maxlength) {p[v][v0] = true;p[v][v] = true;}}D[v0] = 0;finald[v0] = true;for (i = 1; i < circlenum; i++) {min = maxlength;for (w = 0; w < circlenum; w++)if (!finald[w])if (D[w] < min) {v = w;min = D[w];}finald[v] = true;path[v] = path[v] + "->" + circlename[v];for (w = 0; w < circlenum; w++) {if (!finald[w] && (min + arcs[v][w] < D[w])) {D[w] = min + arcs[v][w];path[w] = path[v];p[w][w] = true;}}}for (int j = 0; j < circlenum; ++j) {System.out.println(path[j] + ": "+ String.valueOf(D[j]) + "km");}}public String[] getpath() {return path;}public int[] getD() {return D;}}四、实验结果五、实验体会通过这次实验，懂得了如何通过邻接矩阵存储图，然后利用迪杰斯特拉算法算出最短路径。