java深度优先、非递归深度优先、广度优先迷宫求解可视化

╰+攻爆jí腚メ 2022-05-24 04:42 185阅读 0赞

## 本文将从以下几个维度来求解迷宫最终路径 ##

**1、深度优先递归求解最终路径**  
**2、非递归深度优先走迷宫求解最终路径**  
**3、广度优先走迷宫求解最终路径**

## 通用工具类 ##

import java.awt.*;
    import java.awt.geom.Ellipse2D;
    
    import java.awt.geom.Rectangle2D;
    import java.lang.InterruptedException;
    
    
    public class AlgoVisHelper { 
    
        private AlgoVisHelper(){}
    
        public static final Color Red = new Color(0xF44336);
        public static final Color Pink = new Color(0xE91E63);
        public static final Color Purple = new Color(0x9C27B0);
        public static final Color DeepPurple = new Color(0x673AB7);
        public static final Color Indigo = new Color(0x3F51B5);
        public static final Color Blue = new Color(0x2196F3);
        public static final Color LightBlue = new Color(0x03A9F4);
        public static final Color Cyan = new Color(0x00BCD4);
        public static final Color Teal = new Color(0x009688);
        public static final Color Green = new Color(0x4CAF50);
        public static final Color LightGreen = new Color(0x8BC34A);
        public static final Color Lime = new Color(0xCDDC39);
        public static final Color Yellow = new Color(0xFFEB3B);
        public static final Color Amber = new Color(0xFFC107);
        public static final Color Orange = new Color(0xFF9800);
        public static final Color DeepOrange = new Color(0xFF5722);
        public static final Color Brown = new Color(0x795548);
        public static final Color Grey = new Color(0x9E9E9E);
        public static final Color BlueGrey = new Color(0x607D8B);
        public static final Color Black = new Color(0x000000);
        public static final Color White = new Color(0xFFFFFF);
    
    
        public static void strokeCircle(Graphics2D g, int x, int y, int r){
    
            Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
            g.draw(circle);
        }
    
        public static void fillCircle(Graphics2D g, int x, int y, int r){
    
            Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
            g.fill(circle);
        }
    
        public static void strokeRectangle(Graphics2D g, int x, int y, int w, int h){
    
            Rectangle2D rectangle = new Rectangle2D.Double(x, y, w, h);
            g.draw(rectangle);
        }
    
        public static void fillRectangle(Graphics2D g, int x, int y, int w, int h){
    
            Rectangle2D rectangle = new Rectangle2D.Double(x, y, w, h);
            g.fill(rectangle);
        }
    
        public static void setColor(Graphics2D g, Color color){
            g.setColor(color);
        }
    
        public static void setStrokeWidth(Graphics2D g, int w){
            int strokeWidth = w;
            g.setStroke(new BasicStroke(strokeWidth, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND));
        }
    
        public static void pause(int t) {
            try {
                Thread.sleep(t);
            }
            catch (InterruptedException e) {
                System.out.println("Error sleeping");
            }
        }
    
    }

# 深度优先递归求解最终路径 #

## 数据层 ##

import java.io.BufferedInputStream;
    import java.io.File;
    import java.io.FileInputStream;
    import java.io.IOException;
    import java.util.Scanner;
    
    
    public class MazeData { 
    
        public static final char ROAD = ' ';
        public static final char WALL = '#';
    
        private int entranceX, entranceY;
        private int exitX, exitY;
    
        private int N, M;
        private char[][] maze;                      // 存储数据
        public boolean[][] path;                    // 是否为正确路径
        public boolean[][] visited;                 // 是否访问过
    
        public MazeData(String filename){
    
            if(filename == null)
                throw new IllegalArgumentException("Filename can not be null!");
    
            Scanner scanner = null;
            try{
                File file = new File(filename);
                if(!file.exists())
                    throw new IllegalArgumentException("File " + filename + " doesn't exist");
    
                FileInputStream fis = new FileInputStream(file);
                scanner = new Scanner(new BufferedInputStream(fis), "UTF-8");
    
                // 读取第一行
                String nmline = scanner.nextLine();
                String[] nm = nmline.trim().split("\\s+");
                //System.out.print(nm[0] + ' ' + nm[1]);
    
                N = Integer.parseInt(nm[0]);
                // System.out.println("N = " + N);
                M = Integer.parseInt(nm[1]);
                // System.out.println("M = " + M);
    
                // 读取后续的N行
                visited = new boolean[N][M];
                path = new boolean[N][M];
                maze = new char[N][M];
                for(int i = 0 ; i < N ; i ++){
                    String line = scanner.nextLine();
    
                    // 每行保证有M个字符
                    if(line.length() != M)
                        throw new IllegalArgumentException("Maze file " + filename + " is invalid");
                    for(int j = 0 ; j < M ; j ++)
                        maze[i][j] = line.charAt(j);
                }
            }
            catch(IOException e){
                e.printStackTrace();
            }
            finally {
                if(scanner != null)
                    scanner.close();
            }
    
            entranceX = 1;
            entranceY = 0;
            exitX = N - 2;
            exitY = M - 1;
        }
    
        public int N(){ return N; }
        public int M(){ return M; }
        public int getEntranceX(){
       return entranceX;}
        public int getEntranceY(){
       return entranceY;}
        public int getExitX(){
       return exitX;}
        public int getExitY(){
       return exitY;}
        public char getMaze(int i, int j){
            if(!inArea(i,j))
                throw new IllegalArgumentException("i or j is out of index in getMaze!");
            return maze[i][j];
        }
    
        public boolean inArea(int x, int y){
            return x >= 0 && x < N && y >= 0 && y < M;
        }
        // 打印迷宫文本信息
        public void print(){
            System.out.println(N + " " + M);
            for(int i = 0 ; i < N ; i ++){
                for(int j = 0 ; j < M ; j ++)
                    System.out.print(maze[i][j]);
                System.out.println();
            }
            return;
        }
    
    }

## 视图层 ##

import java.awt.Dimension;
    import java.awt.Graphics;
    import java.awt.Graphics2D;
    
    import javax.swing.JFrame;
    import javax.swing.JPanel;
    
    public class AlgoFrame extends JFrame{ 
    
        private int canvasWidth;
        private int canvasHeight;
    
        public AlgoFrame(String title, int canvasWidth, int canvasHeight){
    
            super(title);
    
            this.canvasWidth = canvasWidth;
            this.canvasHeight = canvasHeight;
    
            AlgoCanvas canvas = new AlgoCanvas();
            setContentPane(canvas);
            pack();
    
            setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            setResizable(false);
    
            setVisible(true);
        }
    
        public AlgoFrame(String title){
    
            this(title, 1024, 768);
        }
    
        public int getCanvasWidth(){
       return canvasWidth;}
        public int getCanvasHeight(){
       return canvasHeight;}
    
        // data
        private MazeData data;
        public void render(MazeData data){
            this.data = data;
            repaint();
        }
    
        private class AlgoCanvas extends JPanel{ 
    
            public AlgoCanvas(){
                // 双缓存
                super(true);
            }
    
            @Override
            public void paintComponent(Graphics g) {
                super.paintComponent(g);
    
                Graphics2D g2d = (Graphics2D)g;
    
                // 抗锯齿
    // RenderingHints hints = new RenderingHints(
    // RenderingHints.KEY_ANTIALIASING,
    // RenderingHints.VALUE_ANTIALIAS_ON);
    // hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
    // g2d.addRenderingHints(hints);
    
                // 具体绘制
                int w = canvasWidth/data.M();
                int h = canvasHeight/data.N();
    
                for(int i = 0 ; i < data.N() ; i ++ )
                    for(int j = 0 ; j < data.M() ; j ++){
                        // 判断是否是墙
                        if (data.getMaze(i,j) == MazeData.WALL)
                            AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);
                        else
                            AlgoVisHelper.setColor(g2d, AlgoVisHelper.White);
                        // 判断是否是正确路线
                        if(data.path[i][j])
                            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Yellow);
    
                        AlgoVisHelper.fillRectangle(g2d, j * w, i * h, w, h);
                    }
            }
    
            @Override
            public Dimension getPreferredSize(){
                return new Dimension(canvasWidth, canvasHeight);
            }
        }
    }

## 控制层 ##

import java.awt.EventQueue;
    
    public class AlgoVisualizer { 
    
        private static int DELAY = 5;               // 等待时间
        private static int blockSide = 8;           // 绘制正方形大小
    
        private MazeData data;
        private AlgoFrame frame;
        // 坐标偏移方向
        private static final int d[][] = {
       {-1,0},{
       0,1},{
       1,0},{
       0,-1}};
    
        public AlgoVisualizer(String mazeFile){
    
            // 初始化数据
            data = new MazeData(mazeFile);
            // 需绘制的迷宫长度宽度乘以需要绘制的大小得出画布高度宽度
            int sceneHeight = data.N() * blockSide;
            int sceneWidth = data.M() * blockSide;
    
            // 初始化视图
            EventQueue.invokeLater(() -> {
                frame = new AlgoFrame("Maze Solver Visualization", sceneWidth, sceneHeight);
    
                new Thread(() -> {
                    run();
                }).start();
            });
        }
    
        public void run(){
    
            setData(-1, -1, false);
            // 如果该迷宫无解，给出提示
            if(!go(data.getEntranceX(), data.getEntranceY()))
                System.out.println("The maze has NO solution!");
    
            setData(-1, -1, false);
        }
    
        // 从(x,y)的位置开始求解迷宫，如果求解成功，返回true；否则返回false
        private boolean go(int x, int y){
            // 是否处于迷宫内
            if(!data.inArea(x,y))
                throw new IllegalArgumentException("x,y are out of index in go function!");
            // 将处理过的坐标记录
            data.visited[x][y] = true;
            setData(x, y, true);
            // 如果到达出口返回true
            if(x == data.getExitX() && y == data.getExitY())
                return true;
            // 遍历四个方向，如果是正确路线返回true，进行绘制
            for(int i = 0 ; i < 4 ; i ++){
                int newX = x + d[i][0];
                int newY = y + d[i][1];
                if(data.inArea(newX, newY) &&
                        data.getMaze(newX,newY) == MazeData.ROAD &&
                        !data.visited[newX][newY])
                    if(go(newX, newY))
                        return true;
            }
    
            // 回溯，该坐标不为正确路线，将路线标识置为false
            setData(x, y, false);
    
            return false;
        }
    
        private void setData(int x, int y, boolean isPath){
            if(data.inArea(x, y))
                data.path[x][y] = isPath;
    
            frame.render(data);
            AlgoVisHelper.pause(DELAY);
        }
    
        public static void main(String[] args) {
    
            String mazeFile = "D:\\gz\\workspace11\\text\\src\\maze_101_101.txt";
    
            AlgoVisualizer vis = new AlgoVisualizer(mazeFile);
        }
    }

## 运行效果图 ##

![这里写图片描述][70]

# 非递归深度优先走迷宫求解最终路径 #

## 数据层 ##

import java.io.BufferedInputStream;
    import java.io.File;
    import java.io.FileInputStream;
    import java.io.IOException;
    import java.util.Scanner;
    
    
    public class MazeData { 
    
        public static final char ROAD = ' ';
        public static final char WALL = '#';
    
        private int entranceX, entranceY;
        private int exitX, exitY;
    
        private int N, M;
        private char[][] maze;
        public boolean[][] path;
        public boolean[][] visited;
        public boolean[][] result;
    
        public MazeData(String filename){
    
            if(filename == null)
                throw new IllegalArgumentException("Filename can not be null!");
    
            Scanner scanner = null;
            try{
                File file = new File(filename);
                if(!file.exists())
                    throw new IllegalArgumentException("File " + filename + " doesn't exist");
    
                FileInputStream fis = new FileInputStream(file);
                scanner = new Scanner(new BufferedInputStream(fis), "UTF-8");
    
                // 读取第一行
                String nmline = scanner.nextLine();
                String[] nm = nmline.trim().split("\\s+");
                //System.out.print(nm[0] + ' ' + nm[1]);
    
                N = Integer.parseInt(nm[0]);
                // System.out.println("N = " + N);
                M = Integer.parseInt(nm[1]);
                // System.out.println("M = " + M);
    
                // 读取后续的N行
                visited = new boolean[N][M];
                path = new boolean[N][M];
                result = new boolean[N][M];
                maze = new char[N][M];
                for(int i = 0 ; i < N ; i ++){
                    String line = scanner.nextLine();
    
                    // 每行保证有M个字符
                    if(line.length() != M)
                        throw new IllegalArgumentException("Maze file " + filename + " is invalid");
                    for(int j = 0 ; j < M ; j ++){
                        maze[i][j] = line.charAt(j);
                        visited[i][j] = false;
                        path[i][j] = false;
                        result[i][j] = false;
                    }
                }
            }
            catch(IOException e){
                e.printStackTrace();
            }
            finally {
                if(scanner != null)
                    scanner.close();
            }
    
            entranceX = 1;
            entranceY = 0;
            exitX = N - 2;
            exitY = M - 1;
        }
    
        public int N(){ return N; }
        public int M(){ return M; }
        public int getEntranceX(){
       return entranceX;}
        public int getEntranceY(){
       return entranceY;}
        public int getExitX(){
       return exitX;}
        public int getExitY(){
       return exitY;}
        public char getMaze(int i, int j){
            if(!inArea(i,j))
                throw new IllegalArgumentException("i or j is out of index in getMaze!");
            return maze[i][j];
        }
    
        public boolean inArea(int x, int y){
            return x >= 0 && x < N && y >= 0 && y < M;
        }
    
        public void print(){
            System.out.println(N + " " + M);
            for(int i = 0 ; i < N ; i ++){
                for(int j = 0 ; j < M ; j ++)
                    System.out.print(maze[i][j]);
                System.out.println();
            }
            return;
        }
    
    }

public class Position {
    
        private int x, y;
        private Position prev;
    
        public Position(int x, int y, Position prev){
            this.x = x;
            this.y = y;
            this.prev = prev;
        }
    
        public Position(int x, int y){
            this(x, y, null);
        }
    
        public int getX(){
       return x;}
        public int getY(){
       return y;}
        public Position getPrev(){
       return prev;}
    }

## 视图层 ##

import java.awt.Dimension;
    import java.awt.Graphics;
    import java.awt.Graphics2D;
    
    import javax.swing.JFrame;
    import javax.swing.JPanel;
    
    public class AlgoFrame extends JFrame{ 
    
        private int canvasWidth;
        private int canvasHeight;
    
        public AlgoFrame(String title, int canvasWidth, int canvasHeight){
    
            super(title);
    
            this.canvasWidth = canvasWidth;
            this.canvasHeight = canvasHeight;
    
            AlgoCanvas canvas = new AlgoCanvas();
            setContentPane(canvas);
            pack();
    
            setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            setResizable(false);
    
            setVisible(true);
        }
    
        public AlgoFrame(String title){
    
            this(title, 1024, 768);
        }
    
        public int getCanvasWidth(){
       return canvasWidth;}
        public int getCanvasHeight(){
       return canvasHeight;}
    
        // data
        private MazeData data;
        public void render(MazeData data){
            this.data = data;
            repaint();
        }
    
        private class AlgoCanvas extends JPanel{ 
    
            public AlgoCanvas(){
                // 双缓存
                super(true);
            }
    
            @Override
            public void paintComponent(Graphics g) {
                super.paintComponent(g);
    
                Graphics2D g2d = (Graphics2D)g;
    
                // 抗锯齿
    // RenderingHints hints = new RenderingHints(
    // RenderingHints.KEY_ANTIALIASING,
    // RenderingHints.VALUE_ANTIALIAS_ON);
    // hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
    // g2d.addRenderingHints(hints);
    
                // 具体绘制
                int w = canvasWidth/data.M();
                int h = canvasHeight/data.N();
    
                for(int i = 0 ; i < data.N() ; i ++ )
                    for(int j = 0 ; j < data.M() ; j ++){
                        // 判断是否为墙
                        if (data.getMaze(i,j) == MazeData.WALL)
                            AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);
                        else
                            AlgoVisHelper.setColor(g2d, AlgoVisHelper.White);
                        // 判断是否为以处理
                        if(data.path[i][j])
                            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Yellow);
                        // 判断是否为正确路径
                        if(data.result[i][j])
                            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
    
                        AlgoVisHelper.fillRectangle(g2d, j * w, i * h, w, h);
                    }
            }
    
            @Override
            public Dimension getPreferredSize(){
                return new Dimension(canvasWidth, canvasHeight);
            }
        }
    }

## 控制层 ##

import java.awt.*;
    import java.util.Stack;
    
    public class AlgoVisualizer { 
    
        private static int DELAY = 5;
        private static int blockSide = 8;
    
        private MazeData data;
        private AlgoFrame frame;
        private static final int d[][] = {
       {-1,0},{
       0,1},{
       1,0},{
       0,-1}};
    
        public AlgoVisualizer(String mazeFile){
    
            // 初始化数据
            data = new MazeData(mazeFile);
            int sceneHeight = data.N() * blockSide;
            int sceneWidth = data.M() * blockSide;
    
            // 初始化视图
            EventQueue.invokeLater(() -> { frame = new AlgoFrame("Maze Solver Visualization", sceneWidth, sceneHeight); new Thread(() -> { run(); }).start(); }); } private void run(){ // 初始绘制 setData(-1, -1, false); Stack<Position> stack = new Stack<Position>(); Position entrance = new Position(data.getEntranceX(), data.getEntranceY()); // 压入起始坐标 stack.push(entrance); // 设置成以处理 data.visited[entrance.getX()][entrance.getY()] = true; boolean isSolved = false; while(!stack.empty()){ Position curPos = stack.pop(); setData(curPos.getX(), curPos.getY(), true); // 如果为出口返回真，并回溯正确路径，改变其绘制颜色 if(curPos.getX() == data.getExitX() && curPos.getY() == data.getExitY()){ isSolved = true; findPath(curPos); break; } for(int i = 0 ; i < 4 ; i ++){ int newX = curPos.getX() + d[i][0]; int newY = curPos.getY() + d[i][1]; // 如果坐标点在迷宫内、并且没有处理、并且等于可以前进的路线则压入,并将其设为以处理 if(data.inArea(newX, newY) && !data.visited[newX][newY] && data.getMaze(newX, newY) == MazeData.ROAD){ stack.push(new Position(newX, newY, curPos)); data.visited[newX][newY] = true; } } } if(!isSolved) System.out.println("The maze has no Solution!"); setData(-1, -1, false); } private void findPath(Position des){ Position cur = des; // 依次调用上一路径坐标，改变其绘制颜色 while(cur != null){ data.result[cur.getX()][cur.getY()] = true; cur = cur.getPrev(); } } private void setData(int x, int y, boolean isPath){ if(data.inArea(x, y)) data.path[x][y] = isPath; frame.render(data); AlgoVisHelper.pause(DELAY); } public static void main(String[] args) { String mazeFile = "D:\\gz\\workspace11\\text\\src\\maze_101_101.txt"; AlgoVisualizer vis = new AlgoVisualizer(mazeFile); } }

## 运行效果图 ##

![这里写图片描述][70 1]

## 广度优先走迷宫求解最终路径 ##

## 控制层（其余沿用非递归深度优先） ##

import java.awt.EventQueue;
    import java.util.LinkedList;
    
    public class AlgoVisualizer { 
    
        private static int DELAY = 5;
        private static int blockSide = 8;
    
        private MazeData data;
        private AlgoFrame frame;
        private static final int d[][] = {
       {-1,0},{
       0,1},{
       1,0},{
       0,-1}};
    
        public AlgoVisualizer(String mazeFile){
    
            // 初始化数据
            data = new MazeData(mazeFile);
            int sceneHeight = data.N() * blockSide;
            int sceneWidth = data.M() * blockSide;
    
            // 初始化视图
            EventQueue.invokeLater(() -> { frame = new AlgoFrame("Maze Solver Visualization", sceneWidth, sceneHeight); new Thread(() -> { run(); }).start(); }); } private void run(){ setData(-1, -1, false); LinkedList<Position> queue = new LinkedList<Position>(); Position entrance = new Position(data.getEntranceX(), data.getEntranceY()); // 入口添加到队尾 queue.addLast(entrance); // 设置以处理 data.visited[entrance.getX()][entrance.getY()] = true; boolean isSolved = false; while(queue.size() != 0){ // 取队列头部元素 Position curPos = queue.pop(); setData(curPos.getX(), curPos.getY(), true); // 如果是出口返回真，并回溯真实路径，改变其绘制颜色 if(curPos.getX() == data.getExitX() && curPos.getY() == data.getExitY()){ isSolved = true; // 回溯真实路径 findPath(curPos); break; } for(int i = 0 ; i < 4 ; i ++){ int newX = curPos.getX() + d[i][0]; int newY = curPos.getY() + d[i][1]; // 如果坐标点在迷宫内、并且没有处理、并且等于可以前进的路线则压入,并将其设为以处理 if(data.inArea(newX, newY) && !data.visited[newX][newY] && data.getMaze(newX, newY) == MazeData.ROAD){ // 压入队尾 queue.addLast(new Position(newX, newY, curPos)); // 设置为以处理 data.visited[newX][newY] = true; } } } if(!isSolved) System.out.println("The maze has no Solution!"); setData(-1, -1, false); } private void findPath(Position des){ Position cur = des; while(cur != null){ data.result[cur.getX()][cur.getY()] = true; cur = cur.getPrev(); } } private void setData(int x, int y, boolean isPath){ if(data.inArea(x, y)) data.path[x][y] = isPath; frame.render(data); AlgoVisHelper.pause(DELAY); } public static void main(String[] args) { String mazeFile = "D:\\gz\\workspace11\\text\\src\\maze_101_101.txt"; AlgoVisualizer vis = new AlgoVisualizer(mazeFile); } }

## 运行效果图 ##

![这里写图片描述][70 2]

# 总结 #

## 如果迷宫有多个解，那么深度优先求得的是第一个解，而广度优先则求得的是最短的解 ##

![这里写图片描述][70 3]

[70]: /images/20220524/bd602a4e4cec442a9f574a233d979072.png
[70 1]: /images/20220524/9a7319e6f28242f2b05d8840bc533f82.png
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