双路快速排序算法及三路快速排序算法可视化

一时失言乱红尘 2022-05-24 03:59 167阅读 0赞

# 双路快速排序算法 #

![这里写图片描述][70]

## 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");
            }
        }
    
    }

## 视图层 ##

import java.awt.Dimension;
    import java.awt.Graphics;
    import java.awt.Graphics2D;
    import java.awt.RenderingHints;
    
    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 TwoWaysQuickSortData data;
        public void render(TwoWaysQuickSortData 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.N();
                for(int i = 0 ; i < data.N() ; i ++ ) {
                    //是否在处理区间中
                    if ( i >= data.l && i <= data.r)
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
                    else
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Grey);
                    //是否是标定点
                    if( i == data.curPivot )
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Indigo);
                    //是否以排序
                    if( i >= data.l + 1 && i <= data.curL)
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);
                    //是否以排序
                    if( i >= data.curR && i <= data.r)
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);
                    //是否以处理
                    if( data.fixedPivots[i] )
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
    
                    AlgoVisHelper.fillRectangle(g2d, i * w, canvasHeight - data.get(i), w - 1, data.get(i));
                }
            }
    
            @Override
            public Dimension getPreferredSize(){
                return new Dimension(canvasWidth, canvasHeight);
            }
        }
    }

## 数据层 ##

import java.util.Arrays;
    
    
    public class TwoWaysQuickSortData { 
    
        public enum Type{
            Default,
            NearlyOrdered,
            Identical
        }
    
        private int[] numbers;
        public int l, r;
        public boolean[] fixedPivots;
        public int curPivot;
        public int curL, curR;
    
        public TwoWaysQuickSortData(int N, int randomBound, Type dataType){
    
            numbers = new int[N];
            fixedPivots = new boolean[N];
    
            int lBound = 1;
            int rBound = randomBound;
            if(dataType == Type.Identical){
                int avgNumber = (lBound + rBound) / 2;
                lBound = avgNumber;
                rBound = avgNumber;
            }
    
            for( int i = 0 ; i < N ; i ++) {
                numbers[i] = (int)(Math.random()*(rBound-lBound+1)) + lBound;
                fixedPivots[i] = false;
            }
    
            if(dataType == Type.NearlyOrdered){
                Arrays.sort(numbers);
                int swapTime = (int)(0.01*N);
                for(int i = 0 ; i < swapTime; i ++){
                    int a = (int)(Math.random()*N);
                    int b = (int)(Math.random()*N);
                    swap(a, b);
                }
            }
        }
    
        public TwoWaysQuickSortData(int N, int randomBound){
            this(N, randomBound, Type.Default);
        }
    
        public int N(){
            return numbers.length;
        }
    
        public int get(int index){
            if( index < 0 || index >= numbers.length)
                throw new IllegalArgumentException("Invalid index to access Sort Data.");
    
            return numbers[index];
        }
    
        public void swap(int i, int j) {
    
            if( i < 0 || i >= numbers.length || j < 0 || j >= numbers.length)
                throw new IllegalArgumentException("Invalid index to access Sort Data.");
    
            int t = numbers[i];
            numbers[i] = numbers[j];
            numbers[j] = t;
        }
    }

## 控制层 ##

import java.awt.EventQueue;
    
    public class AlgoVisualizer {
    
        private static int DELAY = 20;
    
        private TwoWaysQuickSortData data;
        private AlgoFrame frame;
    
        public AlgoVisualizer(int sceneWidth, int sceneHeight, int N, TwoWaysQuickSortData.Type dataType){
    
            // 初始化数据
            data = new TwoWaysQuickSortData(N, sceneHeight, dataType);
    
            // 初始化视图
            EventQueue.invokeLater(() -> {
                frame = new AlgoFrame("Two Ways Quick Sort Visualization", sceneWidth, sceneHeight);
    
                new Thread(() -> {
                    run();
                }).start();
            });
        }
    
        public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){
            this(sceneWidth, sceneHeight, N, TwoWaysQuickSortData.Type.Default);
        }
    
        public void run(){
            //初始化渲染
            setData(-1, -1, -1, -1, -1, -1);
    
            quickSort2Ways(0, data.N()-1);
            //最终渲染
            setData(-1, -1, -1, -1, -1, -1);
        }
    
        private void quickSort2Ways(int l, int r){
    
            if( l > r )
                return;
    
            if( l == r ) {
                setData(l, r, l, -1, -1, -1);
                return;
            }
            //渲染处理区间
            setData(l, r, -1, -1, -1, -1);
    
            int p = partition(l, r);
            quickSort2Ways(l, p-1 );
            quickSort2Ways(p+1, r);
        }
    
        private int partition(int l, int r){
            //随机获取区间一个标定点
            int p = (int)(Math.random()*(r-l+1)) + l;
            //渲染所处理区间及标定点
            setData(l, r, -1, p, -1, -1);
            //起始点与标定点交换
            data.swap(l, p);
            int v = data.get(l);
            setData(l, r, -1, l, -1, -1);
    
            // arr[l+1...i) <= v; arr(j...r] >= v
            int i = l+1, j = r;
            setData(l, r, -1, l, i, j);
            while( true ){
                //当前处理数据是否小于标定值，小于移动
                while( i <= r && data.get(i) < v ){
                    i ++;
                    setData(l, r, -1, l, i, j);
                }
                //当前处理数据是否小大于标定值，大于移动
                while( j >= l+1 && data.get(j) > v ){
                    j --;
                    setData(l, r, -1, l, i, j);
                }
    
                if( i > j )
                    break;
                //如果上面不成立则交换2个标定值的位置
                data.swap( i, j );
                i ++;
                j --;
                setData(l, r, -1, l, i, j);
            }
    
            data.swap(l, j);
            setData(l, r, j, -1, -1, -1);
    
            return j;
        }
    
        private void setData(int l, int r, int fixedPivot, int curPivot, int curL, int curR){
            data.l = l;
            data.r = r;
            if(fixedPivot != -1)
                data.fixedPivots[fixedPivot] = true;
            data.curPivot = curPivot;
            data.curL = curL;
            data.curR = curR;
    
            frame.render(data);
            AlgoVisHelper.pause(DELAY);
        }
    
        public static void main(String[] args) {
    
            int sceneWidth = 800;
            int sceneHeight = 800;
            int N = 100;
    
            AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N, TwoWaysQuickSortData.Type.Default);
            // AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N, TwoWaysQuickSortData.Type.NearlyOrdered);
            // AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N, TwoWaysQuickSortData.Type.Identical);
    
        }
    }

## 运行效果图 ##

![这里写图片描述][70 1]  
**双路快速排序算法避免了在数据几乎相同的情况下退化成O(n^2)级别的算法**

# 三路快速排序算法 #

![这里写图片描述][70 2]

## 三路快速排序算法在大部分值相等的情况下可进化成O(n)级别的算法 ##

## 注：数据层和工具类上例有、不重复了 ##

## 视图层 ##

import java.awt.Dimension;
    import java.awt.Graphics;
    import java.awt.Graphics2D;
    import java.awt.RenderingHints;
    
    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 ThreeWaysQuickSortData data;
        public void render(ThreeWaysQuickSortData 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.N();
                for(int i = 0 ; i < data.N() ; i ++ ) {
                    // 判断当前值是否存在处理区间中
                    if ( i >= data.l && i <= data.r)
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
                    else
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Grey);
                    // 判断当前值是否是标定值
                    if( i == data.curPivot )
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Indigo);
                    // 是否在左区间中
                    if( i >= data.l + 1 && i <= data.curL)
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);
                    // 是否在右区间中
                    if( i >= data.curR && i <= data.r)
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);
                    //是否以排序
                    if( data.fixedPivots[i] )
                        AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
    
                    AlgoVisHelper.fillRectangle(g2d, i * w, canvasHeight - data.get(i), w - 1, data.get(i));
                }
            }
    
            @Override
            public Dimension getPreferredSize(){
                return new Dimension(canvasWidth, canvasHeight);
            }
        }
    }

## 控制层 ##

import java.awt.EventQueue;
    
    
    public class AlgoVisualizer {
    
        private static int DELAY = 20;
    
        private ThreeWaysQuickSortData data;
        private AlgoFrame frame;
    
        public AlgoVisualizer(int sceneWidth, int sceneHeight, int N, ThreeWaysQuickSortData.Type dataType){
    
            // 初始化数据
            data = new ThreeWaysQuickSortData(N, sceneHeight, dataType);
    
            // 初始化视图
            EventQueue.invokeLater(() -> {
                frame = new AlgoFrame("Three Ways Quick Sort Visualization", sceneWidth, sceneHeight);
    
                new Thread(() -> {
                    run();
                }).start();
            });
        }
    
        public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){
            this(sceneWidth, sceneHeight, N, ThreeWaysQuickSortData.Type.Default);
        }
    
        public void run(){
            //初始化渲染视图
            setData(-1, -1, -1, -1, -1, -1);
    
            quickSort3Ways(0, data.N()-1);
            //最终视图渲染
            setData(-1, -1, -1, -1, -1, -1);
        }
    
        private void quickSort3Ways(int l, int r){
    
            if( l > r )
                return;
    
            if( l == r ) {
                setData(l, r, l, -1, -1, -1);
                return;
            }
            //渲染以处理区间
            setData(l, r, -1, -1, -1, -1);
    
            // 随机在arr[l...r]的范围中, 选择一个数值作为标定点pivot
            int p = (int)(Math.random()*(r-l+1)) + l;
            //渲染以处理区间及标定点
            setData(l, r, -1, p, -1, -1);
    
            data.swap(l, p);
            int v = data.get(l);
            //渲染以处理区间
            setData(l, r, -1, l, -1, -1);
    
            int lt = l;     // arr[l+1...lt] < v
            int gt = r + 1; // arr[gt...r] > v
            int i = l+1;    // arr[lt+1...i) == v
            setData(l, r, -1, l, lt, gt);
    
            while( i < gt ){
                //如果小于标定值则把当前值与等于当前值的区间第一个进行交换，i++
                if( data.get(i) < v ){
                    data.swap( i, lt+1);
                    i ++;
                    lt ++;
                }
                //当前值如果大于则与大于标定值区间第一位的前一位交换
                else if( data.get(i) > v ){
                    data.swap( i, gt-1);
                    gt --;
                }
                //否则等于++进行处理
                else // arr[i] == v
                    i ++;
    
                setData(l, r, -1, l, i, gt);
            }
    
            data.swap( l, lt );
            //渲染最终处理的3个区间
            setData(l, r, lt, -1, -1, -1);
    
            quickSort3Ways(l, lt-1 );
            quickSort3Ways(gt, r);
        }
    
        private void setData(int l, int r, int fixedPivot, int curPivot, int curL, int curR){
            data.l = l;
            data.r = r;
            if(fixedPivot != -1){
                data.fixedPivots[fixedPivot] = true;
                int i = fixedPivot;
                while(i < data.N() && data.get(i) == data.get(fixedPivot)){
                    data.fixedPivots[i] = true;
                    i ++;
                }
            }
            data.curPivot = curPivot;
            data.curL = curL;
            data.curR = curR;
    
            frame.render(data);
            AlgoVisHelper.pause(DELAY);
        }
    
        public static void main(String[] args) {
    
            int sceneWidth = 800;
            int sceneHeight = 800;
            int N = 100;
    
            // AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N, ThreeWaysQuickSortData.Type.Default);
            // AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N, ThreeWaysQuickSortData.Type.NearlyOrdered);
             AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N, ThreeWaysQuickSortData.Type.Identical);
    
        }
    }

## 运行效果图 ##

![这里写图片描述][70 3]

[70]: /images/20220524/6f0207250e094744b349c871628e8499.png
[70 1]: /images/20220524/30d67eceec78475a8ad89ff201e20f9a.png
[70 2]: /images/20220524/45cde8b71598487c870cfc7d81024b6b.png
[70 3]: /images/20220524/7d8e6cc6f75d48cd91e6ef105498cd36.png