雙路快速排序演算法

工具類

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");
        }
    }

}

檢視層

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(){
            // 雙快取
            super(true);
        }

        @Override
        public void paintComponent(Graphics g) {
            super.paintComponent(g);

            Graphics2D g2d = (Graphics2D)g;

            // 抗鋸齒
            RenderingHints hints = new RenderingHints(
                    RenderingHints.KEY_ANTIALIASING,
                    RenderingHints.VALUE_ANTIALIAS_ON);
            hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
            g2d.addRenderingHints(hints);

            // 具體繪製
            int w = canvasWidth/data.N();
            for(int i = 0 ; i < data.N() ; i ++ ) {
                //是否在處理區間中
                if ( i >= data.l && i <= data.r)
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
                else
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Grey);
                //是否是標定點
                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);
                //是否以處理
                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);
        }
    }
}

資料層

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;
    }
}

控制層

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){

        // 初始化資料
        data = new TwoWaysQuickSortData(N, sceneHeight, dataType);

        // 初始化檢視
        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);
        //最終渲染
        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;
        }
        //渲染處理區間
        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){
        //隨機獲取區間一個標定點
        int p = (int)(Math.random()*(r-l+1)) + l;
        //渲染所處理區間及標定點
        setData(l, r, -1, p, -1, -1);
        //起始點與標定點交換
        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 ){
            //當前處理資料是否小於標定值，小於移動
            while( i <= r && data.get(i) < v ){
                i ++;
                setData(l, r, -1, l, i, j);
            }
            //當前處理資料是否小大於標定值，大於移動
            while( j >= l+1 && data.get(j) > v ){
                j --;
                setData(l, r, -1, l, i, j);
            }

            if( i > j )
                break;
            //如果上面不成立則交換2個標定值的位置
            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);

    }
}

執行效果圖

雙路快速排序演算法避免了在資料幾乎相同的情況下退化成O(n^2)級別的演算法

三路快速排序演算法

三路快速排序演算法在大部分值相等的情況下可進化成O(n)級別的演算法

注：資料層和工具類上例有、不重複了

檢視層

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(){
            // 雙快取
            super(true);
        }

        @Override
        public void paintComponent(Graphics g) {
            super.paintComponent(g);

            Graphics2D g2d = (Graphics2D)g;

            // 抗鋸齒
            RenderingHints hints = new RenderingHints(
                    RenderingHints.KEY_ANTIALIASING,
                    RenderingHints.VALUE_ANTIALIAS_ON);
            hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
            g2d.addRenderingHints(hints);

            // 具體繪製
            int w = canvasWidth/data.N();
            for(int i = 0 ; i < data.N() ; i ++ ) {
                // 判斷當前值是否存在處理區間中
                if ( i >= data.l && i <= data.r)
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
                else
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Grey);
                // 判斷當前值是否是標定值
                if( i == data.curPivot )
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Indigo);
                // 是否在左區間中
                if( i >= data.l + 1 && i <= data.curL)
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);
                // 是否在右區間中
                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);
        }
    }
}

控制層

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){

        // 初始化資料
        data = new ThreeWaysQuickSortData(N, sceneHeight, dataType);

        // 初始化檢視
        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(){
        //初始化渲染檢視
        setData(-1, -1, -1, -1, -1, -1);

        quickSort3Ways(0, data.N()-1);
        //最終檢視渲染
        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;
        }
        //渲染以處理區間
        setData(l, r, -1, -1, -1, -1);

        // 隨機在arr[l...r]的範圍中, 選擇一個數值作為標定點pivot
        int p = (int)(Math.random()*(r-l+1)) + l;
        //渲染以處理區間及標定點
        setData(l, r, -1, p, -1, -1);

        data.swap(l, p);
        int v = data.get(l);
        //渲染以處理區間
        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 ){
            //如果小於標定值則把當前值與等於當前值的區間第一個進行交換，i++
            if( data.get(i) < v ){
                data.swap( i, lt+1);
                i ++;
                lt ++;
            }
            //當前值如果大於則與大於標定值區間第一位的前一位交換
            else if( data.get(i) > v ){
                data.swap( i, gt-1);
                gt --;
            }
            //否則等於++進行處理
            else // arr[i] == v
                i ++;

            setData(l, r, -1, l, i, gt);
        }

        data.swap( l, lt );
        //渲染最終處理的3個區間
        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);

    }
}

執行效果圖