看的见的算法系列——插入排序

插入排序

原始数据
[8,2,1,7,3,4,2,5]
①选择2，比较前一个数字8，小于8，交换；
在这里插入图片描述
由于交换后2前面没有数字，结束，数字2有序。
②选择1，比较前一个数字8，小于8，交换；前面还有大于1的数字2，交换；

③选择7，比较前一个数字8，小于8，交换；

由于7大于2，比较停止。
以此类推最终我们会得到一个有序的数据。

为可视化服务的工具类

AlgoVisHelper

为其他的工具类提供绘制相关方法。

import javax.swing.*;
import java.awt.*;
import java.awt.geom.*;
import java.lang.InterruptedException;

public class AlgoVisHelper {
    private AlgoVisHelper(){}
	//为画笔提供的颜色
    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);
	//绘制圆形
    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);
    }
	//填充圆形
    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);
    }
	//绘制矩形
    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);
    }
	//填充矩形
    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);
    }
	//为画笔设置颜色
    public static void setColor(Graphics2D g, Color color){
        g.setColor(color);
    }
	//设置画笔的宽度
    public static void setStrokeWidth(Graphics2D g, int w){
        int strokeWidth = w;
        g.setStroke(new BasicStroke(strokeWidth, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND));
    }
	//绘制时的间隔，传入t进行设置
    public static void pause(int t) {
        try {
            Thread.sleep(t);
        }
        catch (InterruptedException e) {
            System.out.println("Error sleeping");
        }
    }
	//绘制图片
    public static void putImage(Graphics2D g, int x, int y, String imageURL){
        ImageIcon icon = new ImageIcon(imageURL);
        Image image = icon.getImage();
        g.drawImage(image, x, y, null);
    }
	//绘制文字
    public static void drawText(Graphics2D g, String text, int centerx, int centery){
        if(text == null)
            throw new IllegalArgumentException("Text is null in drawText function!");
        FontMetrics metrics = g.getFontMetrics();
        int w = metrics.stringWidth(text);
        int h = metrics.getDescent();
        g.drawString(text, centerx - w/2, centery + h);
    }
}

AlgoFrame

import java.awt.Graphics2D;
import java.awt.Graphics;
import java.awt.Dimension;
import java.awt.Color;
import java.awt.RenderingHints;
import javax.swing.*;

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;}

    // TODO: 设置自己的数据
    private Object data;
    public void render(Object 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
            // TODO： 绘制自己的数据data
        }

        @Override
        public Dimension getPreferredSize(){
            return new Dimension(canvasWidth, canvasHeight);
        }
    }
}

AlgoVisualizer

import java.awt.*;
import java.awt.event.KeyAdapter;
import java.awt.event.KeyEvent;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;

public class AlgoVisualizer {

    // TODO: 创建自己的数据
    private Object data;        // 数据
    private AlgoFrame frame;    // 视图

    public AlgoVisualizer(int sceneWidth, int sceneHeight){

        // 初始化数据
        // TODO: 初始化数据

        // 初始化视图
        EventQueue.invokeLater(() -> {
            frame = new AlgoFrame("Welcome", sceneWidth, sceneHeight);
            // TODO: 根据情况决定是否加入键盘鼠标事件监听器
            frame.addKeyListener(new AlgoKeyListener());
            frame.addMouseListener(new AlgoMouseListener());
            new Thread(() -> {
                run();
            }).start();
        });
    }

    // 动画逻辑
    private void run(){

        // TODO: 编写自己的动画逻辑
    }

    // TODO: 根据情况决定是否实现键盘鼠标等交互事件监听器类
    private class AlgoKeyListener extends KeyAdapter{ }
    private class AlgoMouseListener extends MouseAdapter{ }

    public static void main(String[] args) {
        int sceneWidth = 800;
        int sceneHeight = 800;
        // TODO: 根据需要设置其他参数，初始化visualizer
        AlgoVisualizer visualizer = new AlgoVisualizer(sceneWidth, sceneHeight);
    }
}

创建带排序数据

public class InsertSortData {
    private int[] numbers;//带排序数据data
    public int sortedIndex = -1;//已排序的边界
    public int currIndex = -1;//当前比较的边界

    /**
     * @param N {numbers数组的长度}
     * @param randomBound {生成的随机数的上限}
     */
    public InsertSortData(int N, int randomBound){
        numbers = new int[N];
        for(int i=0;i<N;i++)
            numbers[i] = (int) (Math.random()*randomBound)+1;//往numbers数组中添加随机数
    }

    public int size(){
        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;
    }
}

插入排序代码

//插入排序算法代码
for( int i = 0 ; i < data.size() ; i ++ ){
    for(int j = i ; j > 0 && data.get(j) < data.get(j-1) ; j --){
        data.swap(j,j-1);//比前一个数字小，进行交换
    }
}

使用可视化工具类

AlgoVisualizer

// TODO: 创建自己的数据
private InsertSortData data;
private final int DELAY = 40;//设置每次绘制暂停的时间

//修改构造函数相关代码
public AlgoVisualizer(int sceneWidth, int sceneHeight,int size,int randomBound){
    // 初始化数据
    // TODO: 初始化数据
    data = new InsertSortData(size,randomBound);
    //其他代码
}

// 动画逻辑
private void run(){
    // TODO: 编写自己的动画逻辑
    setData(-1,-1);//还没排序之前已排序边界和当前比较位置索引都为-1
    //插入排序算法代码
    for( int i = 0 ; i < data.size() ; i ++ ){
        setData(i, i);
        for(int j = i ; j > 0 && data.get(j) < data.get(j-1) ; j --){
            data.swap(j,j-1);
            setData(i+1, j-1);
        }
    }
    setData(data.size(),-1);//排序之后全部都有序，当前比较位置索引都为-1
}
//使用setData设置边界，同时进行数据的绘制
private void setData(int sortedIndex,int currIndex){
    data.sortedIndex = sortedIndex;
    data.currIndex = currIndex;
    frame.render(data);//根据数据绘图
    AlgoVisHelper.pause(DELAY);
}

public static void main(String[] args) {
    int sceneWidth = 800;
    int sceneHeight = 800;
    // TODO: 根据需要设置其他参数，初始化visualizer
    //设置数组数据为50，最大上限就是设置为窗口的高度
    AlgoVisualizer visualizer = new AlgoVisualizer(sceneWidth, sceneHeight,50,sceneHeight);
}

AlgoFrame

// TODO: 设置自己的数据
private InsertSortData data;

@Override
public void paintComponent(Graphics g) {
    // 具体绘制
    // TODO： 绘制自己的数据data
    int w = canvasWidth/data.size();//每个矩形的宽度
    for(int i=0;i<data.size();i++){
        if(i<=data.sortedIndex){
            AlgoVisHelper.setColor(g2d,AlgoVisHelper.Red);//将已排序部分绘制成红色
        }else
            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Grey);//将未排序部分绘制成灰色
        if( i == data.currIndex )
            AlgoVisHelper.setColor(g2d, AlgoVisHelper.LightBlue);//当前元素绘制成浅蓝色
        AlgoVisHelper.fillRectangle(g2d, i * w, canvasHeight - data.get(i), w - 1, data.get(i));
    }
}

可视化结果

插入排序可视化
从图中我们可以更加清晰的了解插入排序的工作过程。

进化

如果我们对近乎有序的数据使用插入排序，那么插入排序算法时间复杂度将进化至O(n)。我们对代码进行一下修改产生近乎有序的数据。

InsertSortData

public enum Type{//数据类型
    Default,//默认随机数据
    NearlyOrdered//近乎有序的数据
}
public InsertSortData(int N, int randomBound,Type type){
    numbers = new int[N];
    for(int i=0;i<N;i++)
        numbers[i] = (int) (Math.random()*randomBound)+1;//往numbers数组中添加随机数
    if(type == Type.NearlyOrdered){
        Arrays.sort(numbers);//首先对数据进行排序
        int swapTime = (int)(0.02*N);//打乱数字的个数
        for(int i = 0 ; i < swapTime; i ++){//随机选择数据进行交换
            int a = (int)(Math.random()*N);
            int b = (int)(Math.random()*N);
            swap(a, b);
        }
    }
}

AlgoVisualizer

public AlgoVisualizer(int sceneWidth, int sceneHeight,int size,int randomBound,InsertSortData.Type type){
	// TODO: 初始化数据
	data = new InsertSortData(size,randomBound,type);
}

public static void main(String[] args) {
    // TODO: 根据需要设置其他参数，初始化visualizer
    //设置数组数据为50，最大上限就是设置为窗口的高度
    AlgoVisualizer visualizer = new AlgoVisualizer(sceneWidth, sceneHeight,50,sceneHeight,InsertSortData.Type.NearlyOrdered);//对近乎有序的数据使用插入排序
}