目录
1 算法理解
算法可视化
自顶向下
自底向上
1 算法理解
【十大排序算法】（七）归并排序算法_老周聊架构的博客
import java.lang.reflect.Array;
import java.util.*;
public class MergeSort{
// 我们的算法类不允许产生任何实例
private MergeSort(){}
// 将arr[l...mid]和arr[mid+1...r]两部分进行归并
private static void merge(Comparable[] arr, int l, int mid, int r) {
Comparable[] aux = Arrays.copyOfRange(arr, l, r+1);
// 初始化，i指向左半部分的起始索引位置l；j指向右半部分起始索引位置mid+1
int i = l, j = mid+1;
for( int k = l ; k <= r; k ++ ){
if( i > mid ){ // 如果左半部分元素已经全部处理完毕
arr[k] = aux[j-l]; j ++;
}
else if( j > r ){ // 如果右半部分元素已经全部处理完毕
arr[k] = aux[i-l]; i ++;
}
else if( aux[i-l].compareTo(aux[j-l]) < 0 ){ // 左半部分所指元素 < 右半部分所指元素
arr[k] = aux[i-l]; i ++;
}
else{ // 左半部分所指元素 >= 右半部分所指元素
arr[k] = aux[j-l]; j ++;
}
}
}
// 递归使用归并排序,对arr[l...r]的范围进行排序
private static void sort(Comparable[] arr, int l, int r, int depth) {
System.out.print(repeatCharacters('-', depth*2));
System.out.println("Deal with [ " + l + " , " + r + " ]");
if (l >= r)
return;
int mid = (l+r)/2;
sort(arr, l, mid, depth + 1);
sort(arr, mid + 1, r, depth + 1);
merge(arr, l, mid, r);
}
private static String repeatCharacters(char character, int length){
StringBuilder s = new StringBuilder(length);
for(int i = 0 ; i < length ; i ++)
s.append(character);
return s.toString();
}
public static void sort(Comparable[] arr){
int n = arr.length;
sort(arr, 0, n-1, 0);
}
// 测试MergeSort
public static void main(String[] args) {
// Merge Sort是我们学习的第一个O(nlogn)复杂度的算法
// 可以在1秒之内轻松处理100万数量级的数据
// 注意：不要轻易尝试使用SelectionSort, InsertionSort或者BubbleSort处理100万级的数据
// 否则，你就见识了O(n^2)的算法和O(nlogn)算法的本质差异：）
// int N = 1000000;
// Integer[] arr = SortTestHelper.generateRandomArray(N, 0, 100000);
// SortTestHelper.testSort("bobo.algo.MergeSort", arr);
Integer[] arr = new Integer[8];
for(int i = 0 ; i < 8 ; i ++)
{
arr[i] = new Integer(8-i);
// arr[i] = 8 -i;
}
// arr = SortTestHelper.generateRandomArray(50, 1, 50);
MergeSort.sort(arr);
return;
}
}
import java.lang.reflect.Method;
import java.lang.Class;
import java.util.Random;
public class SortTestHelper {
// SortTestHelper不允许产生任何实例
private SortTestHelper(){}
// 生成有n个元素的随机数组,每个元素的随机范围为[rangeL, rangeR]
public static Integer[] generateRandomArray(int n, int rangeL, int rangeR) {
assert rangeL <= rangeR;
Integer[] arr = new Integer[n];
for (int i = 0; i < n; i++)
arr[i] = new Integer((int)(Math.random() * (rangeR - rangeL + 1) + rangeL));
return arr;
}
// 生成一个近乎有序的数组
// 首先生成一个含有[0...n-1]的完全有序数组, 之后随机交换swapTimes对数据
// swapTimes定义了数组的无序程度:
// swapTimes == 0 时, 数组完全有序
// swapTimes 越大, 数组越趋向于无序
public static Integer[] generateNearlyOrderedArray(int n, int swapTimes){
Integer[] arr = new Integer[n];
for( int i = 0 ; i < n ; i ++ )
arr[i] = new Integer(i);
for( int i = 0 ; i < swapTimes ; i ++ ){
int a = (int)(Math.random() * n);
int b = (int)(Math.random() * n);
int t = arr[a];
arr[a] = arr[b];
arr[b] = t;
}
return arr;
}
// 打印arr数组的所有内容
public static void printArray(Object[] arr) {
for (int i = 0; i < arr.length; i++){
System.out.print( arr[i] );
System.out.print( ' ' );
}
System.out.println();
return;
}
// 判断arr数组是否有序
public static boolean isSorted(Comparable[] arr){
for( int i = 0 ; i < arr.length - 1 ; i ++ )
if( arr[i].compareTo(arr[i+1]) > 0 )
return false;
return true;
}
// 测试sortClassName所对应的排序算法排序arr数组所得到结果的正确性和算法运行时间
public static void testSort(String sortClassName, Comparable[] arr){
// 通过Java的反射机制，通过排序的类名，运行排序函数
try{
// 通过sortClassName获得排序函数的Class对象
Class sortClass = Class.forName(sortClassName);
// 通过排序函数的Class对象获得排序方法
Method sortMethod = sortClass.getMethod("sort",new Class[]{Comparable[].class});
// 排序参数只有一个，是可比较数组arr
Object[] params = new Object[]{arr};
long startTime = System.currentTimeMillis();
// 调用排序函数
sortMethod.invoke(null,params);
long endTime = System.currentTimeMillis();
assert isSorted( arr );
System.out.println( sortClass.getSimpleName()+ " : " + (endTime-startTime) + "ms" );
}
catch(Exception e){
e.printStackTrace();
}
}
}
算法可视化
自顶向下
import java.awt.*;
import java.util.Arrays;
public class AlgoVisualizer {
private static int DELAY = 40;
private MergeSortData data;
private AlgoFrame frame;
public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){
// 初始化数据
data = new MergeSortData(N, sceneHeight);
// 初始化视图
EventQueue.invokeLater(() -> {
frame = new AlgoFrame("Merge Sort Visualization", sceneWidth, sceneHeight);
new Thread(() -> {
run();
}).start();
});
}
public void run(){
setData(-1, -1, -1);
mergeSort(0, data.N()-1);
setData(0, data.N()-1, data.N()-1);
}
private void mergeSort(int l, int r){
if( l >= r )
return;
setData(l, r, -1);
int mid = (l+r)/2;
mergeSort(l, mid);
mergeSort(mid+1, r);
merge(l, mid, r);
}
private void merge(int l, int mid, int r){
int[] aux = Arrays.copyOfRange(data.numbers, l, r+1);
// 初始化，i指向左半部分的起始索引位置l；j指向右半部分起始索引位置mid+1
int i = l, j = mid+1;
for( int k = l ; k <= r; k ++ ){
if( i > mid ){ // 如果左半部分元素已经全部处理完毕
data.numbers[k] = aux[j-l]; j ++;
}
else if( j > r ){ // 如果右半部分元素已经全部处理完毕
data.numbers[k] = aux[i-l]; i ++;
}
else if( aux[i-l] < aux[j-l] ){ // 左半部分所指元素 < 右半部分所指元素
data.numbers[k] = aux[i-l]; i ++;
}
else{ // 左半部分所指元素 >= 右半部分所指元素
data.numbers[k] = aux[j-l]; j ++;
}
setData(l, r, k);
}
}
private void setData(int l, int r, int mergeIndex){
data.l = l;
data.r = r;
data.mergeIndex = mergeIndex;
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);
}
}
import java.util.Arrays;
import java.util.Random;
public class MergeSortData {
public int[] numbers;
public int l, r;
public int mergeIndex;
public MergeSortData(int N, int randomBound){
numbers = new int[N];
for( int i = 0 ; i < N ; i ++)
numbers[i] = (int)(Math.random()*randomBound) + 1;
}
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;
}
}
import java.awt.*;
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;}
// data
private MergeSortData data;
public void render(MergeSortData 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 ++ ) {
if ( i >= data.l && i <= data.r)
AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
else
AlgoVisHelper.setColor(g2d, AlgoVisHelper.Grey);
if( i >= data.l && i <= data.mergeIndex )
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);
}
}
}
import java.awt.*;
import java.util.Arrays;
public class AlgoVisualizer {
private static int DELAY = 40;
private MergeSortData data;
private AlgoFrame frame;
public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){
// 初始化数据
data = new MergeSortData(N, sceneHeight);
// 初始化视图
EventQueue.invokeLater(() -> {
frame = new AlgoFrame("Merge Sort Visualization", sceneWidth, sceneHeight);
new Thread(() -> {
run();
}).start();
});
}
public void run(){
setData(-1, -1, -1);
mergeSort(0, data.N()-1);
setData(0, data.N()-1, data.N()-1);
}
private void mergeSort(int l, int r){
if( l >= r )
return;
setData(l, r, -1);
int mid = (l+r)/2;
mergeSort(l, mid);
mergeSort(mid+1, r);
merge(l, mid, r);
}
private void merge(int l, int mid, int r){
int[] aux = Arrays.copyOfRange(data.numbers, l, r+1);
// 初始化，i指向左半部分的起始索引位置l；j指向右半部分起始索引位置mid+1
int i = l, j = mid+1;
for( int k = l ; k <= r; k ++ ){
if( i > mid ){ // 如果左半部分元素已经全部处理完毕
data.numbers[k] = aux[j-l]; j ++;
}
else if( j > r ){ // 如果右半部分元素已经全部处理完毕
data.numbers[k] = aux[i-l]; i ++;
}
else if( aux[i-l] < aux[j-l] ){ // 左半部分所指元素 < 右半部分所指元素
data.numbers[k] = aux[i-l]; i ++;
}
else{ // 左半部分所指元素 >= 右半部分所指元素
data.numbers[k] = aux[j-l]; j ++;
}
setData(l, r, k);
}
}
private void setData(int l, int r, int mergeIndex){
data.l = l;
data.r = r;
data.mergeIndex = mergeIndex;
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);
}
}
