[算法] 随机模拟问题

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内容图文

分钱问题

100个人，初始每人100块钱，每轮每人将1元随机分给另一个人，若干轮过后，100个人的财富分布情况会怎样
画布的原点在左上角，y轴向下

技术分享图片

AlgoVisHelper.java

                 1
                import
                 java.awt.EventQueue;

                 2
                import
                 java.util.Arrays;

                 3
                 4
                public
                class
                 AlgoVisualizer {

                 5
                 6
                private
                static
                int DELAY = 40;
 7privateint[] money;
 8private AlgoFrame frame;
 910public AlgoVisualizer(int sceneWidth, int sceneHeight) {
1112// 初始化数据13         money = newint[100];
14for(int i = 0 ; i < money.length ; i ++) {
15             money[i] = 100;
16        }
1718// 初始化视图19         EventQueue.invokeLater(()->{
20             frame = new AlgoFrame("Welcome",sceneWidth,sceneHeight);
21new Thread(()->{
22                    run();
23            }).start();  
24        });
25    }
2627privatevoid run() {
28while(true) {
29            Arrays.sort(money);
30            frame.render(money);
31            AlgoVisHelper.pause(DELAY);
3233for(int k = 0 ; k < 50 ; k ++ ) {
34for(int i = 0 ; i < money.length ; i ++ ) {
35int j = (int)(Math.random() * money.length);
36                         money[i] -= 1;
37                         money[j] += 1;
38                }
39            }
40        }
41    }
4243publicstaticvoid main(String[] args) {
4445int sceneWidth = 1000;
46int sceneHeight = 800;
4748         AlgoVisualizer visualizer = new AlgoVisualizer(sceneWidth, sceneHeight);
4950    }
51 }

View Code

AlgoVisualizer.java

                 1
                import
                 java.awt.EventQueue;

                 2
                import
                 java.util.Arrays;

                 3
                 4
                public
                class
                 AlgoVisualizer {

                 5
                 6
                private
                static
                int DELAY = 40;
 7privateint[] money;
 8private AlgoFrame frame;
 910public AlgoVisualizer(int sceneWidth, int sceneHeight) {
1112// 初始化数据13         money = newint[100];
14for(int i = 0 ; i < money.length ; i ++) {
15             money[i] = 100;
16        }
1718// 初始化视图19         EventQueue.invokeLater(()->{
20             frame = new AlgoFrame("Welcome",sceneWidth,sceneHeight);
21new Thread(()->{
22                    run();
23            }).start();  
24        });
25    }
2627privatevoid run() {
28while(true) {
29            Arrays.sort(money);
30            frame.render(money);
31            AlgoVisHelper.pause(DELAY);
3233for(int k = 0 ; k < 50 ; k ++ ) {
34for(int i = 0 ; i < money.length ; i ++ ) {
35int j = (int)(Math.random() * money.length);
36                         money[i] -= 1;
37                         money[j] += 1;
38                }
39            }
40        }
41    }
4243publicstaticvoid main(String[] args) {
4445int sceneWidth = 1000;
46int sceneHeight = 800;
4748         AlgoVisualizer visualizer = new AlgoVisualizer(sceneWidth, sceneHeight);
4950    }
51 }

View Code

AlgoFrame.java

                 1
                import
                 java.awt.Color;

                 2
                import
                 java.awt.Dimension;

                 3
                import
                 java.awt.Graphics;

                 4
                import
                 java.awt.Graphics2D;

                 5
                import
                 java.awt.RenderingHints;

                 6
                 7
                import
                 javax.swing.JFrame;

                 8
                import
                 javax.swing.JPanel;

                 9
                10
                public
                class AlgoFrame extends JFrame{
1112privateint canvasWidth;
13privateint canvasHeight;
1415public AlgoFrame(String title, int canvasWidth, int canvasHeight) {
1617super(title);
1819this.canvasWidth = canvasWidth;
20this.canvasHeight = canvasHeight;
2122         AlgoCanvas canvas = new AlgoCanvas();
23        setContentPane(canvas);
24        pack();
2526         setResizable(false);
27        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
28         setVisible(true);
29    }
3031public AlgoFrame(String title) {
32this(title, 1024, 768);
33    }
3435publicint getCanvasWidth() {return canvasWidth;}
36publicint getCanvasHeight() {return canvasHeight;}
3738privateint[] money;
39publicvoid render(int[] money) {
40this.money = money;
41        repaint();
42    }
4344privateclass AlgoCanvas extends JPanel{
4546public AlgoCanvas() {
47super(true);
48        }
4950        @Override
51publicvoid paintComponent(Graphics g) {
5253super.paintComponent(g);
5455             Graphics2D g2d = (Graphics2D)g;
5657//抗锯齿58             RenderingHints hints = new RenderingHints(
59                            RenderingHints.KEY_ANTIALIASING, 
60                            RenderingHints.VALUE_ANTIALIAS_ON);
61            g2d.addRenderingHints(hints);
6263//具体绘制64int w = canvasWidth / money.length;
65for(int i = 0 ; i < money.length ; i ++ ) {
66if(money[i] > 0) {
67                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Blue);
68                    AlgoVisHelper.fillRectangle(g2d, 
69                             i*w + 1, canvasHeight/2 - money[i], w-1, money[i]);
70                }
71elseif(money[i] < 0) {
72                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
73                    AlgoVisHelper.fillRectangle(g2d,
74                             i*w + 1, canvasHeight/2, w-1, -money[i]);
75                }
76            }
77        }
7879        @Override
80public Dimension getPreferredSize() {
81returnnew Dimension(canvasWidth, canvasHeight);
82        }
83    }
84 }

View Code

技术分享图片

蒙特卡洛方法

为解决裂变物质的中子随机扩散问题而提出
通过大量随机样本，了解一个系统，进而得到所要计算的值
红色点的数量-->圆的面积；红色点+绿色点的数量-->方的面积
PI = 4 * 红色点数 / 总点数

技术分享图片

AlgoFrame.java

                 1
                import
                 java.awt.Color;

                 2
                import
                 java.awt.Dimension;

                 3
                import
                 java.awt.Graphics;

                 4
                import
                 java.awt.Graphics2D;

                 5
                import
                 java.awt.Point;

                 6
                import
                 java.awt.RenderingHints;

                 7
                import
                 java.util.LinkedList;

                 8
                 9
                import
                 javax.swing.JFrame;

                10
                import
                 javax.swing.JPanel;

                11
                12
                public
                class AlgoFrame extends JFrame{
13privateint canvasWidth;
14privateint canvasHeight;
1516public AlgoFrame(String title, int canvasWidth, int canvasHeight) {
17super(title);
1819this.canvasWidth = canvasWidth;
20this.canvasHeight = canvasHeight;
2122         AlgoCanvas canvas = new AlgoCanvas();
23        setContentPane(canvas);
24        pack();
2526         setResizable(false);
27        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
28         setVisible(true);
29    }
3031public AlgoFrame(String title) {
32this(title, 1024, 768);
33    }
3435publicint getCanvasWidth() {return canvasWidth;}
36publicint getCanvasHeight() {return canvasHeight;}
3738private MonteCarloPiaData data;
39publicvoid render(MonteCarloPiaData data) {
40this.data = data;
41        repaint();
42    }
4344privateclass AlgoCanvas extends JPanel{
4546public AlgoCanvas() {
47super(true);
48        }
4950        @Override
51publicvoid paintComponent(Graphics g) {
5253super.paintComponent(g);
5455             Graphics2D g2d = (Graphics2D)g;
5657//抗锯齿58             RenderingHints hints = new RenderingHints(
59                                        RenderingHints.KEY_ANTIALIASING, 
60                                        RenderingHints.VALUE_ANTIALIAS_ON);
61            g2d.addRenderingHints(hints);
6263//具体绘制64             Circle circle = data.getCircle();
65             AlgoVisHelper.setStrokeWidth(g2d, 3);
66            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Blue);
67            AlgoVisHelper.strokeCircle(g2d, circle.getX(), circle.getY(), circle.getR());
6869for(int i = 0 ; i < data.getPointsNumber() ; i ++ ) {
70                 Point p = data.getPoint(i);
71if(circle.contain(p))
72                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
73else74                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
75                 AlgoVisHelper.fillCircle(g2d, p.x, p.y, 3);
76            }
77        }
7879        @Override
80public Dimension getPreferredSize() {
81returnnew Dimension(canvasWidth, canvasHeight);
82        }
83    }
84 }

View Code

AlgoVisualizer.java

                 1
                import
                 java.awt.EventQueue;

                 2
                import
                 java.awt.Point;

                 3
                import
                 java.util.LinkedList;

                 4
                 5
                public
                class
                 AlgoVisualizer {

                 6
                 7
                private
                static
                int DELAY = 40;
 8 9private MonteCarloPiaData data;
10private AlgoFrame frame;
11privateint N;
1213public AlgoVisualizer(int sceneWidth, int sceneHeight, int N) {
1415if(sceneWidth != sceneHeight)
16thrownew IllegalArgumentException("This demo must be run in a square");
17// 初始化数据18this.N = N;
19         Circle circle = new Circle(sceneWidth/2, sceneHeight/2, sceneWidth/2);
20         data = new MonteCarloPiaData(circle);
2122// 初始化视图23         EventQueue.invokeLater(()->{
24             frame = new AlgoFrame("Get Pi with Monte Carlo",sceneWidth,sceneHeight);
25new Thread(()->{
26                    run();
27            }).start();  
28        });
29    }
3031// 动画逻辑32privatevoid run() {
33for(int i = 0 ; i < N ; i ++ ) {
3435if(i % 100 == 0) {
36                frame.render(data);
37                AlgoVisHelper.pause(DELAY);
38                System.out.println(data.estimatePi());
39            }
4041int x = (int)(Math.random() * frame.getCanvasWidth());
42int y = (int)(Math.random() * frame.getCanvasHeight());
43             data.addPoint(new Point(x,y));
44        }
45    }
4647publicstaticvoid main(String[] args) {
4849int sceneWidth = 800;
50int sceneHeight = 800;
51int N = 10000;
5253         AlgoVisualizer visualizer = new AlgoVisualizer(sceneWidth, sceneHeight, N);
54    }
55 }

View Code

AlgoVisHelper.java

                 1
                import
                 java.awt.BasicStroke;

                 2
                import
                 java.awt.Color;

                 3
                import
                 java.awt.Graphics2D;

                 4
                import
                 java.awt.geom.Ellipse2D;

                 5
                 6
                public
                class
                 AlgoVisHelper {

                 7
                public
                 AlgoVisHelper() {}

                 8
                 9
                public
                static
                final Color Red = new Color(0xF44336);
10publicstaticfinal Color Pink = new Color(0xE91E63);
11publicstaticfinal Color Purple = new Color(0x9C27B0);
12publicstaticfinal Color DeepPurple = new Color(0x673AB7);
13publicstaticfinal Color Indigo = new Color(0x3F51B5);
14publicstaticfinal Color Blue = new Color(0x2196F3);
15publicstaticfinal Color LightBlue = new Color(0x03A9F4);
16publicstaticfinal Color Cyan = new Color(0x00BCD4);
17publicstaticfinal Color Teal = new Color(0x009688);
18publicstaticfinal Color Green = new Color(0x4CAF50);
19publicstaticfinal Color LightGreen = new Color(0x8BC34A);
20publicstaticfinal Color Lime = new Color(0xCDDC39);
21publicstaticfinal Color Yellow = new Color(0xFFEB3B);
22publicstaticfinal Color Amber = new Color(0xFFC107);
23publicstaticfinal Color Orange = new Color(0xFF9800);
24publicstaticfinal Color DeepOrange = new Color(0xFF5722);
25publicstaticfinal Color Brown = new Color(0x795548);
26publicstaticfinal Color Grey = new Color(0x9E9E9E);
27publicstaticfinal Color BlueGrey = new Color(0x607D8B);
28publicstaticfinal Color Black = new Color(0x000000);
29publicstaticfinal Color White = new Color(0xFFFFFF);
3031publicstaticvoid setStrokeWidth(Graphics2D g2d, int w) {
32int strokeWidth = w;
33         g2d.setStroke(new BasicStroke(strokeWidth, BasicStroke.CAP_ROUND,BasicStroke.JOIN_ROUND));
34    }
35publicstaticvoid setColor(Graphics2D g2d, Color color) {
36        g2d.setColor(color);
37    }
38publicstaticvoid strokeCircle(Graphics2D g2d, int x, int y, int r) {
39         Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
40        g2d.draw(circle);
41    }
42publicstaticvoid fillCircle(Graphics2D g2d, int x, int y, int r) {
43         Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
44        g2d.fill(circle);
45    }
46publicstaticvoid pause(int t) {
47try {
48            Thread.sleep(t);
49        }
50catch(InterruptedException e) {
51             System.out.println("Error in sleeping.");
52        }
53    }
54 }

View Code

Circle.java

                 1
                import
                 java.awt.Point;

                 2
                 3
                public
                class
                 Circle {

                 4
                 5
                public
                int
                 x, y, r;

                 6
                 7
                public Circle(int x, int y, int r ) {
 8this.x = x;
 9this.y = y;
10this.r = r;
11    }
1213publicint getX() { return x; }
14publicint getY() { return y; }
15publicint getR() { return r; }
1617publicboolean contain(Point p) {
18return Math.pow(p.getX() - x, 2) + Math.pow(p.getY() - y, 2) <= r*r;
19    }
20 }

View Code

MonteCarloPiaData.java

                 1
                import
                 java.awt.Point;

                 2
                import
                 java.util.LinkedList;

                 3
                 4
                public
                class
                 MonteCarloPiaData {

                 5
                 6
                private
                 Circle circle;

                 7
                private
                int insideCircle = 0;
 8private LinkedList<Point> points;
 910public MonteCarloPiaData(Circle circle) {
11this.circle = circle;
12         points = new LinkedList<Point>();
13    }
1415public Circle getCircle() {
16return circle;
17    }
1819public Point getPoint(int i) {
20if(i < 0 || i >= points.size())
21thrownew IllegalArgumentException("out of bound in getPoint!");
22return points.get(i);
23    }
2425publicint getPointsNumber() {
26return points.size();
27    }
2829publicvoid addPoint(Point p) {
30        points.add(p);
31if(circle.contain(p))
32             insideCircle ++;
33    }
3435publicdouble estimatePi() {
36if(points.size() == 0)
37return 0.0;
38int circleArea = insideCircle;
39int squareArea = points.size();
40return (double)circleArea*4 / squareArea;
41    }
42 }

View Code

控制台演示

MonteCarloExperiment.java

                 1
                import java.awt.*;
 2 3publicclass MonteCarloExperiment {
 4 5privateint squareSide;
 6privateint N;
 7privateint outputInterval = 100;
 8 9public MonteCarloExperiment(int squareSide, int N) {
10if(squareSide <= 0 || N <= 0)
11thrownew IllegalArgumentException("squareSide and N must larger than 0");
12this.squareSide = squareSide;
13this.N = N;
14    }
1516publicvoid setOutputInterval(int interval) {
17if(interval <= 0)
18thrownew IllegalArgumentException("interval must be larger than 0");
19this.outputInterval = interval;
20    }
2122publicvoid run() {
2324         Circle circle = new Circle(squareSide/2, squareSide/2, squareSide/2);
25         MonteCarloPiData data = new MonteCarloPiData(circle);
2627for(int i = 0 ; i < N ; i ++) {
28if( i % outputInterval == 0 )
29                System.out.println(data.estimatePi());
30int x = (int)(Math.random() * squareSide);
31int y = (int)(Math.random() * squareSide);
32             data.addPoint(new Point(x,y));
33        }
34    }
3536publicstaticvoid main(String[] args) {
3738int squareSide = 800;
39int N = 1000000;
4041         MonteCarloExperiment exp = new MonteCarloExperiment(squareSide, N);
42         exp.setOutputInterval(10000);
43        exp.run();
44    }
45 }

View Code

原文：https://www.cnblogs.com/cxc1357/p/12853746.html

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[算法] 随机模拟问题【代码】【图】

分钱问题100个人，初始每人100块钱，每轮每人将1元随机分给另一个人，若干轮过后，100个人的财富分布情况会怎样画布的原点在左上角，y轴向下AlgoVisHelper.java 1import java.awt.EventQueue;2import java.util.Arrays;3 4publicclass AlgoVisualizer {5 6privatestaticint DELAY = 40;7privateint[] money;8private AlgoFrame frame;910public AlgoVisualizer(int sceneWidth, int sceneHeight) { 1112// 初始化数据13 mo...

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先给出一般的解决“随机生成7位1—29号数的彩票号码”问题的代码： 1 #include<stdio.h>2int main()3{4int j,i[7];//定义数组保存随机生成不同的7位数字 5for(i[0]=1;i[0]<=29;i[0]++)//在1——29中随机生成不同的数字 6for(i[1]=1;i[1]<=29;i[1]++)7 {8if(i[1]==i[0]) continue;9for(i[2]=1;i[2]<=29;i[2]++) 10 { 11if(i[2]==i[1]||i[2]==i[0]) continue; 12for(i[3]=1;i[3]<=29;i[3]++) 13 ...

【算法导论学习-012】n个数随机等概率的抽样m个

算法法导论》P129页课后题5.3-7 suppose we want to create a random sample of the set {1,2,3,…,n}, thatis, an m-element subset S, where0≤m≤n, such that each m-subset is equally likely to be created. One waywould be to set A[i]=i for i=1,2,3,…,n, call RANDOMIZE-IN-PLACE(A),and then take just the first marray elements. This method would make n calls to the RANDOM procedure.If n is much larger t...

随机算法【代码】

随机算法听起来就很不靠谱...但是有的时候还是很有用的，而且也有正解就是随机化的题目。　　要说定义好像也没什么好讲的，要不先看道题吧。　　偷上网：https://www.luogu.org/problemnew/show/P4703　　luogu某次月赛题，当时刚开始看这个题网站就崩溃了，于是也没有怎么想，今天再想还是没有什么思路。　　一开始想到在边上找，又觉得在中间的可能性也很大，所以似乎并没有什么规律。看了题解发现这道题可以用随机化...随机生成...

机器学习笔记(八)——随机梯度上升(下降)算法调优【代码】

前言概述上一篇文章对逻辑回归的原理和基本思想做了一些简要介绍，并通过引入Sigmoid函数和梯度公式成功推导出了梯度上升和梯度下降公式，上文分类实例是依据全批量提升上升法，而本文会介绍全批量梯度上升的一种优化算法——随机梯度上升，如果还未懂得逻辑回归和推理公式原理，还请观看上一篇文章：机器学习笔记(七)——初识逻辑回归、两种方法推导梯度公式。随机梯度上升区别对比在讲解全批量梯度上升和随机梯度上升的区别之前...

数据算法：分治法，Demo随机生成数组输出最大最小值【代码】

分治法递归函数： 1void PartionGet(int starA, int endA, int *meter, int *max, int *min)/* 分治法获取最优解 */ 2{3/* 参数:4 * s 当前分治段的开始下标5 * e 当前分治段的结束下标6 * meter 表的地址7 * max 存储当前搜索到的最大值8 * min 存储当前搜索到的最小值 */ 910if (endA - starA <= 1) /* 获取局部解，并更新全局解 */11 { 12if (meter[starA] > meter[endA]) 13 { 14if (meter[starA]...

Kaggle竞赛入门（四）：随机森林算法的Python实现【代码】

首先导入数据，将数据分为训练集和测试集：import pandas as pd# Load data melbourne_file_path = ‘../input/melbourne-housing-snapshot/melb_data.csv‘ melbourne_data = pd.read_csv(melbourne_file_path) # Filter rows with missing values melbourne_data = melbourne_data.dropna(axis=0) # Choose target and features y = melbourne_data.Price melbourne_features = [‘Rooms‘, ‘Bathroom‘, ‘Landsize‘, ‘Buil...

Javascript 洗牌算法,打乱数组,随机获取元素【代码】

//利用洗牌算法Array.prototype.shuffle=function(){ var i,t,m=this.length; while(m){ i=Math.floor(Math.random()*m--); t=this[m]; this[m]=this[i]; this[i]=t; } return this;}var arr=[1,2,3,4,5];console.log(arr.shuffle());console.log(arr.slice(0,2));原文：http://www.cnblogs.com/izengbin/p/6797503.html

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