C#使用迷宫地图来模拟新冠疫情的传播速度(一)

国家开始发布疫情放开政策，本人于2022-12-21开始感染并发高烧。

最近才康复。有感于此

我们用初始感染源来影响九宫网格来查看新冠的传播速度

小游戏规则如下：

一个感染源可以传播附近相邻的8个网格【类似于扫雷】，假如每个感染源一天只能感染相邻的8个网格，问：一个感染源多久可以感染所有N*M网格

初始所有单元格都是绿色的，初始当前红色的单元格可以感染8个最近的单元格【九宫格】，

并将其他8个单元格设置为红色。

迷宫的单元格没有障碍和阻塞

病毒传染源居于中心将达到最快速度,

新建Windows窗体应用程序NovelCoronavirusDemo，

将默认的Form1重命名为FormNovelVirusSpread，窗体FormNovelVirusSpread设计如图：

为窗体绑定Paint事件FormNovelVirusSpread_Paint，

按钮Init绑定Click事件btnInit_Click，按钮Spread绑定Click事件btnSpread_Click

窗体设计代码如下【FormNovelVirusSpread.Designer.cs】：


namespace NovelCoronavirusDemo
{
    partial class FormNovelVirusSpread
    {
        /// <summary>
        /// 必需的设计器变量。
        /// </summary>
        private System.ComponentModel.IContainer components = null;

        /// <summary>
        /// 清理所有正在使用的资源。
        /// </summary>
        /// <param name="disposing">如果应释放托管资源，为 true；否则为 false。</param>
        protected override void Dispose(bool disposing)
        {
            if (disposing && (components != null))
            {
                components.Dispose();
            }
            base.Dispose(disposing);
        }

        #region Windows 窗体设计器生成的代码

        /// <summary>
        /// 设计器支持所需的方法 - 不要修改
        /// 使用代码编辑器修改此方法的内容。
        /// </summary>
        private void InitializeComponent()
        {
            this.panel1 = new System.Windows.Forms.Panel();
            this.rtxbDisplay = new System.Windows.Forms.RichTextBox();
            this.btnSpread = new System.Windows.Forms.Button();
            this.btnInit = new System.Windows.Forms.Button();
            this.txbColumnCount = new System.Windows.Forms.TextBox();
            this.label2 = new System.Windows.Forms.Label();
            this.txbRowCount = new System.Windows.Forms.TextBox();
            this.label1 = new System.Windows.Forms.Label();
            this.panel1.SuspendLayout();
            this.SuspendLayout();
            // 
            // panel1
            // 
            this.panel1.Controls.Add(this.rtxbDisplay);
            this.panel1.Controls.Add(this.btnSpread);
            this.panel1.Controls.Add(this.btnInit);
            this.panel1.Controls.Add(this.txbColumnCount);
            this.panel1.Controls.Add(this.label2);
            this.panel1.Controls.Add(this.txbRowCount);
            this.panel1.Controls.Add(this.label1);
            this.panel1.Location = new System.Drawing.Point(652, 12);
            this.panel1.Name = "panel1";
            this.panel1.Size = new System.Drawing.Size(320, 618);
            this.panel1.TabIndex = 11;
            // 
            // rtxbDisplay
            // 
            this.rtxbDisplay.Location = new System.Drawing.Point(3, 88);
            this.rtxbDisplay.Name = "rtxbDisplay";
            this.rtxbDisplay.ReadOnly = true;
            this.rtxbDisplay.Size = new System.Drawing.Size(311, 527);
            this.rtxbDisplay.TabIndex = 9;
            this.rtxbDisplay.Text = "";
            // 
            // btnSpread
            // 
            this.btnSpread.Font = new System.Drawing.Font("宋体", 13F, System.Drawing.FontStyle.Bold);
            this.btnSpread.Location = new System.Drawing.Point(209, 3);
            this.btnSpread.Name = "btnSpread";
            this.btnSpread.Size = new System.Drawing.Size(80, 80);
            this.btnSpread.TabIndex = 0;
            this.btnSpread.Text = "Spread";
            this.btnSpread.UseVisualStyleBackColor = true;
            this.btnSpread.Click += new System.EventHandler(this.btnSpread_Click);
            // 
            // btnInit
            // 
            this.btnInit.Font = new System.Drawing.Font("宋体", 13F, System.Drawing.FontStyle.Bold);
            this.btnInit.Location = new System.Drawing.Point(113, 3);
            this.btnInit.Name = "btnInit";
            this.btnInit.Size = new System.Drawing.Size(80, 80);
            this.btnInit.TabIndex = 8;
            this.btnInit.Text = "Init";
            this.btnInit.UseVisualStyleBackColor = true;
            this.btnInit.Click += new System.EventHandler(this.btnInit_Click);
            // 
            // txbColumnCount
            // 
            this.txbColumnCount.Font = new System.Drawing.Font("宋体", 13F, System.Drawing.FontStyle.Bold);
            this.txbColumnCount.Location = new System.Drawing.Point(57, 42);
            this.txbColumnCount.Name = "txbColumnCount";
            this.txbColumnCount.Size = new System.Drawing.Size(38, 27);
            this.txbColumnCount.TabIndex = 7;
            this.txbColumnCount.Text = "6";
            // 
            // label2
            // 
            this.label2.AutoSize = true;
            this.label2.Font = new System.Drawing.Font("宋体", 13F, System.Drawing.FontStyle.Bold);
            this.label2.Location = new System.Drawing.Point(7, 45);
            this.label2.Name = "label2";
            this.label2.Size = new System.Drawing.Size(46, 18);
            this.label2.TabIndex = 6;
            this.label2.Text = "列数";
            // 
            // txbRowCount
            // 
            this.txbRowCount.Font = new System.Drawing.Font("宋体", 13F, System.Drawing.FontStyle.Bold);
            this.txbRowCount.Location = new System.Drawing.Point(57, 9);
            this.txbRowCount.Name = "txbRowCount";
            this.txbRowCount.Size = new System.Drawing.Size(38, 27);
            this.txbRowCount.TabIndex = 5;
            this.txbRowCount.Text = "5";
            // 
            // label1
            // 
            this.label1.AutoSize = true;
            this.label1.Font = new System.Drawing.Font("宋体", 13F, System.Drawing.FontStyle.Bold);
            this.label1.Location = new System.Drawing.Point(7, 12);
            this.label1.Name = "label1";
            this.label1.Size = new System.Drawing.Size(46, 18);
            this.label1.TabIndex = 4;
            this.label1.Text = "行数";
            // 
            // FormNovelVirusSpread
            // 
            this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 12F);
            this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
            this.ClientSize = new System.Drawing.Size(984, 642);
            this.Controls.Add(this.panel1);
            this.Name = "FormNovelVirusSpread";
            this.Text = "新冠病毒传播演示";
            this.Paint += new System.Windows.Forms.PaintEventHandler(this.FormNovelVirusSpread_Paint);
            this.panel1.ResumeLayout(false);
            this.panel1.PerformLayout();
            this.ResumeLayout(false);

        }

        #endregion

        private System.Windows.Forms.Panel panel1;
        private System.Windows.Forms.RichTextBox rtxbDisplay;
        private System.Windows.Forms.Button btnSpread;
        private System.Windows.Forms.Button btnInit;
        private System.Windows.Forms.TextBox txbColumnCount;
        private System.Windows.Forms.Label label2;
        private System.Windows.Forms.TextBox txbRowCount;
        private System.Windows.Forms.Label label1;
    }
}

新建网格对象实体类Grid，Grid类的源代码如下：

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace NovelCoronavirusDemo
{
    /// <summary>
    /// 一个单元格,由行索引，列索引，是否已被感染等属性组成
    /// </summary>
    public class Grid
    {
        /// <summary>
        /// 网格所在的行的索引
        /// </summary>
        public int RowIndex { get; set; }

        /// <summary>
        /// 网格所在的列的索引
        /// </summary>
        public int ColumnIndex { get; set; }

        /// <summary>
        /// 是否已被感染新冠
        /// </summary>
        public bool IsInfected { get; set; }

        /// <summary>
        /// 是否已访问
        /// </summary>
        public bool IsVisited { get; set; }

        /// <summary>
        /// 打印该网格对象
        /// </summary>
        /// <returns></returns>
        public override string ToString()
        {
            return $"{{Row={RowIndex},Column={ColumnIndex},IsInfected={IsInfected}}}";
        }
    }
}

新建操作类MazeGridUtil，MazeGridUtil类的源代码如下：

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace NovelCoronavirusDemo
{
    /// <summary>
    /// 网格地图可以认为是一个N*M的行列式，也可以认为是一个二维数组，每个元素都是一个单元格Grid
    /// </summary>
    public class MazeGridUtil
    {
        /// <summary>
        /// 行数
        /// </summary>
        public int RowCount { get; set; }
        /// <summary>
        /// 列数
        /// </summary>
        public int ColumnCount { get; set; }
        /// <summary>
        /// 网格行列式
        /// </summary>
        public Grid[,] GridArray { get; set; }
        /// <summary>
        /// 初始化网格地图：需指定行数和列数
        /// </summary>
        /// <param name="rowCount">行数</param>
        /// <param name="columnCount">列数</param>
        public MazeGridUtil(int rowCount, int columnCount) 
        {
            RowCount = rowCount;
            ColumnCount = columnCount;
            GridArray = new Grid[RowCount, ColumnCount];
            for (int i = 0; i < RowCount; i++)
            {
                for (int j = 0; j < ColumnCount; j++)
                {
                    GridArray[i, j] = new Grid()
                    {
                        RowIndex = i,
                        ColumnIndex = j,
                        IsInfected = false,
                        IsVisited = false
                    };
                }
            }
        }

        /// <summary>
        /// 获取所有已感染的并且未访问的单元格
        /// </summary>
        /// <returns></returns>
        public static List<Grid> GetAllInfectedAndUnvisited(MazeGridUtil mazeGridUtil)
        {
            List<Grid> mazeGrids = new List<Grid>();
            for (int i = 0; i < mazeGridUtil.RowCount; i++)
            {
                for (int j = 0; j < mazeGridUtil.ColumnCount; j++)
                {
                    if (mazeGridUtil.GridArray[i, j].IsInfected && !mazeGridUtil.GridArray[i, j].IsVisited)
                    {
                        //考虑到可能会重复，这里过滤掉重复的
                        if (!mazeGrids.Contains(mazeGridUtil.GridArray[i, j]))
                        {
                            mazeGrids.Add(mazeGridUtil.GridArray[i, j]);
                        }
                    }
                }
            }
            return mazeGrids;
        }

        /// <summary>
        /// 将当前已感染的单元格的相邻的8个九宫格设置为已感染新冠状态
        /// </summary>
        /// <param name="mazeGrids">所有已感染的并且未访问的单元格</param>
        /// <param name="mazeGridUtil"></param>
        public static void InfectEightGrid(List<Grid> mazeGrids, MazeGridUtil mazeGridUtil) 
        {
            for (int index = 0; index < mazeGrids.Count; index++)
            {
                int i = mazeGrids[index].RowIndex;//i对应行Row
                int j = mazeGrids[index].ColumnIndex;//j对应列Column
                mazeGridUtil.GridArray[i, j].IsVisited = true;
                //将当前已感染的单元格的相邻的8个九宫格设置为感染
                if (i - 1 >= 0 && j - 1 >= 0)
                {
                    if (!mazeGridUtil.GridArray[i - 1, j - 1].IsInfected)
                    {
                        mazeGridUtil.GridArray[i - 1, j - 1].IsInfected = true;
                    }
                }
                if (i - 1 >= 0)
                {
                    if (!mazeGridUtil.GridArray[i - 1, j].IsInfected)
                    {
                        mazeGridUtil.GridArray[i - 1, j].IsInfected = true;
                    }
                }
                if (j + 1 < mazeGridUtil.ColumnCount && i - 1 >= 0)
                {
                    if (!mazeGridUtil.GridArray[i - 1, j + 1].IsInfected)
                    {
                        mazeGridUtil.GridArray[i - 1, j + 1].IsInfected = true;
                    }
                }

                if (j - 1 >= 0)
                {
                    if (!mazeGridUtil.GridArray[i, j - 1].IsInfected)
                    {
                        mazeGridUtil.GridArray[i, j - 1].IsInfected = true;
                    }
                }
                if (j + 1 < mazeGridUtil.ColumnCount)
                {
                    if (!mazeGridUtil.GridArray[i, j + 1].IsInfected)
                    {
                        mazeGridUtil.GridArray[i, j + 1].IsInfected = true;
                    }
                }

                if (j - 1 >= 0 && i + 1 < mazeGridUtil.RowCount)
                {
                    if (!mazeGridUtil.GridArray[i + 1, j - 1].IsInfected)
                    {
                        mazeGridUtil.GridArray[i + 1, j - 1].IsInfected = true;
                    }
                }
                if (i + 1 < mazeGridUtil.RowCount)
                {
                    if (!mazeGridUtil.GridArray[i + 1, j].IsInfected)
                    {
                        mazeGridUtil.GridArray[i + 1, j].IsInfected = true;
                    }
                }
                if (i + 1 < mazeGridUtil.RowCount && j + 1 < mazeGridUtil.ColumnCount)
                {
                    if (!mazeGridUtil.GridArray[i + 1, j + 1].IsInfected)
                    {
                        mazeGridUtil.GridArray[i + 1, j + 1].IsInfected = true;
                    }
                }
            }
        }

        /// <summary>
        /// 是否已全部感染
        /// </summary>
        /// <returns></returns>
        public static bool IsAllSpread(MazeGridUtil mazeGridUtil)
        {
            bool isAce = true;//是否全部感染
            for (int i = 0; i < mazeGridUtil.RowCount; i++)
            {
                bool existOK = false;//是否存在未感染
                for (int j = 0; j < mazeGridUtil.ColumnCount; j++)
                {
                    if (!mazeGridUtil.GridArray[i, j].IsInfected)
                    {
                        isAce = false;
                        existOK = true;
                        break;
                    }
                }
                if (existOK)
                {
                    break;
                }
            }
            return isAce;
        }
    }
}

窗体FormNovelVirusSpread.cs源代码如下：

using MazeDemo;
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;

namespace NovelCoronavirusDemo
{
    public partial class FormNovelVirusSpread : Form
    {
        /// <summary>
        /// 是否已描绘病毒源，确保只描绘病毒源一次
        /// </summary>
        bool isDrawVirusSource = false;
        /// <summary>
        /// 病毒感染全部网格所需天数
        /// </summary>
        int spreadDays = 0;
        MazeGridUtil mazeGridUtil = null;
        public FormNovelVirusSpread()
        {
            InitializeComponent();
        }

        /// <summary>
        /// 显示文本框内容
        /// </summary>
        /// <param name="message"></param>
        private void DisplayContent(string message)
        {
            this.BeginInvoke(new Action(() =>
            {
                if (rtxbDisplay.TextLength > 10240)
                {
                    rtxbDisplay.Clear();
                }
                rtxbDisplay.AppendText(message + "\n");
                rtxbDisplay.ScrollToCaret();
            }));
        }

        /// <summary>
        /// 检查输入
        /// </summary>
        /// <param name="txb"></param>
        /// <param name="commentStr"></param>
        /// <param name="count"></param>
        /// <returns></returns>
        private bool CheckInputCount(TextBox txb, string commentStr, out int count)
        {
            if (!int.TryParse(txb.Text, out count))
            {
                MessageBox.Show($"[{commentStr}]请输入正整数", "错误");
                txb.Focus();
                return false;
            }
            if (count <= 0 || count >= 100)
            {
                MessageBox.Show($"[{commentStr}]范围是【1~99】，请重新输入", "错误");
                txb.Focus();
                return false;
            }
            return true;
        }

        /// <summary>
        /// 窗体的重绘事件，调用Invalidate()会触发重绘事件
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void FormNovelVirusSpread_Paint(object sender, PaintEventArgs e)
        {
            if (mazeGridUtil == null) 
            {
                return;
            }
            int sideLength = 50;//正方形【迷宫的一个网格MazeGrid】的边长。
            float fontSize = 13;//打印的起点、终点文字的字体大小
            //以边长为50为例：因当前窗体的高度为606，去除窗体顶部和底部的高度【约56】，只能正常显示11行。因Panel控件的横坐标为705，因此只能显示14列。
            if (mazeGridUtil.RowCount <= 11 && mazeGridUtil.ColumnCount <= 14)
            {
                sideLength = 50;
                fontSize = 13;
            }
            else if (mazeGridUtil.RowCount <= 22 && mazeGridUtil.ColumnCount <= 28)
            {
                //如果行数在22行之内，列数在28列之内，则将网格的边长设置25
                sideLength = 25;
                fontSize = 8;
            }
            else
            {
                //如果行数、列数过大（行数大于22，列数大于28）。则应该将界面变大，并增加滚动条
                sideLength = 25;
                fontSize = 8;
                if (mazeGridUtil.RowCount > 22)
                {
                    this.Height = this.Height + (mazeGridUtil.RowCount - 22) * sideLength;
                }
                if (mazeGridUtil.ColumnCount > 28)
                {
                    this.Width = this.Width + (mazeGridUtil.ColumnCount - 28) * sideLength;
                    //Panel操作面板要整体向右移动，即X坐标增加
                    panel1.Location = new Point(panel1.Location.X + (mazeGridUtil.ColumnCount - 28) * sideLength, panel1.Location.Y);
                }
            }
            Graphics graphics = e.Graphics;
            for (int i = 0; i < mazeGridUtil.RowCount; i++)
            {
                for (int j = 0; j < mazeGridUtil.ColumnCount; j++)
                {
                    //注意：第一行是Y坐标没变，X坐标在变化。因此i是纵坐标 j是横坐标
                    Rectangle rect = new Rectangle(sideLength * j, sideLength * i, sideLength, sideLength);
                    graphics.DrawRectangle(new Pen(Color.Red), rect);
                    if (mazeGridUtil.GridArray[i, j].IsInfected)
                    {
                        graphics.FillRectangle(new SolidBrush(Color.Red), rect);//如果已感染
                    }
                    else
                    {
                        graphics.FillRectangle(Brushes.SpringGreen, rect);
                    }
                    //绘制网格的(行索引，列索引)
                    AddTextAlignCenter(graphics, $"({i},{j})", new Font("宋体", fontSize), rect);
                }
            }
            //画横线
            for (int i = 0; i < mazeGridUtil.RowCount + 1; i++)
            {
                graphics.DrawLine(Pens.Black, 0, sideLength * i, sideLength * mazeGridUtil.ColumnCount, sideLength * i);
            }
            //画纵线
            for (int j = 0; j < mazeGridUtil.ColumnCount + 1; j++)
            {
                graphics.DrawLine(Pens.Black, sideLength * j, 0, sideLength * j, sideLength * mazeGridUtil.RowCount);
            }
            if (!isDrawVirusSource)
            {
                isDrawVirusSource = true;
                //设置新冠病毒源为红色，居中显示
                Rectangle rectEnd = new Rectangle(sideLength * ((mazeGridUtil.ColumnCount - 1) / 2), sideLength * ((mazeGridUtil.RowCount - 1) / 2), sideLength, sideLength);
                graphics.FillRectangle(new SolidBrush(Color.Red), rectEnd);
                AddTextAlignCenter(graphics, "病毒源", new Font("宋体", fontSize), rectEnd);
                mazeGridUtil.GridArray[(mazeGridUtil.RowCount - 1) / 2, (mazeGridUtil.ColumnCount - 1) / 2].IsInfected = true;
                DisplayContent($"新冠传播的病毒源为【({(mazeGridUtil.RowCount - 1) / 2},{(mazeGridUtil.ColumnCount - 1) / 2})】...");
            }
        }

        /// <summary>
        /// 将显示的文字放在矩形的中间
        /// </summary>
        /// <param name="graphics"></param>
        /// <param name="text"></param>
        /// <param name="font"></param>
        /// <param name="rect"></param>
        private void AddTextAlignCenter(Graphics graphics, string text, Font font, Rectangle rect)
        {
            SizeF sizeF = graphics.MeasureString(text, font);
            float destX = rect.X + (rect.Width - sizeF.Width) / 2;
            float destY = rect.Y + (rect.Height - sizeF.Height) / 2;
            graphics.DrawString(text, font, Brushes.Black, destX, destY);
        }

        private void btnInit_Click(object sender, EventArgs e)
        {
            int rowCount;//行数
            int columnCount;//列数
            if (!CheckInputCount(txbRowCount, "行数", out rowCount))
            {
                return;
            }
            if (!CheckInputCount(txbColumnCount, "列数", out columnCount))
            {
                return;
            }
            isDrawVirusSource = false;
            spreadDays = 0;
            DisplayContent($"正在生成新冠传播网格地图【{rowCount}行{columnCount}列】，请稍候...");

            mazeGridUtil = new MazeGridUtil(rowCount, columnCount);
            //重绘迷宫，新的开始
            this.Invalidate();
        }

        /// <summary>
        /// 新冠病毒感染附近的8个单元格
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void btnSpread_Click(object sender, EventArgs e)
        {
            spreadDays++;
            //获取所有已感染的并且未访问的单元格
            List<Grid> mazeGrids = MazeGridUtil.GetAllInfectedAndUnvisited(mazeGridUtil);
            MazeGridUtil.InfectEightGrid(mazeGrids, mazeGridUtil);
            
            this.Invalidate();//触发paint事件
            //重新获取已感染的单元格
            mazeGrids = MazeGridUtil.GetAllInfectedAndUnvisited(mazeGridUtil);
            DisplayContent($"第【{spreadDays}】天，新冠传播已感染网格个数【{mazeGrids.Count}】,分别为【{string.Join(";", mazeGrids.Select(grid => $"({grid.RowIndex},{grid.ColumnIndex})"))}】");
            bool isAce = MazeGridUtil.IsAllSpread(mazeGridUtil);//是否全部感染
            if (isAce)
            {
                DisplayContent($"已全部感染新冠病毒,网格地图已被病毒沦陷,所需天数【{spreadDays}】");
                MessageBox.Show($"已全部感染新冠病毒,网格地图已被病毒沦陷,所需天数【{spreadDays}】", "Ace");
            }
        }
    }
}