C#-Code

        public int glob_counter { get; private set; }
        public List<int[]> solutions { get; private set; }

C#-Code

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Media;
using System.Windows.Media.Imaging;

using System.Windows.Forms;

namespace aufgabe_95_WPF
{
    public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();
        }

        private struct GUI
        {
            public int nqueens;
            public bool bo_draw;
            public int nsleep;
            public bool bo_rb_l;
            public bool bo_rb_r;
        }

        GUI gui = new GUI();
        void update_gui()
        {
            gui.nqueens = (int)slider_nqueens.Value;
            gui.nsleep = (int)slider_sleep.Value;
            gui.bo_draw = (bool)cb_1.IsChecked;
            gui.bo_rb_l = (bool)rb_l.IsChecked;
            gui.bo_rb_r = (bool)rb_r.IsChecked;
            this.lb_nqueens.Content = $"queens: {this.gui.nqueens,2}";
            this.lb_sleep.Content = $"sleep(ms): {this.gui.nsleep,4}";
            this.textBox.Text = sguistate();
        }
        string sguistate() => $"n_queens: {gui.nqueens}{NL}n_sleep: {gui.nsleep}{NL}bo_draw: {gui.bo_draw}{NL}bo_short_steps: {gui.bo_rb_l}{NL}bo_big_steps: {gui.bo_rb_r}{NL}";

        string NL = Environment.NewLine;
        System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();

        bool[][] board;
        int[] queens;
        QueensProblem qp;
        int glob_counter;
        List<int[]> glob_solutions = new List<int[]>();

        double canvas_h, canvas_w;
        string textbox_content;

        private void bt_reset_Click(object sender, RoutedEventArgs e)
        {
            update_gui();
            board = new bool[gui.nqueens][];
            for (var i = 0; i < board.Length; i++)
                board[i] = new bool[gui.nqueens];

            queens = Enumerable.Repeat(-1, gui.nqueens).ToArray();
            qp = new QueensProblem(gui.nqueens);

            this.textBox.Clear();
            canvas_h = this.Canvas.ActualHeight; canvas_w = this.Canvas.ActualWidth;
            textbox_content = $"canvas: {canvas_h.ToString("n0")} x {canvas_h.ToString("n0")}";
            this.textBox.Text = textbox_content + NL + sguistate();
            update_canvas(this.board, this.queens);
            lb_result.Content = string.Empty;
            glob_counter = 0;
            glob_solutions = new List<int[]>();
        }

        private void bt_run_Click(object sender, RoutedEventArgs e)
        {
            bt_reset_Click(null, null);

            sw.Restart();

            int[] queens_copy = null;
            bool[][] board_copy = null;
            int max_firfirst_col = (int)Math.Ceiling(gui.nqueens / 2.0);
            for (int first_col = 0; first_col < max_firfirst_col; first_col++)
            {
                queens_copy = new int[queens.Length];
                queens.CopyTo(queens_copy, 0);
                queens_copy[first_col] = 0;

                board_copy = board.DeepCopy(); 

                int[] coord = qp.attacked[0][first_col];
                for (var i = 0; i < coord.Length; i += 2)
                    board_copy[coord[i]][coord[i + 1]] = true;

                if (gui.bo_draw)
                {
                    update_canvas(board_copy, queens_copy, gui.bo_rb_l);
                    System.Threading.Thread.Sleep(gui.nsleep);
                }
                int found = 0;
                run(1, board_copy, queens_copy, ref found, gui.bo_draw, true);

                int faktor = 2;
                if (gui.nqueens % 2 == 1 && first_col == max_firfirst_col - 1)
                    faktor = 1;
                glob_counter += faktor * found;
                lb_result.Content = $"after loop {first_col + 1} glob_counter is {glob_counter.ToString("n0")}";
                System.Windows.Forms.Application.DoEvents();
            }
            update_canvas(board_copy, glob_solutions[glob_solutions.Count - 1]);
            $"ready {glob_counter}    {sw.Elapsed.Duration()}".m();
        }


        private void run(int reihe, bool[][] board, int[] queens, ref int found, bool bo_draw, bool bo_run)
        {
            if (!bo_run)
                return;

            bool[][] board_copy = board.DeepCopy();
            int[] queens_copy = new int[queens.Length];
            queens.CopyTo(queens_copy, 0);

            if (reihe == gui.nqueens)
            {
                if (gui.bo_draw)
                {
                    update_canvas(board_copy, queens_copy);
                    System.Threading.Thread.Sleep(gui.nsleep);
                }
                found++;
                glob_solutions.Add(queens);
                this.lb_result.Content = $"found so far: {glob_solutions.Count.ToString("n0")}";
                System.Windows.Forms.Application.DoEvents();
                return;                
            }
            else
            {
                List<int> empty = new List<int>();
                for (var col = 0; col < board[reihe].Length; col++)
                    if (!board[reihe][col])
                        empty.Add(col);

                if (empty.Count == 0)
                    return;

                foreach(int ccol in empty)
                {
                    board_copy = board.DeepCopy();
                    queens_copy = new int[queens.Length];
                    queens.CopyTo(queens_copy, 0);
                    queens_copy[ccol] = reihe;
                    for (var j = 0; j < qp.attacked[reihe][ccol].Length; j += 2)
                        board_copy[qp.attacked[reihe][ccol][j]][qp.attacked[reihe][ccol][j + 1]] = true;

                    if (bo_draw)
                    {
                        update_canvas(board_copy, queens_copy, gui.bo_rb_l);
                        System.Threading.Thread.Sleep(gui.nsleep);
                    }
                    run(reihe + 1, board_copy, queens_copy, ref found, bo_draw, bo_run);
                }
                return;
            }
        }

        private void slider_ValueChanged(object sender, RoutedPropertyChangedEventArgs<double> e)
        {
            if (bo_loaded) update_gui();                
        }

        bool bo_loaded = false;
        private void Window_Loaded(object sender, RoutedEventArgs e)
        {
            bo_loaded = true;
        }

        private void cb_1_Click(object sender, RoutedEventArgs e)
        {
            update_gui();
        }

        private void bt_count_Click(object sender, RoutedEventArgs e)
        {
            bt_reset_Click(null, null);
            sw.Restart();
            QueensProblem qp2 = new QueensProblem(gui.nqueens, true);
            string s_erg = $"{qp2.glob_counter.ToString("n0")} position found in {sw.Elapsed.Duration()}";
            this.textBox.Text = s_erg;
            s_erg.m();
        }

        private void update_canvas(bool[][] board, int[] queens, bool bo_attacked = false)
        {
            this.Canvas.Children.Clear();
            double w = Math.Min(canvas_h, canvas_w) / gui.nqueens;
            for(var i = 0; i < board.Length; i++)
                for(var j = 0; j < board[i].Length; j++)
                {
                    double y = i * w;
                    double x = j * w;
                    System.Windows.Shapes.Rectangle rect;
                    rect = new System.Windows.Shapes.Rectangle();
                    rect.Stroke = new SolidColorBrush(Colors.Black);

                    SolidColorBrush c = new SolidColorBrush(Colors.Wheat); 
                    if (bo_attacked && board[i][j])
                        c = new SolidColorBrush(Colors.Red);
                    else
                    {
                        if((i % 2 == 0) && (j % 2 != 0) || (i % 2 != 0) && (j % 2 == 0))
                            c = new SolidColorBrush(Colors.SandyBrown);
                    }
                    if (queens[j] == i)
                    {
                        //c = new SolidColorBrush(Colors.Black); //falls queen2.jpg nicht vorhanden ist
                        BitmapImage theImage = new BitmapImage
                            (new Uri(@"..\..\pics_and_txt\queen2.jpg", UriKind.Relative));
                        ImageBrush myImageBrush = new ImageBrush(theImage);
                        Canvas TempCanvas = new Canvas();
                        TempCanvas.Width = w;
                        TempCanvas.Height = w;
                        TempCanvas.Background = myImageBrush;
                        Canvas.SetLeft(TempCanvas, x);
                        Canvas.SetTop(TempCanvas, y);
                        this.Canvas.Children.Add(TempCanvas);
                    }
                    else
                    {
                        rect.Fill = c;
                        rect.Width = w;
                        rect.Height = w;
                        Canvas.SetLeft(rect, x);
                        Canvas.SetTop(rect, y);
                        this.Canvas.Children.Add(rect);
                    }                    
                }
            System.Windows.Forms.Application.DoEvents();
        }
    }

    public class QueensProblem
    {
        int n;
        bool[][] board;
        public int[][][] attacked { get;  private set; }
        public int glob_counter { get; private set; }
        public List<int[]> solutions { get; private set; }
        private int[] queens;

        public QueensProblem(int nqueens, bool bo_run_loop = false)
        {
            this.n = nqueens;
            this.board = new bool[n][];
            for (var i = 0; i < board.Length; i++)
                this.board[i] = new bool[n];
            this.attacked = new int[n][][];
            for (var i = 0; i < n; i++)
            {
                this.attacked[i] = new int[n][];
                for (var j = 0; j < this.attacked[i].Length; j++)
                {
                    List<int> temp = new List<int>(ListAttacked(i, j));
                    this.attacked[i][j] = new int[temp.Count];
                    temp.ToArray().CopyTo(this.attacked[i][j], 0);
                }
            }
            queens = Enumerable.Repeat(-1, n).ToArray();
            List<int[]> solutions = new List<int[]>();
            if (bo_run_loop)
                run_loop();
        }

        List<int> ListAttacked(int iy, int ix)
        {
            List<int> result = new List<int>();
            int counter = 1;
            for (int i = iy + 1; i < n; i++)
            {
                { result.Add(i); result.Add(ix); }
                if (ix - counter >= 0)
                    { result.Add(i); result.Add(ix - counter); }
                if (ix + counter < n)
                    { result.Add(i); result.Add(ix + counter); }
                counter++;           }
            return result;
        }

        void run(int reihe, bool[][] board, int[] queens, ref int found)
        {
            bool[][] board_copy = DeepCopy(board);
            int[] queens_copy = new int[queens.Length];
            queens.CopyTo(queens_copy, 0);

            if (reihe == n)
            {
                found++;
                solutions.Add(queens_copy);
                return;
            }
            else
            {
                List<int> empty = new List<int>();
                for (var col = 0; col < board[reihe].Length; col++)
                    if (!board[reihe][col])
                        empty.Add(col);

                if (empty.Count == 0)
                    return;

                foreach (int ccol in empty)
                {
                    board_copy = DeepCopy(board);
                    queens_copy = new int[queens.Length];
                    queens.CopyTo(queens_copy, 0);
                    queens_copy[ccol] = reihe;
                    for (var j = 0; j < attacked[reihe][ccol].Length; j += 2)
                        board_copy[attacked[reihe][ccol][j]][attacked[reihe][ccol][j + 1]] = true;
                    run(reihe + 1, board_copy, queens_copy, ref found);
                }
            }
        }
        
        void run_loop()
        {            
            int max_first_col = (int)Math.Ceiling(n / 2.0);
            for (int first_col = 0; first_col < max_first_col; first_col++)
            {
                int[] queens_copy = new int[queens.Length];
                queens.CopyTo(queens_copy, 0);
                queens_copy[first_col] = 0;

                bool[][] board_copy = DeepCopy(board);

                int[] coord = attacked[0][first_col];
                for (var i = 0; i < coord.Length; i += 2)
                    board_copy[coord[i]][coord[i + 1]] = true;
                int found = 0;
                run(1, board_copy, queens_copy, ref found);

                int faktor = 2;
                if (n % 2 == 1 && first_col == max_first_col - 1)
                    faktor = 1;
                glob_counter += faktor * found;
            }
        }

        T[][] DeepCopy<T>(T[][] x)
        {
            T[][] result = new T[x.Length][];
            for (var i = 0; i < result.Length; i++)
            {
                result[i] = new T[x[i].Length];
                x[i].CopyTo(result[i], 0);
            }
            return result;
        }
    }

    public static class tools
    {
        public static string ToMyString(this bool[][] a)
        {
            StringBuilder sb = new StringBuilder();
            for (var i = 0; i < a.Length; i++)
            {
                for (var j = 0; j < a[i].Length; j++)
                {
                    int temp = a[i][j] ? 1 : 0;
                    sb.Append($"{temp,2}");
                }
                 sb.AppendLine();
            }
            return sb.ToString();
        }

        public static string ToMyString(this int[][][] a)
        {
            StringBuilder sb = new StringBuilder();
            for(var i = 0; i < a.Length; i++)
                for(var j = 0; j < a[i].Length; j++)
                {
                    sb.Append($"{i} {j}: ");
                    for (var k = 0; k < a[i][j].Length; k++)
                        sb.Append($"{a[i][j][k],2}");
                    sb.AppendLine();
                }
            return sb.ToString();
        }

        public static string ToMyString(this List<int> a)
        {
            StringBuilder sb = new StringBuilder();
            for (var i = 0; i < a.Count; i++)
              sb.Append($"{a[i],2}");
            return sb.ToString();
        }

        public static void m(this string s) => System.Windows.MessageBox.Show(s);

        public static T[][] DeepCopy<T>(this T[][] x)
        {
            T[][] result = new T[x.Length][];
            for (var i = 0; i < result.Length; i++)
            {
                result[i] = new T[x[i].Length];
                x[i].CopyTo(result[i], 0);
            }
            return result;
        }

        public static string Duration(this TimeSpan ts) => String.Format("{0:00}:{1:00}:{2:00}.{3:00}",
            ts.Hours, ts.Minutes, ts.Seconds, ts.Milliseconds / 10);
    }
}

C#-Code

<Window x:Class="aufgabe_95_WPF.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:aufgabe_95_WPF"
        mc:Ignorable="d"
        Title="n x n queens problem" Height="441.445" Width="745.018" FontFamily="Courier New" Background="{DynamicResource {x:Static SystemColors.ActiveCaptionBrushKey}}" WindowState="Maximized" Loaded="Window_Loaded">
    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="1*"/>
            <ColumnDefinition Width="5"/>
            <ColumnDefinition Width="1*"/>
        </Grid.ColumnDefinitions>
        <Grid.RowDefinitions>
            <RowDefinition Height="75"/>
            <RowDefinition Height="1*"/>
            <RowDefinition Height="30"/>
        </Grid.RowDefinitions>
        <GridSplitter x:Name="gridSplitter" Grid.Column="1" HorizontalAlignment="Stretch" Margin="0" Grid.Row="1" Width="5"/>
        <StackPanel  Margin="0" Orientation="Horizontal" Grid.ColumnSpan="3">

            <Button x:Name="bt_reset" Content="reset" Width="75" Margin="5,0" Click="bt_reset_Click" Height="35"/>

            <GroupBox x:Name="gb_2" Height="50" Header=" slider queens " Margin="5,0">
                <StackPanel Orientation="Horizontal">
                    <Slider x:Name="slider_nqueens" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="0,0,5,0" Minimum="1" Maximum="20" Width="100" TickPlacement="BottomRight" Value="8" ValueChanged="slider_ValueChanged"/>
                    <Label x:Name="lb_nqueens" Content="queens:  8" Margin="0,0,15,0" HorizontalAlignment="Center" VerticalAlignment="Center"></Label>
                </StackPanel>
            </GroupBox>

            <GroupBox x:Name="gb_4" Height="50" Header=" drawing " Margin="5,0">
                <StackPanel Orientation="Horizontal">
                    <CheckBox x:Name="cb_1" Content="drawing" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="5,0" Click="cb_1_Click" IsChecked="True"></CheckBox>
                    <RadioButton x:Name="rb_l" Content="short steps " IsChecked="True" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="5,0,0,0"/>
                    <RadioButton x:Name="rb_r" Content="big steps   " HorizontalAlignment="Center" VerticalAlignment="Center" Margin="5,0"/>
                </StackPanel>
            </GroupBox>

            <GroupBox x:Name="gb_3" Height="50" Header=" slider sleep ">
                <StackPanel Orientation="Horizontal">
                    <Slider x:Name="slider_sleep" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="0,0,5,0" Maximum="5000" Width="100" TickFrequency="250" TickPlacement="BottomRight" ValueChanged="slider_ValueChanged" Value="1000"/>
                    <Label x:Name="lb_sleep" Content="sleep(ms):    0" Margin="0,0,20,0" HorizontalAlignment="Center" VerticalAlignment="Center"></Label>
                </StackPanel>
            </GroupBox>

            <Button x:Name="bt_run" Content="run" Width="75" Margin="15,0,5,0" Click="bt_run_Click" Height="35" />
            <Button x:Name="bt_count" Content=" just count " Margin="15,0,5,0" Height="35" Click="bt_count_Click" />

        </StackPanel>
        <StackPanel Height="25" Margin="0" Orientation="Horizontal" Grid.ColumnSpan="3" Grid.Row="2">
            <Label x:Name="lb_version"  HorizontalAlignment="Center" VerticalAlignment="Center" Content="2018/11/05 VERSION 2018/11/06" Margin="5,0,0,0"></Label>
            <Label x:Name="lb_result" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="5,0,0,0"></Label>
        </StackPanel>
        <Canvas x:Name="Canvas" Margin="5,50,5,5" Grid.Row="1" Background="{DynamicResource {x:Static SystemColors.ControlBrushKey}}"/>
        <Expander Grid.Column="2" Grid.Row="1" IsExpanded="True">
            <GroupBox x:Name="groupBox" Grid.Column="2" Header="INFO" Margin="5" Grid.Row="1">
                <TextBox x:Name="textBox" Margin="5" Text="TextBox" VerticalScrollBarVisibility="Auto" AcceptsReturn="True" AcceptsTab="True" HorizontalScrollBarVisibility="Auto" FontSize="36" FontWeight="Bold"/>
            </GroupBox>
        </Expander>

    </Grid>
</Window>