From 9797b3c6f560cbdaa86c7b7dbb1a309adc98357a Mon Sep 17 00:00:00 2001
From: Rokas Puzonas <rokas.puz@gmail.com>
Date: Sat, 11 Feb 2023 14:37:41 +0200
Subject: [PATCH] Add project files.

---
 Lab1/BMP File Format.url |   5 +
 Lab1/BMP formatas.docx   | Bin 0 -> 21257 bytes
 Lab1/BMPImage.cs         | 359 +++++++++++++++++++++++++++++++++++++++
 Lab1/Lab1.csproj         |   8 +
 Lab1/Program.cs          | 138 +++++++++++++++
 Lab1/README.md           |  34 ++++
 Labs.sln                 |  25 +++
 7 files changed, 569 insertions(+)
 create mode 100644 Lab1/BMP File Format.url
 create mode 100644 Lab1/BMP formatas.docx
 create mode 100644 Lab1/BMPImage.cs
 create mode 100644 Lab1/Lab1.csproj
 create mode 100644 Lab1/Program.cs
 create mode 100644 Lab1/README.md
 create mode 100644 Labs.sln

diff --git a/Lab1/BMP File Format.url b/Lab1/BMP File Format.url
new file mode 100644
index 0000000..4691316
--- /dev/null
+++ b/Lab1/BMP File Format.url	
@@ -0,0 +1,5 @@
+[{000214A0-0000-0000-C000-000000000046}]
+Prop3=19,2
+[InternetShortcut]
+IDList=
+URL=http://www.ece.ualberta.ca/~elliott/ee552/studentAppNotes/2003_w/misc/bmp_file_format/bmp_file_format.htm
diff --git a/Lab1/BMP formatas.docx b/Lab1/BMP formatas.docx
new file mode 100644
index 0000000000000000000000000000000000000000..a86ed45349094b44b3e20f57cbce3a49d0131866
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diff --git a/Lab1/BMPImage.cs b/Lab1/BMPImage.cs
new file mode 100644
index 0000000..75a4cea
--- /dev/null
+++ b/Lab1/BMPImage.cs
@@ -0,0 +1,359 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using System.IO;
+
+namespace Lab1
+{
+    internal struct Color
+    {
+        public byte r = 0, g = 0, b = 0;
+
+        public Color(byte r, byte g, byte b)
+        {
+            this.r = r;
+            this.g = g;
+            this.b = b;
+        }
+
+        public Color(Color color)
+        {
+            this.r = color.r;
+            this.g = color.g;
+            this.b = color.b;
+        }
+
+        public override string ToString()
+        {
+            return $"Color({r}, {g}, {b})";
+        }
+    }
+
+    internal class BMPImage
+    {
+        public uint width, height;
+        public Color[] data;
+
+        public BMPImage(uint width, uint height)
+        {
+            Debug.Assert(width > 0, "Width must be at least 1");
+            Debug.Assert(height > 0, "Height must be at least 1");
+
+            this.width = width;
+            this.height = height;
+
+            this.data = new Color[width * height];
+        }
+
+        public void SetPixel(int x, int y, int r, int g, int b)
+        {
+            if (x < 0 || y < 0 || x >= width || y >= height) return;
+            data[width * y + x].r = (byte)r;
+            data[width * y + x].g = (byte)g;
+            data[width * y + x].b = (byte)b;
+        }
+
+        public Color GetPixel(int x, int y)
+        {
+            if (x < 0 || y < 0 || x >= width || y >= height) return new Color(0, 0, 0);
+            return new Color(data[width * y + x]);
+        }
+
+        public void SetPixel(int x, int y, Color color)
+        {
+            SetPixel(x, y, color.r, color.g, color.b);
+        }
+
+        public void Fill(Color color)
+        {
+            Rectangle(0, 0, (int)width, (int)height, color);
+        }
+
+        public void Rectangle(int x, int y, int width, int height, Color color)
+        {
+            for (int dy = 0; dy < height; dy++)
+            {
+                for (int dx = 0; dx < width; dx++)
+                {
+                    SetPixel(x + dx, y + dy, color);
+                }
+            }
+        }
+
+        private static void swap(ref int a, ref int b)
+        {
+            int c = a;
+            a = b;
+            b = c;
+        }
+
+        public void Line(int x1, int y1, int x2, int y2, Color color)
+        {
+            int dx = x2 - x1;
+            int dy = y2 - y1;
+
+            if (dx == 0 && dy == 0)
+            {
+                SetPixel(x1, y1, color);
+                return;
+            }
+
+            if (Math.Abs(dx) > Math.Abs(dy))
+            {
+                if (x1 > x2)
+                {
+                    swap(ref x1, ref x2);
+                    swap(ref y1, ref y2);
+                }
+
+                for (int x = x1; x <= x2; ++x)
+                {
+                    int y = dy * (x - x1) / dx + y1;
+                    SetPixel(x, y, color);
+                }
+            } else
+            {
+                if (y1 > y2)
+                {
+                    swap(ref x1, ref x2);
+                    swap(ref y1, ref y2);
+                }
+
+                for (int y = y1; y <= y2; ++y)
+                {
+                    int x = dx * (y - y1) / dy + x1;
+                    SetPixel(x, y, color);
+                }
+            }
+        }
+
+        private static void SortPointsByX(ref int x1, ref int y1, ref int x2, ref int y2, ref int x3, ref int y3)
+        {
+            if (x1 > x2)
+            {
+                swap(ref x1, ref x2);
+                swap(ref y1, ref y2);
+            }
+
+            if (x1 > x3)
+            {
+                swap(ref x1, ref x3);
+                swap(ref y1, ref y3);
+            }
+
+            if (x2 > x3)
+            {
+                swap(ref x2, ref x3);
+                swap(ref y2, ref y3);
+            }
+        }
+
+        public void Triangle(int x1, int y1, int x2, int y2, int x3, int y3, Color color)
+        {
+            SortPointsByX(ref x1, ref y1, ref x2, ref y2, ref x3, ref y3);
+
+            if (x2 - x1 == 0) return;
+            if (x3 - x1 == 0) return;
+            if (x3 - x2 == 0) return;
+            if (x3 - x1 == 0) return;
+
+            for (int x = x1; x <= x2; x++)
+            {
+                int yEdge1 = (y2 - y1) * (x - x1) / (x2 - x1) + y1;
+                int yEdge2 = (y3 - y1) * (x - x1) / (x3 - x1) + y1;
+                for (int y = Math.Min(yEdge1, yEdge2); y < Math.Max(yEdge1, yEdge2); y++)
+                {
+                    SetPixel(x, y, color);
+                }
+            }
+
+            for (int x = x2; x <= x3; x++)
+            {
+                int yEdge1 = (y3 - y2) * (x - x2) / (x3 - x2) + y2;
+                int yEdge2 = (y3 - y1) * (x - x1) / (x3 - x1) + y1;
+                for (int y = Math.Min(yEdge1, yEdge2); y < Math.Max(yEdge1, yEdge2); y++)
+                {
+                    SetPixel(x, y, color);
+                }
+            }
+        }
+
+        public void Circle(int x, int y, int radius, Color color)
+        {
+            for (int dy = -(int)radius; dy < radius; dy++)
+            {
+                for (int dx = -(int)radius; dx < radius; dx++)
+                {
+                    if (dx*dx + dy*dy < radius*radius)
+                    {
+                        SetPixel(x + dx, y + dy, color);
+                    }
+                }
+            }
+        }
+
+        private static void WriteBytes(FileStream f, params byte[] bytes)
+        {
+            f.Write(bytes);
+        }
+
+        private static void WriteUInt16(FileStream f, UInt16 number)
+        {
+            WriteBytes(f,
+                (byte)((number >> 8 * 0) & 0xFF),
+                (byte)((number >> 8 * 1) & 0xFF)
+            );
+        }
+        private static void WriteUInt32(FileStream f, UInt32 number)
+        {
+            WriteBytes(f,
+                (byte)((number >> 8 * 0) & 0xFF),
+                (byte)((number >> 8 * 1) & 0xFF),
+                (byte)((number >> 8 * 2) & 0xFF),
+                (byte)((number >> 8 * 3) & 0xFF)
+            );
+        }
+
+        private static ushort DetermineBPP(ICollection<Color> colors)
+        {
+            int count = colors.Count;
+            if (count <= 2)
+            {
+                return 1;
+            } else if (count <= 16)
+            {
+                return 4;
+            } else if (count <= 256)
+            {
+                return 8;
+            }
+            return 24;
+        }
+
+        private static uint GetScanlineSize(uint width, uint bpp)
+        {
+            return ((width * bpp + 31) / 32 * 32) / 8u;
+        }
+
+        private byte[] EncodePixelData(uint bpp, List<Color> usedColors)
+        {
+            uint scanline = GetScanlineSize(width, bpp);
+            byte[] pixelData = new byte[height * scanline];
+            if (bpp == 1)
+            {
+                for (int y = 0; y < height; y++)
+                {
+                    int idx = 0;
+                    for (int x = 0; x < width; x += 8)
+                    {
+                        byte pix1 = (byte)(usedColors.IndexOf(GetPixel(x + 0, y)) & 1);
+                        byte pix2 = (byte)(usedColors.IndexOf(GetPixel(x + 1, y)) & 1);
+                        byte pix3 = (byte)(usedColors.IndexOf(GetPixel(x + 2, y)) & 1);
+                        byte pix4 = (byte)(usedColors.IndexOf(GetPixel(x + 3, y)) & 1);
+                        byte pix5 = (byte)(usedColors.IndexOf(GetPixel(x + 4, y)) & 1);
+                        byte pix6 = (byte)(usedColors.IndexOf(GetPixel(x + 5, y)) & 1);
+                        byte pix7 = (byte)(usedColors.IndexOf(GetPixel(x + 6, y)) & 1);
+                        byte pix8 = (byte)(usedColors.IndexOf(GetPixel(x + 7, y)) & 1);
+                        pixelData[scanline * y + idx] = (byte)(pix1 << 7 | pix2 << 6 | pix3 << 5 | pix4 << 4 | pix5 << 3 | pix6 << 2 | pix7 << 1 | pix8 << 0);
+                        idx++;
+                    }
+                }
+            }
+            else if (bpp == 4)
+            {
+                for (int y = 0; y < height; y++)
+                {
+                    int idx = 0;
+                    for (int x = 0; x < width; x += 2)
+                    {
+                        byte pix1 = (byte)(usedColors.IndexOf(GetPixel(x + 0, y)) & 0xF);
+                        byte pix2 = (byte)(usedColors.IndexOf(GetPixel(x + 1, y)) & 0xF);
+                        pixelData[scanline * y + idx] = (byte)(pix1 << 4 | pix2 << 0);
+                        idx++;
+                    }
+                }
+            }
+            else if (bpp == 8)
+            {
+                for (int y = 0; y < height; y++)
+                {
+                    for (int x = 0; x < width; x++)
+                    {
+                        pixelData[scanline * y + x] = (byte)(usedColors.IndexOf(GetPixel(x, y)) & 0xFF);
+                    }
+                }
+            }
+            else if (bpp == 24)
+            {
+                for (int y = 0; y < height; y++)
+                {
+                    for (int x = 0; x < width; x++)
+                    {
+                        Color color = GetPixel(x, y);
+                        pixelData[scanline * y + 3 * x + 0] = color.b;
+                        pixelData[scanline * y + 3 * x + 1] = color.g;
+                        pixelData[scanline * y + 3 * x + 2] = color.r;
+                    }
+                }
+            }
+            else
+            {
+                throw new NotImplementedException();
+            }
+
+            return pixelData;
+        }
+
+        public void Write(string filename)
+        {
+            List<Color> usedColors = new List<Color>();
+            for (int i = 0; i < width*height; i++)
+            {
+                if (!usedColors.Contains(data[i]))
+                {
+                    usedColors.Add(data[i]);
+                }
+            }
+
+            ushort bpp = DetermineBPP(usedColors);
+            byte[] pixelData = EncodePixelData(bpp, usedColors);
+
+            using (FileStream f = new FileStream(filename, FileMode.Create, FileAccess.Write))
+            {
+                // Write header
+                WriteBytes(f, 0x42, 0x4d); // signature
+                WriteUInt32(f, 0);         // file size
+                WriteUInt32(f, 0);         // reserved
+                WriteUInt32(f, 0);         // data offset
+
+                // Write info header
+                WriteUInt32(f, 40);        // info header size, always 40
+                WriteUInt32(f, width);     // width
+                WriteUInt32(f, height);    // height
+                WriteUInt16(f, 1);         // number of planes
+                WriteUInt16(f, bpp);       // bits per pixel
+                WriteUInt32(f, 0);         // compression
+                WriteUInt32(f, 0);         // size of compressed image
+                WriteUInt32(f, 0);         // x pixel per meter
+                WriteUInt32(f, 0);         // y pixel per meter
+                WriteUInt32(f, 0);         // colors used
+                WriteUInt32(f, 0);         // important colors, 0 = all
+
+                if (bpp <= 8)
+                {
+                    foreach (Color color in usedColors)
+                    {
+                        WriteBytes(f, color.b, color.g, color.r, 0);
+                    }
+                    for (int i = 0; i < Math.Pow(2, bpp) - usedColors.Count; i++)
+                    {
+                        WriteBytes(f, 0, 0, 0, 0);
+                    }
+                }
+
+                // Write pixel data
+                f.Write(pixelData);
+            }
+        }
+    }
+}
diff --git a/Lab1/Lab1.csproj b/Lab1/Lab1.csproj
new file mode 100644
index 0000000..41f1d5a
--- /dev/null
+++ b/Lab1/Lab1.csproj
@@ -0,0 +1,8 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>Exe</OutputType>
+    <TargetFramework>net6.0</TargetFramework>
+  </PropertyGroup>
+
+</Project>
diff --git a/Lab1/Program.cs b/Lab1/Program.cs
new file mode 100644
index 0000000..ea2830b
--- /dev/null
+++ b/Lab1/Program.cs
@@ -0,0 +1,138 @@
+using System;
+using System.Collections.Generic;
+using System.IO;
+
+namespace Lab1
+{
+    class Program
+    {
+        // O(n^5)
+        public static double T1(int[] n, int size)
+        {
+            if (size >= 1)
+            {
+                int sum = 0;
+                for (int i = 0; i < Math.Pow(size, 5); i++)
+                {
+                    sum += i;
+                }
+                return 2 * T1(n, size / 9) + sum;
+            }
+            return 0;
+        }
+
+        public static double T1(int[] n)
+        {
+            return T1(n, n.Length);
+        }
+
+        // O(n)
+        public static double T2(int[] n, int size)
+        {
+            if (size >= 1)
+            {
+                int sum = 0;
+                for (int i = 0; i < size; i++)
+                {
+                    sum += i;
+                }
+                return T2(n, size / 6) + T2(n, size / 7) + sum;
+            }
+            return 0;
+        }
+
+        public static double T2(int[] n)
+        {
+            return T2(n, n.Length);
+        }
+
+        // O(n^2)
+        public static double T3(int[] n, int size)
+        {
+            if (size >= 1)
+            {
+                int sum = 0;
+                for (int i = 0; i < size; i++)
+                {
+                    sum += i;
+                }
+                return T3(n, size - 8) + T3(n, size - 6) + sum;
+            }
+            return 0;
+        }
+
+        public static double T3(int[] n)
+        {
+            return T3(n, n.Length);
+        }
+
+        // O(log4(n))
+        public static void TrianglesRecursive(BMPImage image, int x, int y, uint width, uint height)
+        {
+            if (width <= 3 || height <= 3) return;
+
+            image.Triangle(
+                x + (int)(width / 3 * 1  ), (y + (int)height / 3 * 2),
+                x + (int)(width / 3 * 2  ), (y + (int)height / 3 * 2),
+                x + (int)(width / 3 * 1.5), (y + (int)height / 3 * 1),
+                new Color(0, 0, 0)
+            );
+
+            TrianglesRecursive(
+                image, x, y, width/3, height/3
+            );
+            TrianglesRecursive(
+                image, x + (int)width/3*2, y, width / 3, height / 3
+            );
+            TrianglesRecursive(
+                image, x, y + (int)height/3*2, width / 3, height / 3
+            );
+            TrianglesRecursive(
+                image, x + (int)width / 3 * 2, y + (int)height / 3 * 2, width / 3, height / 3
+            );
+        }
+
+        public static void Triangles()
+        {
+            BMPImage image = new BMPImage(1000, 1000);
+            image.Fill(new Color(255, 255, 255));
+            TrianglesRecursive(image, 0, 0, image.width, image.height);
+            image.Write("result.bmp");
+        }
+
+        public static double TestFunc(Func<int[], double> T, uint n)
+        {
+            int[] data = new int[n];
+            for (int i = 0; i < n; i++)
+            {
+                data[i] = i;
+            }
+
+            var before = DateTime.Now;
+            T(data);
+            var duration = DateTime.Now - before;
+            return duration.TotalSeconds;
+        }
+
+        static void Main()
+        {
+            // T1(10) => 0.0056552
+            // T1(20) => 0.0699722
+            // T1(40) => 2.1500858
+            // T1(50) => 6.4564238
+
+            // T2(100)           => 0.0039419
+            // T2(1_000_000)     => 0.0048064
+            // T2(250_000_000)   => 0.3011757
+            // T2(500_000_000)   => 0.6046134
+            // T2(1_000_000_000) => 1.1902643
+
+            // T3(100) => 0.0041945
+            // T3(150) => 0.0759872
+            // T3(180) => 1.4428123
+            // T3(190) => 3.9067703
+
+            //Triangles();
+        }
+    }
+}
diff --git a/Lab1/README.md b/Lab1/README.md
new file mode 100644
index 0000000..640a70d
--- /dev/null
+++ b/Lab1/README.md
@@ -0,0 +1,34 @@
+# Lab1
+
+## 1 užduotis
+Kiekvienai rekurentinei lygčiai (gautai atlikus užduoties pasirinkimo testą):
+
+* Realizuoti metodą, kuris atitiktų pateiktos rekurentinės lygties sudėtingumą, t. y.
+	programinio kodo rekursinių iškvietimų ir kiekvieno iškvietimo metu atliekamų veiksmų
+	priklausomybę nuo duomenų. Metodas per parametrus turi priimti masyvą, kurio duomenų kiekis
+	yra rekurentinės lygties kintamasis n (arba masyvą ir indeksų rėžius, kurie atitinkamai
+	nurodo masyvo nagrinėjamų elementų indeksus atitinkamame iškvietime) (2 balai).
+
+* Kiekvienam realizuotam metodui atlikti programinio kodo analizę, parodant jog jis atitinka
+	pateiktą rekurentinę lygtį (1 balas).
+
+* Išspręskite rekurentinę lygtį ir apskaičiuokite jos asimptotinį sudėtingumą (taikoma
+	pagrindinė teorema, medžių ar kitas sprendimo metodas) (1 balas)
+
+* Atlikti eksperimentinį tyrimą (našumo testus: vykdymo laiką ir veiksmų skaičių) ir patikrinkite
+	ar apskaičiuotas metodo asimptotinis sudėtingumas atitinka eksperimentinius rezultatus (1 balas).
+
+## 2 užduoties dalis
+Naudojant rekursiją ir nenaudojant grafinių bibliotekų sudaryti nurodytos struktūros
+BMP formato ( gautą atlikus užduoties pasirinkimo testą):
+
+* Programos rezultatas BMP formato bylos demonstruojančios programos rekursijas. (3 balai)
+
+* Eksperimentiškai nustatykite darbo laiko ir veiksmų skaičiaus priklausomybę nuo generuojamo
+	paveikslėlio dydžio (taškų skaičiaus). Gautus rezultatus atvaizduokite grafikais.
+	Grafiką turi sudaryti nemažiau kaip 5 taškai ir paveikslėlio taškų skaičius turi didėti
+	proporcingai (kartais). (1 balas)
+
+* Analitiškai įvertinkite procedūros, kuri generuoja paveikslėlį, veiksmų skaičių sudarydami
+	rekurentinę lygtį ir ją išspręskite. Gautas rezultatas turi patvirtinti eksperimentinius
+	rezultatus (našumo testus: vykdymo laiką ir veiksmų skaičių). (1 balas)
diff --git a/Labs.sln b/Labs.sln
new file mode 100644
index 0000000..f7c0701
--- /dev/null
+++ b/Labs.sln
@@ -0,0 +1,25 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 17
+VisualStudioVersion = 17.1.32328.378
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "Lab1", "Lab1\Lab1.csproj", "{497767A1-722A-4F48-86E5-C2AE6E0B9C9A}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{497767A1-722A-4F48-86E5-C2AE6E0B9C9A}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{497767A1-722A-4F48-86E5-C2AE6E0B9C9A}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{497767A1-722A-4F48-86E5-C2AE6E0B9C9A}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{497767A1-722A-4F48-86E5-C2AE6E0B9C9A}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {E792B7A8-715B-485D-AB55-1DC957C988CF}
+	EndGlobalSection
+EndGlobal