TriForce

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TriForce

Team Members

  1. David Ferri, Sudoku Solver
  2. Vincent Terpstra, Julia Sets
  3. Raymond Kiguru, EasyBMP

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Progress

Assignment 1: Sudoku Solver

Sudoku Solver Profiling

Source code from: https://www.geeksforgeeks.org/sudoku-backtracking-7/

Original Code: 

// A Backtracking program  in C++ to solve Sudoku problem 
#include <stdio.h> 
 
// UNASSIGNED is used for empty cells in sudoku grid 
#define UNASSIGNED 0 
 
// N is used for the size of Sudoku grid. Size will be NxN 
#define N 9 
 
// This function finds an entry in grid that is still unassigned 
bool FindUnassignedLocation(int grid[N][N], int &row, int &col); 
 
// Checks whether it will be legal to assign num to the given row, col 
bool isSafe(int grid[N][N], int row, int col, int num); 
 
/* Takes a partially filled-in grid and attempts to assign values to 
  all unassigned locations in such a way to meet the requirements 
  for Sudoku solution (non-duplication across rows, columns, and boxes) */
bool SolveSudoku(int grid[N][N]) 
{ 
   int row, col; 
 
   // If there is no unassigned location, we are done 
   if (!FindUnassignedLocation(grid, row, col)) 
      return true; // success! 
 
   // consider digits 1 to 9 
   for (int num = 1; num <= 9; num++) 
   { 
       // if looks promising 
       if (isSafe(grid, row, col, num)) 
       { 
           // make tentative assignment 
           grid[row][col] = num; 
 
           // return, if success, yay! 
           if (SolveSudoku(grid)) 
               return true; 
 
           // failure, unmake & try again 
           grid[row][col] = UNASSIGNED; 
       } 
   } 
   return false; // this triggers backtracking 
} 
 
/* Searches the grid to find an entry that is still unassigned. If 
   found, the reference parameters row, col will be set the location 
   that is unassigned, and true is returned. If no unassigned entries 
   remain, false is returned. */
bool FindUnassignedLocation(int grid[N][N], int &row, int &col) 
{ 
   for (row = 0; row < N; row++) 
       for (col = 0; col < N; col++) 
           if (grid[row][col] == UNASSIGNED) 
               return true; 
   return false; 
} 
 
/* Returns a boolean which indicates whether an assigned entry 
  in the specified row matches the given number. */
bool UsedInRow(int grid[N][N], int row, int num) 
{ 
   for (int col = 0; col < N; col++) 
       if (grid[row][col] == num) 
           return true; 
   return false; 
} 
 
/* Returns a boolean which indicates whether an assigned entry 
  in the specified column matches the given number. */
bool UsedInCol(int grid[N][N], int col, int num) 
{ 
   for (int row = 0; row < N; row++) 
       if (grid[row][col] == num) 
           return true; 
   return false; 
} 
 
/* Returns a boolean which indicates whether an assigned entry 
  within the specified 3x3 box matches the given number. */
bool UsedInBox(int grid[N][N], int boxStartRow, int boxStartCol, int num) 
{ 
   for (int row = 0; row < 3; row++) 
       for (int col = 0; col < 3; col++) 
           if (grid[row+boxStartRow][col+boxStartCol] == num) 
               return true; 
   return false; 
} 
 
/* Returns a boolean which indicates whether it will be legal to assign 
  num to the given row,col location. */
bool isSafe(int grid[N][N], int row, int col, int num) 
{ 
   /* Check if 'num' is not already placed in current row, 
      current column and current 3x3 box */
   return !UsedInRow(grid, row, num) && 
          !UsedInCol(grid, col, num) && 
          !UsedInBox(grid, row - row%3 , col - col%3, num)&& 
           grid[row][col]==UNASSIGNED; 
} 
 
/* A utility function to print grid  */
void printGrid(int grid[N][N]) 
{ 
   for (int row = 0; row < N; row++) 
   { 
      for (int col = 0; col < N; col++) 
            printf("%2d", grid[row][col]); 
       printf("\n"); 
   } 
} 
 
/* Driver Program to test above functions */
int main() 
{ 
   // 0 means unassigned cells 
   int grid[N][N] = {{3, 0, 6, 5, 0, 8, 4, 0, 0}, 
                     {5, 2, 0, 0, 0, 0, 0, 0, 0}, 
                     {0, 8, 7, 0, 0, 0, 0, 3, 1}, 
                     {0, 0, 3, 0, 1, 0, 0, 8, 0}, 
                     {9, 0, 0, 8, 6, 3, 0, 0, 5}, 
                     {0, 5, 0, 0, 9, 0, 6, 0, 0}, 
                     {1, 3, 0, 0, 0, 0, 2, 5, 0}, 
                     {0, 0, 0, 0, 0, 0, 0, 7, 4}, 
                     {0, 0, 5, 2, 0, 6, 3, 0, 0}}; 
   if (SolveSudoku(grid) == true) 
         printGrid(grid); 
   else
        printf("No solution exists"); 
 
   return 0; 
} 



$ g++ sudokuC.cpp  -std=c++0x -o Sudoku
$ ./Sudoku
3 1 6 5 7 8 4 9 2
5 2 9 1 3 4 7 6 8
4 8 7 6 2 9 5 3 1
2 6 3 4 1 5 9 8 7
9 7 4 8 6 3 1 2 5
8 5 1 7 9 2 6 4 3
1 3 8 9 4 7 2 5 6
6 9 2 3 5 1 8 7 4
7 4 5 2 8 6 3 1 9
$ gprof -p -b ./Sudoku gmon.out > 9x9.flt



// A Backtracking program  in C++ to solve Sudoku problem 
#include <stdio.h> 
 
// UNASSIGNED is used for empty cells in sudoku grid 
#define UNASSIGNED 0 
 
// N is used for the size of Sudoku grid. Size will be NxN 
#define N 16 
 
// This function finds an entry in grid that is still unassigned 
bool FindUnassignedLocation(int grid[N][N], int &row, int &col); 
 
// Checks whether it will be legal to assign num to the given row, col 
bool isSafe(int grid[N][N], int row, int col, int num); 
 
/* Takes a partially filled-in grid and attempts to assign values to 
 all unassigned locations in such a way to meet the requirements 
 for Sudoku solution (non-duplication across rows, columns, and boxes) */
bool SolveSudoku(int grid[N][N]) 
{ 
   int row, col; 
 
   // If there is no unassigned location, we are done 
   if (!FindUnassignedLocation(grid, row, col)) 
      return true; // success! 
 
   // consider digits 1 to 16
   for (int num = 1; num <= 16; num++) 
   { 
       // if looks promising 
       if (isSafe(grid, row, col, num)) 
       { 
           // make tentative assignment 
           grid[row][col] = num; 
 
           // return, if success, yay! 
           if (SolveSudoku(grid)) 
               return true; 
 
           // failure, unmake & try again 
           grid[row][col] = UNASSIGNED; 
       } 
   } 
   return false; // this triggers backtracking 
} 
 
/* Searches the grid to find an entry that is still unassigned. If 
  found, the reference parameters row, col will be set the location 
  that is unassigned, and true is returned. If no unassigned entries 
  remain, false is returned. */
bool FindUnassignedLocation(int grid[N][N], int &row, int &col) 
{ 
   for (row = 0; row < N; row++) 
       for (col = 0; col < N; col++) 
           if (grid[row][col] == UNASSIGNED) 
               return true; 
   return false; 
} 
 
/* Returns a boolean which indicates whether an assigned entry 
  in the specified row matches the given number. */
bool UsedInRow(int grid[N][N], int row, int num) 
{ 
   for (int col = 0; col < N; col++) 
       if (grid[row][col] == num) 
           return true; 
   return false; 
} 
 
/* Returns a boolean which indicates whether an assigned entry 
  in the specified column matches the given number. */
bool UsedInCol(int grid[N][N], int col, int num) 
{ 
   for (int row = 0; row < N; row++) 
       if (grid[row][col] == num) 
           return true; 
   return false; 
} 
 
/* Returns a boolean which indicates whether an assigned entry 
   within the specified 4x4 box matches the given number. */
 bool UsedInBox(int grid[N][N], int boxStartRow, int boxStartCol, int num) 
 { 
   for (int row = 0; row < 4; row++) 
       for (int col = 0; col < 4; col++) 
           if (grid[row+boxStartRow][col+boxStartCol] == num) 
               return true; 
   return false; 
 } 
 
/* Returns a boolean which indicates whether it will be legal to assign 
   num to the given row,col location. */
   bool isSafe(int grid[N][N], int row, int col, int num) 
{ 
   /* Check if 'num' is not already placed in current row, 
      current column and current 4x4 box */
   return !UsedInRow(grid, row, num) &&
           !UsedInCol(grid, col, num) &&
           !UsedInBox(grid, row - row%4 , col - col%4, num)&& 
           grid[row][col]==UNASSIGNED; 
} 
 
/* A utility function to print grid  */
void printGrid(int grid[N][N]) 
{ 
   for (int row = 0; row < N; row++) 
   { 
      for (int col = 0; col < N; col++) 
            printf("%2d", grid[row][col]); 
       printf("\n"); 
   } 
} 
 
/* Driver Program to test above functions */
int main() 
{ 
   //https://puzzlemadness.co.uk/16by16giantsudoku/
   // 0 means unassigned cells 
   int grid[N][N] = {{0,  8,   0,  0,  0,  0,  0,  3,  0,  0,  0, 10,  9,  7, 11, 0}, 
                     {0,  9,  15, 13,  0, 10,  0,  0,  2,  6,  8, 16,  0,  0,  0, 0}, 				  
                     {0,  0,  16,  0, 15,  0,  8,  0,  9,  0,  0,  0,  6,  0,  2, 0}, 				  
                     {1,  0,   2,  0,  9, 11,  4,  6, 15,  3,  5,  7,  0,  0, 12, 0}, 					  
                     {16, 6,   4,  0,  5,  2,  0,  0,  1,  0,  0,  0, 11,  0,  0, 12},						  
                     {5,  11,  0,  0,  0,  3,  0, 15,  0, 16,  0, 13,  0,  1,  0, 8}, 					  
                     {0,  0,   3,  0,  0,  6, 11, 14,  0,  5,  7,  0,  0,  9,  0, 0}, 				  
                     {0,  0,   0, 14,  8,  0, 10,  0,  0, 11, 12,  0,  0,  0,  0, 0},				  
                     {0,  7,  13,  0,  0,  0,  0, 12,  0,  8,  9,  0,  0,  0,  3, 0},				  
                     {0,  0,  11,  9,  0,  7,  0,  0,  0,  0,  0, 12,  0,  8, 16, 5},
                     {0,  0,  10,  0, 11, 13,  0,  0,  0,  0,  0,  3, 12,  0,  6, 0},				  
                     {0,  5,   0,  0, 10, 15,  0,  1,  7,  2,  0,  0, 14, 11,  0, 0},				  
                     {0,  0,   5,  0,  0, 12, 14,  0,  0, 10,  0,  0, 15,  0,  0, 4},					  
                     {9,  0,  14,  6,  0,  0,  1,  0, 16,  0,  2,  0,  3,  0, 13, 0},					  
                     {8,  13,  0,  4,  0,  0,  0,  0, 12,  7,  3,  0,  0,  6,  0, 0},				  
                     {0,  16, 12,  0,  0,  5,  0,  9,  0, 13, 14,  4,  1,  0,  0, 0}}; 
   if (SolveSudoku(grid) == true) 
         printGrid(grid); 
   else
        printf("No solution exists"); 
 
   return 0; 
}

25x25 Puzzle: 

   int grid[N][N] = {{1,  0,   4,  0, 25,  0, 19,  0,  0,  10,  21, 8,  0,  14, 0,  6,  12,   9,  0,  0,  0,  0,  0,  0,  5}, 
                     {5,  0,  19, 23, 24,  0, 22,  12,  0,  0,  16, 6,  0,  20,  0,  18,  0,   25,  14,  13,  10, 11,  0,  1,  15}, 
                     {0,  0,   0,  0,  0,  0,  21,  5,  0,  20,  11,  10,  0,  1,  0,  4,  8,   24,  23,  15,  18,  0,  16,  22,  19},				  
                     {0,  7,  21,  8, 18,  0,  0,  0, 11,  0,  5,  0,  0,  24, 0,  0,  0,   17,  22,  1,  9,  6,  25,  0,  0}, 					  
                     {0, 13,  15,  0, 22, 14,  0,  18,  0,  16,  0,  0, 0,  4,  0,  0,  0,   19,  0,  0,  0,  24,  20,  21,  17},				  
                     {12, 0,  11,  0,  6,  0,  0, 0,  0, 15,  0, 0,  0,  0,  21,  25,  19,   0,  4,  0,  22,  14,  0,  20,  0},				  
                     {8,  0,   0, 21,  0, 16, 0, 0,  0,  2,  0,  3,  0,  0,  0,  0,  17,   23,  18,  22,  0,  0,  0,  24,  6},  
                     {4,  0,  14, 18,  7,  9, 0,  22,  21, 19, 0,  0,  0,  2,  0,  5,  0,   0,  0,  6,  16,  15,  0,  11,  12},				  
                     {22, 0,  24,  0, 23,  0,  0, 11,  0,  7,  0,  0,  4,  0,  14,  0,  2,   12,  0,  8,  5,  19,  0,  25,  9},
		      {20, 0,   0,  0,  5,  0,  0,  0,  0,  17,  9, 0,  12,  18, 0,  1,  0,   0,  7,  24,  0,  0,  0,  13,  4},					  
 		      {13, 0,   0,  5,  0,  2,  23,  14,  4,  18,  22,  0, 17,  0,  0,  20,  0,   1,  9,  21,  12,  0,  0,  8,  11},					  
 		      {14, 23,  0, 24,  0,  0,  0,  0,  0,  0,  0,  0, 20, 25,  0,  3,  4,   13,  0,  11,  21,  9,  5,  18,  22},			  
 		      {7,  0,   0, 11, 17, 20, 24,  0,  0, 0,  3,  4, 1,  12,  0,  0,  6,   14,  0,  5,  25,  13,  0,  0,  0},	  
 		      {0,  0,  16,  9,  0, 17,  11,  7, 10,  25,  0,  0,  0,  13, 6,  0,  0,   18,  0,  0,  19,  4,  0,  0,  20},  
 		      {6,  15,  0, 19,  4, 13,  0,  0, 5,  0,  18,  11,  0,  0,  9,  8,  22,   16,  25,  10,  7,  0,  0,  0,  0},  
                      {0,  0,   0,  2,  0,  0, 10, 19,  3,  0,  1,  0,  22,  9,  4,  11,  15,   0,  20,  0,  0,  8,  23,  0,  25}, 				       
 		      {0,  24,  8, 13,  1,  0, 0,  4,  20, 0, 17,  14,  0,  0,  18,  0,  16,   22,  5,  0,  11,  0,  10,  0,  0}, 
                      {23, 10,  0,  0,  0,  0,  0, 0,  18,  0,  6,  0,  16,  0,  0,  17,  1,   0,  13,  0,  0,  3,  19,  12,  0}, 
 		      {25,  5,  0, 14, 11,  0,  17,  0,  8,  24,  13, 0,  19,  23, 15,  9,  0,   0,  12,  0,  20,  0,  22,  0,  7},					  
 		      {0,   0, 17,  4,  0, 22,  15,  0,  23,  11,  12,  25, 0,  0,  0,  0,  18,   8,  0,  7,  0,  0,  14,  0,  13},				  
 		      {19,  6, 23, 22,  8,  0,  0,  1,  25,  4,  14,  2, 0, 3,  7,  13,  10,   11,  16,  0,  0,  0,  0,  0,  0},				  
 		      {0,   4,  0, 17,  0,  3, 0,  24,  0, 8,  20,  23, 11,  10,  25,  22,  0,   0,  0,  12,  13,  2,  18,  6,  0},					  
 		      {0,   0,  7, 16,  0,  0,  6,  17, 2,  21,  0,  18,  0,  0, 0,  19,  0,   0,  8,  0,  0,  0,  0,  4,  0},					  
 		      {18,  9, 25,  1,  2, 11,  0,  0, 13,  22,  4,  0,  21,  0,  5,  0,  23,   7,  0,  0,  15,  0,  3,  0,  8},						  
 		      {0,  21, 10,  0,  0, 12,  0,  20,  16, 0, 19,  0,  0,  0,  0,  15,  14,   4,  2,  18,  23,  25,  11,  7,  0}};


For 9x9 Sudoku Puzzle (3x3 squares) 

Flat profile:
Each sample counts as 0.01 seconds.
 no time accumulated

  %   cumulative   self              self     total           
 time   seconds   seconds    calls  Ts/call  Ts/call  name    
  0.00      0.00     0.00     6732     0.00     0.00  isSafe(int (*) [9], int, int, int)
  0.00      0.00     0.00     6732     0.00     0.00  UsedInRow(int (*) [9], int, int)
  0.00      0.00     0.00     2185     0.00     0.00  UsedInCol(int (*) [9], int, int)
  0.00      0.00     0.00     1078     0.00     0.00  UsedInBox(int (*) [9], int, int, int)
  0.00      0.00     0.00      770     0.00     0.00  FindUnassignedLocation(int (*) [9], int&, int&)
  0.00      0.00     0.00        1     0.00     0.00  SolveSudoku(int (*) [9])
  0.00      0.00     0.00        1     0.00     0.00  printGrid(int (*) [9])

For 16x16 Sudoku Puzzle (4x4 squares) Puzzle from: [1] 

Flat profile:
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
 39.04     15.00    15.00 28071636     0.00     0.00  FindUnassignedLocation(int (*) [16], int&, int&)
 36.19     28.90    13.90 449145092     0.00     0.00  UsedInRow(int (*) [16], int, int)
 10.60     32.97     4.07 120354547     0.00     0.00  UsedInCol(int (*) [16], int, int)
  4.97     34.88     1.91 41212484     0.00     0.00  UsedInBox(int (*) [16], int, int, int)
  4.59     36.65     1.76        1     1.76    38.39  SolveSudoku(int (*) [16])
  4.55     38.39     1.75 449145092     0.00     0.00  isSafe(int (*) [16], int, int, int)
  0.01     38.40     0.01                             frame_dummy
  0.00     38.40     0.00        1     0.00     0.00  printGrid(int (*) [16])

For 25x25 Sudoku Puzzle (5x5 squares) Puzzle from: http://www.sudoku-download.net/sudoku_25x25.php 

Flat profile:
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls  Ks/call  Ks/call  name    
 48.76   1052.18  1052.18 425478951     0.00     0.00  UsedInRow(int (*) [25], int, int)
 25.24   1596.81   544.63 876012758     0.00     0.00  FindUnassignedLocation(int (*) [25], int&, int&)
 12.48   1866.03   269.21 590817023     0.00     0.00  UsedInCol(int (*) [25], int, int)
  4.83   1970.24   104.21 425478951     0.00     0.00  isSafe(int (*) [25], int, int, int)
  4.79   2073.51   103.27        1     0.10     2.17  SolveSudoku(int (*) [25])
  4.35   2167.39    93.89 1355081265     0.00     0.00  UsedInBox(int (*) [25], int, int, int)
  0.01   2167.56     0.17                             frame_dummy
  0.00   2167.56     0.00        1     0.00     0.00  printGrid(int (*) [25])

Assignment 1: EasyBMP

EasyBMP Bitmap image library (Sample Program: Image to black and white renderer)

Library: http://easybmp.sourceforge.net/

Sample code: 
/**/
#include "EasyBMP.h"

using namespace std;
int main(int argc, char* argv[]) {
        // Create a new Bitmap image with EasyBMP
        BMP Background;
        Background.ReadFromFile(argv[1]);
        BMP Output;
        int picWidth = Background.TellWidth();
        int picHeight = Background.TellHeight();
        Output.SetSize(Background.TellWidth(), Background.TellHeight());
        Output.SetBitDepth(1);
        for (int i = 1; i < picWidth - 1; ++i) {
                for (int j = 1; j < picHeight - 1; ++j) {
                        int col = (Background(i, j)->Blue + Background(i, j)->Green + 10 * Background(i, j)->Red) / 12;
                        if (col > 127) {
                                Output(i, j)->Red = 255;
                                Output(i, j)->Blue = 255;
                                Output(i, j)->Green = 255;
                        }
                        else {
                               Output(i, j)->Red = 0;
                               Output(i, j)->Blue = 0;
                               Output(i, j)->Green = 0;
                        }
                }
        }
        Output.WriteToFile(argv[2]);
        return 0;
}
/**/

The program was compiled using the following commands: 

g++ -c -pg -g BW.cpp EasyBMP.cpp
g++ -pg BW.o EasyBMP.o -o BW
rm *.o

Attempted to run the program with a number of files (8K resolution):

Cabin small.jpg Cabin2 small.jpg

Flat profile (Cabin): 
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total
 time   seconds   seconds    calls   s/call   s/call  name
 31.38      1.74     1.74 33177600     0.00     0.00  BMP::FindClosestColor(RGBApixel&)
 23.52      3.04     1.30 198921624    0.00     0.00  BMP::operator()(int, int)
  9.95      3.59     0.55        2     0.28     0.28  BMP::SetSize(int, int)
  7.60      4.01     0.42 41663472     0.00     0.00  BMP::GetColor(int)
  6.87      4.39     0.38                             main
  5.43      4.69     0.30 74841076     0.00     0.00  IntPow(int, int)
  3.62      4.89     0.20 74841072     0.00     0.00  BMP::TellNumberOfColors()
  3.35      5.07     0.19     4320     0.00     0.00  BMP::Write1bitRow(unsigned char*, int, int)
  2.53      5.21     0.14 124990416    0.00     0.00  IntSquare(int)
  2.17      5.33     0.12     4320     0.00     0.00  BMP::Read24bitRow(unsigned char*, int, int)
  1.63      5.42     0.09        2     0.05     0.05  BMP::~BMP()
  0.90      5.47     0.05                             GetEasyBMPwarningState()
  0.72      5.51     0.04        1     0.04     0.04  _GLOBAL__sub_I_EasyBMPwarnings
  0.18      5.52     0.01        2     0.01     0.01  BMP::TellWidth()
  0.18      5.53     0.01        1     0.01     2.99  BMP::WriteToFile(char const*)
  0.00      5.53     0.00       16     0.00     0.00  SafeFread(char*, int, int, _IO_FILE*)
  0.00      5.53     0.00        6     0.00     0.00  IsBigEndian()
  0.00      5.53     0.00        2     0.00     0.00  EasyBMPcheckDataSize()
  0.00      5.53     0.00        2     0.00     0.00  BMP::TellHeight()
  0.00      5.53     0.00        2     0.00     0.00  BMP::SetBitDepth(int)
  0.00      5.53     0.00        2     0.00     0.00  BMP::BMP()
  0.00      5.53     0.00        2     0.00     0.00  BMFH::BMFH()
  0.00      5.53     0.00        2     0.00     0.00  BMIH::BMIH()
  0.00      5.53     0.00        1     0.00     0.00  _GLOBAL__sub_I_main
  0.00      5.53     0.00        1     0.00     0.00  __static_initialization_and_destruction_0(int, int)
  0.00      5.53     0.00        1     0.00     0.00  __static_initialization_and_destruction_0(int, int)
  0.00      5.53     0.00        1     0.00     0.40  BMP::ReadFromFile(char const*)
  0.00      5.53     0.00        1     0.00     0.00  BMP::CreateStandardColorTable()
Flat profile (Lake): 
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total
 time   seconds   seconds    calls   s/call   s/call  name
 30.60      1.71     1.71 33177600     0.00     0.00  BMP::FindClosestColor(RGBApixel&)
 21.12      2.89     1.18 198921624    0.00     0.00  BMP::operator()(int, int)
 10.20      3.46     0.57        2     0.29     0.29  BMP::SetSize(int, int)
  8.59      3.94     0.48                             main
  6.26      4.29     0.35 76982189     0.00     0.00  IntPow(int, int)
  6.08      4.63     0.34 43804585     0.00     0.00  BMP::GetColor(int)
  5.55      4.94     0.31 76982185     0.00     0.00  BMP::TellNumberOfColors()
  3.76      5.15     0.21     4320     0.00     0.00  BMP::Write1bitRow(unsigned char*, int, int)
  3.76      5.36     0.21 131413755    0.00     0.00  IntSquare(int)
  2.15      5.48     0.12     4320     0.00     0.00  BMP::Read24bitRow(unsigned char*, int, int)
  1.07      5.54     0.06        2     0.03     0.03  BMP::~BMP()
  0.54      5.57     0.03                             GetEasyBMPwarningState()
  0.36      5.59     0.02        1     0.02     0.02  _GLOBAL__sub_I_EasyBMPwarnings
  0.00      5.59     0.00       16     0.00     0.00  SafeFread(char*, int, int, _IO_FILE*)
  0.00      5.59     0.00        6     0.00     0.00  IsBigEndian()
  0.00      5.59     0.00        2     0.00     0.00  EasyBMPcheckDataSize()
  0.00      5.59     0.00        2     0.00     0.00  BMP::TellHeight()
  0.00      5.59     0.00        2     0.00     0.00  BMP::SetBitDepth(int)
  0.00      5.59     0.00        2     0.00     0.00  BMP::TellWidth()
  0.00      5.59     0.00        2     0.00     0.00  BMP::BMP()
  0.00      5.59     0.00        2     0.00     0.00  BMFH::BMFH()
  0.00      5.59     0.00        2     0.00     0.00  BMIH::BMIH()
  0.00      5.59     0.00        1     0.00     0.00  _GLOBAL__sub_I_main
  0.00      5.59     0.00        1     0.00     0.00  __static_initialization_and_destruction_0(int, int)
  0.00      5.59     0.00        1     0.00     0.00  __static_initialization_and_destruction_0(int, int)
  0.00      5.59     0.00        1     0.00     3.13  BMP::WriteToFile(char const*)
  0.00      5.59     0.00        1     0.00     0.41  BMP::ReadFromFile(char const*)
  0.00      5.59     0.00        1     0.00     0.00  BMP::CreateStandardColorTable()

Assignment 1: Julia Set

This portion of the assignment focuses on Julia sets with the quadratic formula: 

 fc(z) = z^2 + c;
 Where c and z are complex numbers

Psuedo code 

 for(Pixel pix in image){
     pix.color = colorFunction(escapeValue(pix.loc, julia));
 }

 escapeValue(Complex loc, Complex julia){
     int cycles = 0;
     while(|loc| <=2 && ++cycles < MAXCYCLES){
        loc = loc * loc + julia;
     }
     return cycles;
 }
Julia.cpp 
 /**
  * Julia.cpp
  * Vincent Terpstra
  * Feb 18 / 2019
  * Functions to display a Mandlebrot set
  */

 #include <iostream>
 #include <math.h>
 #include "Bitmap.h"

 #define MAXCYCLES 1000
 #define ITER 1
 #define PI 3.14159

 void calcJulia(int* array, int width, int height, float jR, float jI);
 void createBMP(int* array, int width, int height);

 int main(int size, const char ** args) {
     int height = (size > 1) ? atoi(args[1]) : 1000;
     int width = height / 2 * 3;

     int * array = new int[height * width];
     float jI = -0.4f;
     float jR =  0.6f;
     float angle = 2.0f / ITER * PI;
     float cosA = cos(angle);
     float sinA = sin(angle);
     for(int i = 0; i < ITER; i++){
         calcJulia(array, width, height, jI, jR);
         createBMP(array, width, height);
 
         //rotate the Julia point
         float tmp = jI;
         jI = cosA * jI - sinA * jR;
         jR = cosA * jR + sinA * tmp;
     }
 
     delete[] array;
     return 0;
 }
 /**
  * calcDepth
  *      finds the escape value of the Julia set
  *      inputs sR, sI: starting position on the map
  *          jR, jI: values of the julia set
  *      exits when |s| > 2 or reached MAXCYCLES
  *      return the 
  */
 int calcDepth(float sR, float sI, const float jR, const float jI){
     int cycle = 0;
     while(sR * sR + sI * sI <= 4 && ++cycle < MAXCYCLES){
         // s(next) = s * s + j
         float tmp = sR;
         sR = sR * sR - sI * sI + jR;
         sI = 2 * tmp * sI + jI;
     }
     return cycle;
 }

 /**
  * calcJulia
  *  Function to calculate the values from (-1.5, 1.5),(-1, 1) in the Julia set
  *      saves the values onto the array
  */
 void calcJulia(int * array, int width, int height, const float jR, const float jI){
   float delta = 2 / (float)height;
   float x, y = -1;
   for(int i = 0; i < height; i++){
       x = -1.5f;
       for(int j = 0; j < width; j++){
           *array++ = calcDepth(x, y, jR, jI);
           x+=delta;
       }
       y += delta;
   }
 }

 struct Pix {
   float val;
   int r, g, b;
   Pix(float val, int r, int g, int b) : 
       val(val), r(r), g(g), b(b) {}
 };

 bool lerp(float clr, Pix& first, Pix& second, Bitmap & map);

 /**
  * createBMP
  *  maps the values in the array to a .bmp file
  *  linear interpolates between color values
  */
 void createBMP(int * array, int width, int height){
   static int idx = 0;
   char name[] = "julia000.bmp";
       name[5] = (idx / 100) + '0';
       name[6] = ((idx / 10) % 10) + '0';
       name[7] = (idx % 10) + '0';
   Bitmap map (name, width, height);
   //idx++;
   const int pix = width * height;
   struct Pix 
       clr0(0, 20, 20, 30),
       clr1(10, 20, 10, 100),
       clr2(180, 20, 170, 205), 
       clr3(MAXCYCLES, 0, 0, 0);
   const int * pMax = array + width * height;
   while(array < pMax){
       float clr = *array++;
       bool draw = 
           lerp(clr, clr0, clr1, map) || 
           lerp(clr, clr1, clr2, map) || 
           lerp(clr, clr2, clr3, map);
   }
 }

 /**
  * Function to linearly interpolate color values and draw to the Bitmap
  */
 bool lerp(float clr, Pix& first, Pix& second, Bitmap & map){
   if(clr <= second.val){
       float diff = (clr - first.val) / (second.val - first.val);
       map << first.b + diff * (second.b - first.b);
       map << first.g + diff * (second.g - first.g);
       map << first.r + diff * (second.r - first.r);
       return true;
   }
   return false;
 }

To view the full c++ code github link

This code is tested using the parameters 

 Range R(-1.5, 1.5) I(-1, 1)
 Image height(1000) width(1500)
 MAXCYCLES 1000
 Julia values = .72 * e(i θ): θ[0, 2π] : 100 intervals

 Flat profile:
 Each sample counts as 0.01 seconds.
   %   cumulative   self              self     total           
  time   seconds   seconds    calls  ms/call  ms/call  name    
  91.82     80.04    80.04                             calcJulia(int*, int, int, float, float)
   2.28     82.03     1.99 450000000     0.00     0.00  Bitmap::operator<<(float)
   2.12     83.87     1.85 197791886     0.00     0.00  lerp(float, Pix&, Pix&, Bitmap&)
   0.29     84.12     0.25                             createBMP(int*, int, int)
   0.13     84.23     0.11      100     1.10     1.10  Bitmap::Bitmap(char const*, int, int)
   0.00     84.23     0.00      100     0.00     0.00  generateBitmapImage(unsigned char*, int, int, char const*)
   0.00     84.23     0.00      100     0.00     0.00  createBitmapFileHeader(int, int, int)
   0.00     84.23     0.00      100     0.00     0.00  createBitmapInfoHeader(int, int)
   0.00     84.23     0.00      100     0.00     0.00  Bitmap::~Bitmap()
   0.00     84.23     0.00        1     0.00     0.00  _GLOBAL__sub_I_main
Generated Image of Julia set at (-0.4, 0.6)

Julia.jpg

Assignment 2

Assignment 3

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