TriForce

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randomName'); DROP TABLE projects;--

Team Members

1. David Ferri, Some responsibility
2. Vincent Terpstra, Some other responsibility
3. Raymond Kiguru, Responsibility++

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Progress

Assignment 1

Sudoku Solver Profiling

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; 
} 

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])