/// <summary>
/// This will solve the puzzle by using a recursive Backtracking algorthim
/// </summary>
/// <remarks>
/// This is a brute force routine
/// </remarks>
/// <param name="puzzle"></param>
/// <param name="cells"></param>
/// <param name="index"></param>
private static void SolveRecursive(Puzzle puzzle, Puzzle.Cell[] cells, int index)
{
int minIndex = cells.GetLowerBound(0);
int maxIndex = cells.GetUpperBound(0);
// Check the index, and exit if the index is outside the boundries
if (index < minIndex || index > maxIndex)
{
return;
}
// Much easier to reference a single cell in the beginning than array[index] the whole time
Puzzle.Cell cell = cells[index];
// Need to bypass if this cell is Locked.
if (cell.IsLocked)
{
// Call recursively sending the next index to process
SolveRecursive(puzzle, cells, index + 1);
}
else
{
// Re-Initialize the cell's value
cell.Value = null;
// Check to see if the puzzle is solved, if so, break out of the routine all together
// Iterate through all the possible values for this cell
while (!Validator.IsSolved(puzzle))
{
if (cell.Value.GetValueOrDefault() < Puzzle.MAX_VALUE)
{
// Increment current cell
// Note: The Increment method has logic to determine if the cell is Locked already
cell.Increment();
// Determine if we stay on the current cell (to obtain a valid value) or move to the next cell
// Call recursively sending the next index to process
if (!Validator.IsExistValue(puzzle, cell))
{
SolveRecursive(puzzle, cells, index + 1);
}
}
else
{
// Re-Initialize the cell's value if the current value is at the max value
cell.Value = null;
// By breaking out of the loop, we are forcing the method to return to the previous call
break;
}
}
}
}
/// <summary>
/// Checks to see if cell's value already exists in the cell's current row, column and quadrient
/// </summary>
/// <param name="cell"></param>
/// <returns></returns>
internal static bool IsExistValue(Puzzle puzzle, Puzzle.Cell cell)
{
bool ret = false;
Puzzle.Cell[] cells = null;
Puzzle.Cell[] filteredCells = null;
// Check current row to determine if the cell's value already exists by iterating through all the columns in that row
cells = Utils.Transpose <Puzzle.Cell>(puzzle.ToArray(),
cell.Row,
1,
0,
Puzzle.PUZZLE_GRID_SIZE);
// Need to remove the cell that we are checking against
filteredCells = cells.Where(x => x.Column != cell.Column)
.ToArray();
ret = ret || IsExistValue(cell.Value.GetValueOrDefault(), filteredCells);
// Check current column to determine if the cell's value already exists by iterating through all the rows in that column
cells = Utils.Transpose <Puzzle.Cell>(puzzle.ToArray(),
0,
Puzzle.PUZZLE_GRID_SIZE,
cell.Column,
1);
// Need to remove the cell that we are checking against
filteredCells = cells.Where(x => x.Row != cell.Row)
.ToArray();
ret = ret || IsExistValue(cell.Value.GetValueOrDefault(), filteredCells);
// Check current quadrient to determine if the cell's value already exists by iterating through all the rows and columns in that quadrient
// Determine quadrient
int quadRow = (cell.Row / Puzzle.QUADRIENT_GRID_SIZE);
int quadCol = (cell.Column / Puzzle.QUADRIENT_GRID_SIZE);
cells = Utils.Transpose <Puzzle.Cell>(puzzle.ToArray(),
(quadRow * Puzzle.QUADRIENT_GRID_SIZE),
Puzzle.QUADRIENT_GRID_SIZE,
(quadCol * Puzzle.QUADRIENT_GRID_SIZE),
Puzzle.QUADRIENT_GRID_SIZE);
// Need to remove the cell that we are checking against
filteredCells = cells.Where(x => !((x.Row == cell.Row) && (x.Column == cell.Column)))
.ToArray();
ret = ret || IsExistValue(cell.Value.GetValueOrDefault(), filteredCells);
return(ret);
}
/// <summary>
/// This will randomly pick a cell from the given puzzle
/// </summary>
/// <remarks>
/// If the picked cell has a value or is locked, then a new cell will be randomly chosen
/// </remarks>
/// <param name="puzzle"></param>
/// <returns></returns>
private Puzzle.Cell GetRandomCell(Puzzle puzzle)
{
int row = 0;
int col = 0;
Puzzle.Cell cell = null;
Random random = new Random();
do
{
row = random.Next(0, Puzzle.PUZZLE_GRID_SIZE);
col = random.Next(0, Puzzle.PUZZLE_GRID_SIZE);
cell = puzzle.GetCell(row, col);
} while (cell.IsLocked || cell.Value.HasValue);
return(cell);
}
/// <summary>
/// Populate puzzle with random values
/// </summary>
/// <remarks>
/// This will perform some validations to make sure the random value can be placed within the specified cell
/// </remarks>
/// <param name="puzzle"></param>
private void Populate(Puzzle puzzle)
{
int value = 0;
Random random = new Random();
// Loop for the number of random number values to generate
for (int i = 0; i < NumberOfRandomValues; i++)
{
Puzzle.Cell cell = GetRandomCell(puzzle);
// Loop until we have a valid random number in a random cell
do
{
cell.Value = null; // Clear out previous value
cell = GetRandomCell(puzzle);
value = random.Next(Puzzle.MIN_VALUE, Puzzle.MAX_VALUE + 1);
cell.Value = Convert.ToByte(value);
} while (Validator.IsExistValue(puzzle, cell));
// Lock cell so that value cannot be changed
cell.IsLocked = true;
}
}
/// <summary>
/// This will solve the puzzle by using a non-recursive Backtracking algorthim
/// </summary>
/// <remarks>
/// This is a brute force routine
/// </remarks>
/// <param name="puzzle"></param>
/// <param name="cells"></param>
private static void SolveNonRecursive(Puzzle puzzle)
{
// Much easier to work with a single dimensional array, so lets transpose it
Puzzle.Cell[] cells = Utils.Transpose <Puzzle.Cell>(puzzle.ToArray(),
0,
Puzzle.PUZZLE_GRID_SIZE,
0,
Puzzle.PUZZLE_GRID_SIZE);
int minIndex = cells.GetLowerBound(0);
int maxIndex = cells.GetUpperBound(0);
int index = minIndex;
int directionFactor = 0; // 1 to move forward, -1 to move backward
// Loop until we have either solved or exhusted our routine
while (!Validator.IsSolved(puzzle) && index >= minIndex)
{
// Check to see if we have gone beyond the boundries, change the index factor
if (index > maxIndex)
{
index = maxIndex;
directionFactor = -1;
}
// Much easier to reference a single cell in the beginning than array[index] the whole time
Puzzle.Cell cell = cells[index];
// Need to bypass if this cell is IsLocked. (if cell is locked keep the directionFactor the same)
if (!cell.IsLocked)
{
// Iterate through all the possible values for this cell
if (cell.Value.GetValueOrDefault() < Puzzle.MAX_VALUE)
{
// Increment current cell
// Note: The Increment method has logic to determine if the cell is Locked already
cell.Increment();
// Determine if we stay on the current cell (to obtain a valid value) or move to the next cell
if (Validator.IsExistValue(puzzle, cell))
{
directionFactor = 0; // Stay on current cell
}
else
{
directionFactor = 1; // Move to next cell
}
}
else
{
// Re-Initialize the cell's value if the current value is at the max value
cell.Value = null;
// Set the direction factor to the previous cell
directionFactor = -1;
}
}
else
{
// The index will not change if the first cell is locked and the directionFactor is zero
if (directionFactor == 0)
{
directionFactor = 1;
}
}
// Change the index by the direction factor
index += directionFactor;
}
}
