/// <summary>
/// Solves a maze using a non-recursive breath-first approach.
/// </summary>
public override void SolveMaze()
{
// Apply all pre-treament logics, if any
PreTreatmentLogics.ForEach(p => p.PreTreatMazeToSolve());
// Set all parent gridpoints to null at the start
PathToSolveMaze = MazeToSolve.MazeGridpoints.Select(mazeGridpoint =>
new MazeSolutionElement
{
ParentMazeGridpoint = null,
MazeGridpoint = mazeGridpoint.Value
}).ToList();
var queueToSolveMaze = new Queue <MazeGridpoint>();
// Pick the first satisfactory gridpoint as the starting point
var startMazeGridpoint = MazeToSolve.MazeGridpoints.Values.First(m => m.IsStartPoint && m.DirectionsAvailable.Count > 0);
queueToSolveMaze.Enqueue(startMazeGridpoint);
var finalMazeGridpoint = SearchForSolution(queueToSolveMaze);
var finalMazeSolutionElement = PathToSolveMaze.Single(m => m.MazeGridpoint == finalMazeGridpoint);
ConstructPathToSolveMaze(finalMazeSolutionElement);
}
private MazeGridpoint SearchForSolution(Queue <MazeGridpoint> queueToSolveMaze)
{
// As long as there are still elements in the queue to check, keep going
while (queueToSolveMaze.Any())
{
var currentMazeGridpoint = queueToSolveMaze.Dequeue();
currentMazeGridpoint.HasBeenVisited = true;
MazeToSolve.NotifyMazeHasBeenUpdated();
MazeToSolve.NotifyMazeToBeRedrawnUpdated();
_foundMazeFinishPoint = MazeToSolve.CheckIfAtFinish(currentMazeGridpoint);
// Quit now if the end of the maze was found
if (_foundMazeFinishPoint)
{
return(currentMazeGridpoint);
}
// Investigate each direction available at the current gridpoint
foreach (var direction in currentMazeGridpoint.DirectionsAvailable.OpenPaths)
{
if (!MazeToSolve.IsValidPositionInMaze(currentMazeGridpoint, direction))
{
continue;
}
var nextMazeGridpoint = MazeToSolve.ProceedToNewGridpoint(currentMazeGridpoint, direction);
if (MazeToSolve.CheckIfAtDeadEnd(nextMazeGridpoint) || nextMazeGridpoint.HasBeenVisited)
{
continue;
}
// Set up the parent gridpoint for each direction that is valid
var nextMazeSolutionElement = PathToSolveMaze.Single(m => m.MazeGridpoint == nextMazeGridpoint);
nextMazeSolutionElement.ParentMazeGridpoint = currentMazeGridpoint;
nextMazeGridpoint.HasBeenVisited = true;
// Make sure we haven't found the end of the maze for each direction
_foundMazeFinishPoint = MazeToSolve.CheckIfAtFinish(nextMazeGridpoint);
if (_foundMazeFinishPoint)
{
return(nextMazeGridpoint);
}
// If its not the end of the maze, queue it up for another round down the line
queueToSolveMaze.Enqueue(nextMazeGridpoint);
Console.WriteLine("X : " + nextMazeGridpoint.Position.X + ", Y : " + nextMazeGridpoint.Position.Y + " Direction : " + direction);
}
}
throw new Exception("Maze Solver Error: Sorry, maze could not be solved. The maze image provided may be invalid.");
}
// To find the path to the solution, simply unwind the solution element tree
// from the finsh point to the start using recursion.
private void ConstructPathToSolveMaze(MazeSolutionElementTree mazeSolutionElementTree)
{
if (mazeSolutionElementTree.ParentSolutionElement != null)
{
ConstructPathToSolveMaze(mazeSolutionElementTree.ParentSolutionElement);
}
var mazeSolutionElement = new MazeSolutionElement
{
MazeGridpoint = mazeSolutionElementTree.MazeGridpoint
};
PathToSolveMaze.Add(mazeSolutionElement);
mazeSolutionElementTree.ParentSolutionElement = null;
}
/// <summary>
/// Given a direction to proceed, this logic determines what the next maze gridpoint will be. In cases
/// where we have reached a dead-end, this may mean backtracking to the last gridpoint where another
/// choice was available.
/// </summary>
private MazeGridpoint DetermineNextMazeGridPoint(MazeGridpoint currentMazeGridpoint, DirectionEnum directionToProceed)
{
var nextMazeGridpoint = MazeToSolve.ProceedToNewGridpoint(currentMazeGridpoint, directionToProceed);
if (MazeToSolve.CheckIfAtDeadEnd(nextMazeGridpoint) || nextMazeGridpoint.HasBeenVisited)
{
// We have arrived at a dead-end, so this cannot have been the right direction to proceed
currentMazeGridpoint.DirectionsAvailable[directionToProceed] = false;
if (currentMazeGridpoint.DirectionsAvailable.Count == 1)
{
// Go back to the last gridpoint where there were more than two choices about the direction to proceed
var lastValidMazeSolutionElement = PathToSolveMaze.LastOrDefault(p => p.MazeGridpoint.DirectionsAvailable.Count > 2);
if (lastValidMazeSolutionElement == null)
{
throw new Exception("Maze Solver Error: Sorry, maze could not be solved. The maze image provided may be invalid.");
}
var directionProceededAtLastValidMazeGridPoint = lastValidMazeSolutionElement.DirectionProceeded;
// Since the path resulted in a dead-end, it cannot have been the reight direction to proceed
lastValidMazeSolutionElement.MazeGridpoint.DirectionsAvailable[directionProceededAtLastValidMazeGridPoint] = false;
// Truncate the path back to the last valid point to take a new direction
PathToSolveMaze = PathToSolveMaze.Where(p => p.StepNumber < lastValidMazeSolutionElement.StepNumber).ToList();
return(lastValidMazeSolutionElement.MazeGridpoint);
}
return(currentMazeGridpoint);
}
// The step numbers will be indexed starting with zero
var stepNumber = PathToSolveMaze.Count;
var mazeSolutionElement = new MazeSolutionElement
{
StepNumber = stepNumber,
MazeGridpoint = currentMazeGridpoint,
DirectionProceeded = directionToProceed
};
PathToSolveMaze.Add(mazeSolutionElement);
return(nextMazeGridpoint);
}
private void ConstructPathToSolveMaze(MazeSolutionElement mazeSolutionElement)
{
var pathToSolveMaze = new List <MazeSolutionElement>();
pathToSolveMaze.Add(mazeSolutionElement);
// Go back from parent to parent to find the tree that results in a solution
// The starting solution element will have a parent that is null
while (pathToSolveMaze.Last().ParentMazeGridpoint != null)
{
var previousMazeGridpoint = mazeSolutionElement.ParentMazeGridpoint;
var previousMazeSolutionElement = PathToSolveMaze.Single(m => m.MazeGridpoint == previousMazeGridpoint);
pathToSolveMaze.Add(previousMazeSolutionElement);
mazeSolutionElement = previousMazeSolutionElement;
}
PathToSolveMaze = pathToSolveMaze;
}
/// <summary>
/// Solves the maze using a brute force algorithm approach.
/// </summary>
public override void SolveMaze()
{
// Apply all pre-treament logics, if any
PreTreatmentLogics.ForEach(p => p.PreTreatMazeToSolve());
// Set all parent gridpoints to null at the start
var currentMazeGridpoint = MazeToSolve.MazeGridpoints.Values.First(m => m.IsStartPoint && m.DirectionsAvailable.Count > 0);
// Keep on looking so long as we haven't reached the finish
while (!MazeToSolve.CheckIfAtFinish(currentMazeGridpoint))
{
currentMazeGridpoint.HasBeenVisited = true;
// Picked a direction and go in that direction
var directionToProceed = DirectionPickerLogic.PickDirectionToProceed(PathToSolveMaze, currentMazeGridpoint);
if (directionToProceed == DirectionEnum.None)
{
throw new Exception("Maze Solver Error: Sorry, maze could not be solved. The maze image provided may be invalid.");
}
currentMazeGridpoint = DetermineNextMazeGridPoint(currentMazeGridpoint, directionToProceed);
Console.WriteLine("X : " + currentMazeGridpoint.Position.X + ", Y : " + currentMazeGridpoint.Position.Y + " Direction : " + directionToProceed);
MazeToSolve.NotifyMazeHasBeenUpdated();
MazeToSolve.NotifyMazeToBeRedrawnUpdated();
}
// Once out of the loop, the current gridpoint will be the final gridpoint
var finalMazeSolutionElement = new MazeSolutionElement
{
StepNumber = PathToSolveMaze.Count,
MazeGridpoint = currentMazeGridpoint,
DirectionProceeded = DirectionEnum.None
};
PathToSolveMaze.Add(finalMazeSolutionElement);
}
