MP7
Mazes

Each SquareMaze object represents a randomlygenerated square maze and its solution. More...
#include "maze.h"
Public Member Functions  
SquareMaze ()  
Noparameter constructor. More...  
void  makeMaze (int width, int height) 
Makes a new SquareMaze of the given height and width. More...  
bool  canTravel (int x, int y, int dir) const 
This uses your representation of the maze to determine whether it is possible to travel in the given direction from the square at coordinates (x,y). More...  
void  setWall (int x, int y, int dir, bool exists) 
Sets whether or not the specified wall exists. More...  
vector< int >  solveMaze () 
Solves this SquareMaze. More...  
PNG *  drawMaze () const 
Draws the maze without the solution. More...  
PNG *  drawMazeWithSolution () 
This function calls drawMaze, then solveMaze; it modifies the PNG from drawMaze to show the solution vector and the exit. More...  
Each SquareMaze object represents a randomlygenerated square maze and its solution.
(Note that by "square maze" we mean a maze in which each cell is a square; the maze itself need not be a square.)

inline 
Noparameter constructor.
Creates an empty maze.
void SquareMaze::makeMaze  (  int  width, 
int  height  
) 
Makes a new SquareMaze of the given height and width.
If this object already represents a maze it will clear all the existing data before doing so. You will start with a square grid (like graph paper) with the specified height and width. You will select random walls to delete without creating a cycle, until there are no more walls that could be deleted without creating a cycle. Do not delete walls on the perimeter of the grid.
Hints: You only need to store 2 bits per square: the "down" and "right" walls. The finished maze is always a tree of corridors.)
width  The width of the SquareMaze (number of cells) 
height  The height of the SquareMaze (number of cells) 
bool SquareMaze::canTravel  (  int  x, 
int  y,  
int  dir  
)  const 
This uses your representation of the maze to determine whether it is possible to travel in the given direction from the square at coordinates (x,y).
For example, after makeMaze(2,2), the possible input coordinates will be (0,0), (0,1), (1,0), and (1,1).
You can not step off of the maze or through a wall.
This function will be very helpful in solving the maze. It will also be used by the grading program to verify that your maze is a tree that occupies the whole grid, and to verify your maze solution. So make sure that this function works!
x  The x coordinate of the current cell 
y  The y coordinate of the current cell 
dir  The desired direction to move from the current cell 
void SquareMaze::setWall  (  int  x, 
int  y,  
int  dir,  
bool  exists  
) 
Sets whether or not the specified wall exists.
This function should be fast (constant time). You can assume that in grading we will not make your maze a nontree and then call one of the other member functions. setWall should not prevent cycles from occurring, but should simply set a wall to be present or not present. Our tests will call setWall to copy a specific maze into your implementation.
x  The x coordinate of the current cell 
y  The y coordinate of the current cell 
dir  Either 0 (right) or 1 (down), which specifies which wall to set (same as the encoding explained in canTravel). You only need to support setting the bottom and right walls of every square in the grid. 
exists  true if setting the wall to exist, false otherwise 
vector< int > SquareMaze::solveMaze  (  ) 
Solves this SquareMaze.
For each square on the bottom row (maximum y coordinate), there is a distance from the origin (i.e. the topleft cell), which is defined as the length (measured as a number of steps) of the only path through the maze from the origin to that square.
Select the square in the bottom row with the largest distance from the origin as the destination of the maze. solveMaze() returns the winning path from the origin to the destination as a vector of integers, where each integer represents the direction of a step, using the same encoding as in canTravel().
If multiple paths of maximum length exist, use the one with the destination cell that has the smallest x value.
Hint: this function should run in time linear in the number of cells in the maze.
PNG * SquareMaze::drawMaze  (  )  const 
Draws the maze without the solution.
First, create a new PNG. Set the dimensions of the PNG to (width*10+1,height*10+1). where height and width were the arguments to makeMaze. Blacken the entire topmost row and leftmost column of pixels, except the entrance (1,0) through (9,0). For each square in the maze, call its maze coordinates (x,y). If the right wall exists, then blacken the pixels with coordinates ((x+1)*10,y*10+k) for k from 0 to 10. If the bottom wall exists, then blacken the pixels with coordinates (x*10+k, (y+1)*10) for k from 0 to 10.
The resulting PNG will look like the sample image, except there will be no exit from the maze and the red line will be missing.
PNG * SquareMaze::drawMazeWithSolution  (  ) 
This function calls drawMaze, then solveMaze; it modifies the PNG from drawMaze to show the solution vector and the exit.
Start at pixel (5,5). Each direction in the solution vector corresponds to a trail of 11 red pixels in the given direction. If the first step is downward, color pixels (5,5) through (5,15) red. (Red is 0,1,0.5,1 in HSLA). Then if the second step is right, color pixels (5,15) through (15,15) red. Then if the third step is up, color pixels (15,15) through (15,5) red. Continue in this manner until you get to the end of the solution vector, so that your output looks analogous the above picture.
Make the exit by undoing the bottom wall of the destination square: call the destination maze coordinates (x,y), and whiten the pixels with coordinates (x*10+k, (y+1)*10) for k from 1 to 9.