001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
package algs41;
import stdlib.*;
/* ***********************************************************************
 *  Compilation:  javac Maze.java
 *  Execution:    java Maze.java N
 *  Dependecies:  StdDraw.java
 *
 *  Generates a perfect N-by-N maze using depth-first search with a stack.
 *
 *  % java Maze 62
 *
 *  Note: this program generalizes nicely to finding a random tree
 *        in a graph.
 *
 *************************************************************************/

public class XMaze {
  private final int N;           // dimension of maze
  private boolean[][] north;     // is there a wall to north of cell i, j
  private boolean[][] east;
  private boolean[][] south;
  private boolean[][] west;
  private boolean[][] visited;
  //private double size;
  private boolean done = false;

  public XMaze(int N) {
    this.N = N;
    StdDraw.setXscale(0, N+2);
    StdDraw.setYscale(0, N+2);
    init();
    generate();
  }

  private void init() {
    // initialize border cells as already visited
    visited = new boolean[N+2][N+2];
    for (int x = 0; x < N+2; x++) visited[x][0] = visited[x][N+1] = true;
    for (int y = 0; y < N+2; y++) visited[0][y] = visited[N+1][y] = true;


    // initialze all wells as present
    north = new boolean[N+2][N+2];
    east  = new boolean[N+2][N+2];
    south = new boolean[N+2][N+2];
    west  = new boolean[N+2][N+2];
    for (int x = 0; x < N+2; x++)
      for (int y = 0; y < N+2; y++)
        north[x][y] = east[x][y] = south[x][y] = west[x][y] = true;
  }


  // generate the maze
  private void generate(int x, int y) {
    visited[x][y] = true;

    // while there is an univisited neighbor
    while (!visited[x][y+1] || !visited[x+1][y] || !visited[x][y-1] || !visited[x-1][y]) {

      // pick random neighbor (could use Knuth's trick instead)
      while (true) {
        double r = Math.random();
        if (r < 0.25 && !visited[x][y+1]) {
          north[x][y] = south[x][y+1] = false;
          generate(x, y + 1);
          break;
        }
        else if (r >= 0.25 && r < 0.50 && !visited[x+1][y]) {
          east[x][y] = west[x+1][y] = false;
          generate(x+1, y);
          break;
        }
        else if (r >= 0.5 && r < 0.75 && !visited[x][y-1]) {
          south[x][y] = north[x][y-1] = false;
          generate(x, y-1);
          break;
        }
        else if (r >= 0.75 && r < 1.00 && !visited[x-1][y]) {
          west[x][y] = east[x-1][y] = false;
          generate(x-1, y);
          break;
        }
      }
    }
  }

  // generate the maze starting from lower left
  private void generate() {
    generate(1, 1);


    // delete some random walls
    for (int i = 0; i < N; i++) {
      int x = (int) (1 + Math.random() * (N-1));
      int y = (int) (1 + Math.random() * (N-1));
      north[x][y] = south[x][y+1] = false;
    }
    // add some random walls
    for (int i = 0; i < N; i++) {
      int x = (int) (N / 2 + Math.random() * (N / 2));
      int y = (int) (N / 2 + Math.random() * (N / 2));
      east[x][y] = west[x+1][y] = true;
    }


  }



  // solve the maze using depth first search
  private void solve(int x, int y) {
    if (x == 0 || y == 0 || x == N+1 || y == N+1) return;
    if (done || visited[x][y]) return;
    visited[x][y] = true;

    StdDraw.setPenColor(StdDraw.BLUE);
    StdDraw.filledCircle(x + 0.5, y + 0.5, 0.25);
    StdDraw.show(30);

    // reached middle
    if (x == N/2 && y == N/2) done = true;

    if (!north[x][y]) solve(x, y + 1);
    if (!east[x][y])  solve(x + 1, y);
    if (!south[x][y]) solve(x, y - 1);
    if (!west[x][y])  solve(x - 1, y);

    if (done) return;

    StdDraw.setPenColor(StdDraw.GRAY);
    StdDraw.filledCircle(x + 0.5, y + 0.5, 0.25);
    StdDraw.show(30);
  }

  // solve the maze starting from the start state
  public void solve() {
    for (int x = 1; x <= N; x++)
      for (int y = 1; y <= N; y++)
        visited[x][y] = false;
    done = false;
    solve(1, 1);
  }

  // display the maze in turtle graphics
  public void draw() {
    StdDraw.setPenColor(StdDraw.RED);
    StdDraw.filledCircle(0.5*N + 0.5, 0.5*N + 0.5, 0.375);
    StdDraw.filledCircle(1.5, 1.5, 0.375);

    StdDraw.setPenColor(StdDraw.BLACK);
    for (int x = 1; x <= N; x++) {
      for (int y = 1; y <= N; y++) {
        if (south[x][y]) StdDraw.line(x, y, x + 1, y);
        if (north[x][y]) StdDraw.line(x, y + 1, x + 1, y + 1);
        if (west[x][y])  StdDraw.line(x, y, x, y + 1);
        if (east[x][y])  StdDraw.line(x + 1, y, x + 1, y + 1);
      }
    }
    StdDraw.show(1000);
  }



  // a test client
  public static void main(String[] args) {
    args = new String[] { "12" };

    int N = Integer.parseInt(args[0]);
    XMaze maze = new XMaze(N);
    StdDraw.show(0);
    maze.draw();
    maze.solve();
  }

}