Question

Once this is instantiated and method traverse(0,0) is invoked, it will automatically solve the maze showing 7 as the path and 3 as “tried paths”.
I’m trying to understand this code but I get stuck at the first else statement in the traverse method.

public class Maze
{
    private final int TRIED = 3;
    private final int PATH = 7;
    private int[][] grid = { {1,1,1,0,1,1,0,0,0,1,1,1,1},
                             {1,0,1,1,1,0,1,1,1,1,0,0,1},
                             {0,0,0,0,1,0,1,0,1,0,1,0,0},
                             {1,1,1,0,1,1,1,0,1,0,1,1,1},
                             {1,0,1,0,0,0,0,1,1,1,0,0,1},
                             {1,0,1,1,1,1,1,1,0,1,1,1,1},
                             {1,0,0,0,0,0,0,0,0,0,0,0,0},
                             {1,1,1,1,1,1,1,1,1,1,1,1,1} };

public boolean traverse (int row, int column)
{
    boolean done = false;
    if (valid (row, column))
    {
       grid[row][column] = TRIED;
       // this cell has been tried
       if (row == grid.length-1 && column == grid[0].length-1)
          done = true;
          // the maze is solved
       else
       {
          done = traverse (row+1, column); 
          // down
          if (!done)
          done = traverse (row, column+1); 
          // right
          if (!done)
          done = traverse (row-1, column);
          // up

          if (!done)
          done = traverse (row, column-1);
          // left
       }
    if (done)
    // this location is part of the final path
    grid[row][column] = PATH;
    }
    return done;
}

//-----------------------------------------------------------------
//  Determines if a specific location is valid.
//-----------------------------------------------------------------
private boolean valid (int row, int column)
{
    boolean result = false;
    // check if cell is in the bounds of the matrix
    if (row >= 0 && row < grid.length && column >= 0 &&
       column < grid[row].length)
       // check if cell is not blocked and not previously tried
       if (grid[row][column] == 1)
       result = true;
       return result;
}

To my knowledge,

done = traverse (row+1, column); 

This line is a recursive call and will move it down once, and will run the method again but what if it’s not valid? Doesn’t the whole method stop? I don’t understand where the flow of control shifts after a certain spot is not valid.

For example, if [1][0] is not valid, does the control shift back to the [0][0] call and process the “going right” statement? Where and what does it mean by if (!done), i mean done only equals true when the maze is completely solved and if it is valid, done will equal true, so wouldn’t the whole thing just stop?

Answer 1

Here’s your method:

public boolean traverse (int row, int column)
{
    boolean done = false;
    if (valid (row, column))
    {
       ...
    }
    return done;
}

Therefore, if the point is not valid, it will skip all of the testing and just return false.