Maze solving

Maze solving
You are encouraged to solve this task according to the task description, using any language you may know.

For a maze generated by this task, write a function that finds (and displays) the shortest path between two cells. Note that because these mazes are generated by the Depth-first search algorithm, they contain no circular paths, and a simple depth-first tree search can be used.

PicoLisp

<lang PicoLisp>(de shortestPath (Goal This Maze)

  (let (Path NIL  Best NIL  Dir " > ")
     (recur (This Path Dir)
        (when (and This (not (: mark)))
           (push 'Path (cons This Dir))
           (if (== Goal This)
              (unless (and Best (>= (length Path) (length Best)))
                 (setq Best Path) )
              (=: mark T)
              (recurse (: west) Path " > ")
              (recurse (: east) Path " < ")
              (recurse (: south) Path " \^ ")
              (recurse (: north) Path " v ")
              (=: mark NIL) ) ) )
     (disp Maze 0
        '((Fld) (if (asoq Fld Best) (cdr @) "   ")) ) ) )</lang>

Using the maze produced in Maze generation#PicoLisp, this finds the shortest path from the top-left cell 'a8' to the bottom-right exit 'k1':

: (shortestPath 'a8 'k1 (maze 11 8))
   +   +---+---+---+---+---+---+---+---+---+---+
 8 | >   >   v | >   v |                       |
   +   +   +   +   +   +   +---+   +---+---+   +
 7 |   |   | >   ^ | v |   |       |       |   |
   +---+   +---+---+   +   +   +---+   +   +   +
 6 |   |       |     v |   |           |   |   |
   +   +---+   +---+   +---+---+---+   +   +---+
 5 |       |       | >   >   >   v |   |       |
   +---+   +---+   +---+---+---+   +---+---+   +
 4 |   |       |       |       | v | >   >   v |
   +   +---+   +---+   +---+   +   +   +---+   +
 3 |       |       |   |       | v | ^   < | v |
   +   +---+---+   +   +   +   +   +---+   +   +
 2 |       |       |   |   |   | v | >   ^ | v |
   +   +   +   +---+   +   +---+   +   +---+   +
 1 |   |               |         >   ^ |     >
   +---+---+---+---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h   i   j   k

Tcl

Works with: Tcl version 8.6

This script assumes that the contents of the generation task have already been sourced. Note that the algorithm implemented here does not assume that the maze is free of circuits, and in the case that there are multiple routes, it finds the shortest one because it is a breadth-first search (by virtue of the queue variable being used as a queue). <lang tcl>oo::define maze {

   method solve {} {

### Initialization of visited matrix and location/path queue set visited [lrepeat $x [lrepeat $y 0]] set queue {0 0 {}}

### Loop to do the searching ### while 1 { # Check for running out of path; an error in maze construction if {[llength $queue] == 0} { error "cannot reach finish" } # Visit the next square from the queue set queue [lassign $queue cx cy path] if {[lindex $visited $cx $cy]} continue lset visited $cx $cy 1 lappend path $cx $cy # Check for reaching the goal if {$cx == $x-1 && $cy == $y-1} break # Add the square in each direction to the queue if a move there is legal foreach {dx dy} {0 1 1 0 0 -1 -1 0} { set nx [expr {$cx + $dx}]; set ny [expr {$cy + $dy}] if { $nx >= 0 && $nx < $x && $ny >= 0 && $ny < $y && ($dx && idx($verti, min($cx,$nx), $cy) || $dy && idx($horiz, $cx, min($cy,$ny))) } then { lappend queue $nx $ny $path } } }

### Loop to set up the path rendering ### # (-2,-2) is just a marker that isn't next to the maze at all, so # guaranteeing the use of the last 'else' clause foreach {cx cy} $path {nx ny} [concat [lrange $path 2 end] -2 -2] { if {$nx-$cx == 1} { lset content $cx $cy "v" } elseif {$nx-$cx == -1} { lset content $cx $cy "^" } elseif {$ny-$cy == -1} { lset content $cx $cy "<" } else { lset content $cx $cy ">" } }

### Return the path ### return $path

   }

}

1. Do the solution (we ignore the returned path here...)

m solve

1. Print it out

puts [m view]</lang> Example output:

+   +---+---+---+---+---+---+---+---+---+---+
| v     |                                   |
+   +---+   +---+---+---+---+---+---+---+   +
| v |       | >   v | >   v |   |           |
+   +   +---+   +   +   +   +   +   +---+   +
| v     | >   ^ | v | ^ | v |   |       |   |
+   +---+   +---+   +   +   +   +---+   +---+
| v | >   ^ | v   < | ^ | v |       |   |   |
+   +   +---+   +---+   +   +   +---+   +   +
| >   ^ | v   < | >   ^ | v |       |       |
+---+---+   +---+   +---+   +---+   +---+---+
| v   <   < | >   ^ | v   < | >   >   >   v |
+   +---+---+   +---+   +---+   +---+---+   +
| >   v |     ^   < | >   >   ^ |       | v |
+---+   +---+---+   +---+---+---+   +   +   +
|     >   >   >   ^ |               |     >  
+---+---+---+---+---+---+---+---+---+---+---+