Version 1 of Knight's Tour

Updated 2008-02-28 23:47:33 by PT

The Knight's Tour is a Computer Science problem that involves calculating a path for the Knight in chess such that it travels to every square on the chess board once only. See the Wikipedia page for some more details on this problem [L1 ].

 # Copyright (C) 2008 Pat Thoyts <[email protected]>
 #
 # Do a knight's tour of a chessboard.

 package require Tk 8.5

 # Return a list of accessible squares from a given square
 proc ValidMoves {square} {
     set moves {}
     foreach pair {{-1 -2} {-2 -1} {-2 1} {-1 2} {1 2} {2 1} {2 -1} {1 -2}} {
         set col [expr {($square % 8) + [lindex $pair 0]}]
         set row [expr {($square / 8) + [lindex $pair 1]}]
         if {$row > -1 && $row < 8 && $col > -1 && $col < 8} {
             lappend moves [expr {$row * 8 + $col}]
         }
     }
     return $moves
 }

 # Return the number of available moves for this square
 proc CheckSquare {square} {
     variable visited
     set moves 0
     foreach test [ValidMoves $square] {
         if {[lsearch -exact -integer $visited $test] == -1} {
             incr moves
         }
     }
     return $moves
 }

 # Select the next square to move to. Returns -1 if there are no available
 # squares remaining that we can move to.
 proc Next {square} {
     variable visited
     set minimum 9
     set nextSquare -1
     foreach testSquare [ValidMoves $square] {
         if {[lsearch -exact -integer $visited $testSquare] == -1} {
             set count [CheckSquare $testSquare]
             if {$count < $minimum} {
                 set minimum $count
                 set nextSquare $testSquare
             }
         }
     }
     return $nextSquare
 }

 # Display a square number as a standard chess square notation.
 proc N {square} {
     return [format %c%d [expr {97 + $square % 8}] \
                 [expr {$square / 8 + 1}]]
 }

 # Move the knight
 proc MovePiece {last square} {
     variable visited
     variable delay
     .f.txt insert end "[llength $visited]. [N $last] .. [N $square]\n" {}
     .f.txt see end
     .f.c itemconfigure [expr {1+$last}] -state normal -outline black
     after [expr {$delay/2}] [list .f.c itemconfigure \
                 [expr {1+$square}] -state normal -outline red]
     .f.c itemconfigure [expr {1+$square}] -outline red
     .f.c coords knight [lrange [.f.c coords [expr {1+$square}]] 0 1]
     lappend visited $square
     set next [Next $square]
     if {$next ne -1} {
         after $delay [list MovePiece $square $next]
     } else {
         .b1 configure -state normal
         if {[llength $visited] == 64} {
             .f.txt insert end "Success\n" {}
         } else {
             .f.txt insert end "FAILED!\n" {}
         }
     }
 }

 proc Tour {} {
     variable visited {}
     .f.txt delete 1.0 end
     .b1 configure -state disabled
     for {set n 0} {$n < 64} {incr n} {
         .f.c itemconfigure $n -state disabled -outline black
     }
     # Failures: d6 (43)
     set initial [expr {int(rand() * 64)}]
     after idle [list MovePiece $initial $initial]
 }

 proc SetDelay {new} {
     variable delay [expr {int($new)}]
 }

 proc CreateGUI {} {
     wm title . "Knights tour"
     wm withdraw .
     set f [ttk::frame .f]
     set c [canvas $f.c -width 240 -height 240]
     text $f.txt -width 10 -height 1 -background white \
         -yscrollcommand [list $f.vs set] -font {Arial 8}
     ttk::scrollbar $f.vs -command [list $f.txt yview]

     variable delay 1000
     ttk::label .ls -text Speed
     ttk::scale .sc  -from 2 -to 2000 -command [list SetDelay] \
         -variable [namespace which -variable delay]
     ttk::button .b1 -text Start -command Tour
     ttk::button .b2 -text Exit -command {destroy .}
     set square 0
     for {set row 7} {$row != -1} {incr row -1} {
         for {set col 0} {$col < 8} {incr col} {
             if {(($col & 1) ^ ($row & 1))} {
                 set fill "#906010" ; set dfill "#533200"
             } else {
                 set fill "#f0e0a0" ; set dfill "#c0c090"
             }
             set coords [list [expr {$col * 30 + 3}] [expr {$row * 30 + 3}] \
                             [expr {$col * 30 + 29}] [expr {$row * 30 + 29}]]
             $c create rectangle $coords -fill $fill -disabledfill $dfill \
                 -width 2 -state disabled
         }
     }
     catch {eval font create KnightFont -size 18}
     $c create text -80 -80 -font KnightFont -text "\u265e" \
         -anchor nw -tags knight

     grid $c $f.txt $f.vs  -sticky news
     grid rowconfigure    $f 0 -weight 1
     grid columnconfigure $f 1 -weight 1

     grid $f - - - -sticky news
     grid .ls .sc .b1 .b2 -sticky e
     grid rowconfigure . 0 -weight 1
     grid columnconfigure . 0 -weight 1

     bind . <Control-F2> {console show}
     bind . <Return> {.b1 invoke}
     bind . <Escape> {.b2 invoke}
     wm deiconify .
     tkwait window .
 }

 if {!$tcl_interactive} {
     set r [catch [linsert $argv 0 CreateGUI] err]
     if {$r} {
         tk_messageBox -icon error -title "Error" -message $err
     }
     exit $r
 }

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