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# Copyright (C) 2008 Pat Thoyts <patthoyts@users.sourceforge.net>
#
# Calculate a Knight's tour of a chessboard.
#
# This uses Warnsdorff's rule to calculate the next square each
# time. This specifies that the next square should be the one that
# has the least number of available moves.
#
# Using this rule it is possible to get to a position where
# there are no squares available to move into. In this implementation
# this occurs when the starting square is d6.
#
# To solve this fault an enhancement to the rule is that if we
# have a choice of squares with an equal score, we should choose
# the one nearest the edge of the board.
#
# If the call to the Edgemost function is commented out you can see
# this occur.
#
# You can drag the knight to a specific square to start if you wish.
# If you let it repeat then it will choose random start positions
# for each new tour.
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 $testSquare
} elseif {$count == $minimum} {
set nextSquare [Edgemost $nextSquare $testSquare]
}
}
}
return $nextSquare
}
# Select the square nearest the edge of the board
proc Edgemost {a b} {
set colA [expr {3-int(abs(3.5-($a%8)))}]
set colB [expr {3-int(abs(3.5-($b%8)))}]
set rowA [expr {3-int(abs(3.5-($a/8)))}]
set rowB [expr {3-int(abs(3.5-($b/8)))}]
return [expr {($colA * $rowA) < ($colB * $rowB) ? $a : $b}]
}
# 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}]]
}
# Perform a Knight's move and schedule the next move.
proc MovePiece {dlg last square} {
variable visited
variable delay
variable continuous
$dlg.f.txt insert end "[llength $visited]. [N $last] .. [N $square]\n" {}
$dlg.f.txt see end
$dlg.f.c itemconfigure [expr {1+$last}] -state normal -outline black
$dlg.f.c itemconfigure [expr {1+$square}] -state normal -outline red
$dlg.f.c coords knight [lrange [$dlg.f.c coords [expr {1+$square}]] 0 1]
lappend visited $square
set next [Next $square]
if {$next ne -1} {
variable aid [after $delay [list MovePiece $dlg $square $next]]
} else {
$dlg.tf.b1 configure -state normal
if {[llength $visited] == 64} {
variable initial
if {$initial == $square} {
$dlg.f.txt insert end "Closed tour!"
} else {
$dlg.f.txt insert end "Success\n" {}
if {$continuous} {
after [expr {$delay * 2}] [namespace code \
[list Tour $dlg [expr {int(rand() * 64)}]]]
}
}
} else {
$dlg.f.txt insert end "FAILED!\n" {}
}
}
}
# Begin a new tour of the board given a random start position
proc Tour {dlg {square {}}} {
variable visited {}
$dlg.f.txt delete 1.0 end
$dlg.tf.b1 configure -state disabled
for {set n 0} {$n < 64} {incr n} {
$dlg.f.c itemconfigure $n -state disabled -outline black
}
if {$square eq {}} {
set square [expr {[$dlg.f.c find closest \
{*}[$dlg.f.c coords knight] 0 65]-1}]
}
variable initial $square
after idle [list MovePiece $dlg $initial $initial]
}
proc Stop {} {
variable aid
catch {after cancel $aid}
}
proc Exit {dlg} {
Stop
destroy $dlg
}
proc SetDelay {new} {
variable delay [expr {int($new)}]
}
proc DragStart {w x y} {
$w dtag selected
$w addtag selected withtag current
variable dragging [list $x $y]
}
proc DragMotion {w x y} {
variable dragging
if {[info exists dragging]} {
$w move selected [expr {$x - [lindex $dragging 0]}] \
[expr {$y - [lindex $dragging 1]}]
variable dragging [list $x $y]
}
}
proc DragEnd {w x y} {
set square [$w find closest $x $y 0 65]
$w coords selected [lrange [$w coords $square] 0 1]
$w dtag selected
variable dragging ; unset dragging
}
proc CreateGUI {} {
catch {destroy .knightstour}
set dlg [toplevel .knightstour]
wm title $dlg "Knights tour"
wm withdraw $dlg
set f [ttk::frame $dlg.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 600
variable continuous 0
ttk::frame $dlg.tf
ttk::label $dlg.tf.ls -text Speed
ttk::scale $dlg.tf.sc -from 8 -to 2000 -command [list SetDelay] \
-variable [namespace which -variable delay]
ttk::checkbutton $dlg.tf.cc -text Repeat \
-variable [namespace which -variable continuous]
ttk::button $dlg.tf.b1 -text Start -command [list Tour $dlg]
ttk::button $dlg.tf.b2 -text Exit -command [list Exit $dlg]
set square 0
for {set row 7} {$row != -1} {incr row -1} {
for {set col 0} {$col < 8} {incr col} {
if {(($col & 1) ^ ($row & 1))} {
set fill tan3 ; set dfill tan4
} else {
set fill bisque ; set dfill bisque3
}
set coords [list [expr {$col * 30 + 4}] [expr {$row * 30 + 4}] \
[expr {$col * 30 + 30}] [expr {$row * 30 + 30}]]
$c create rectangle $coords -fill $fill -disabledfill $dfill \
-width 2 -state disabled
}
}
catch {eval font create KnightFont -size -24}
$c create text 0 0 -font KnightFont -text "\u265e" \
-anchor nw -tags knight -fill black -activefill "#600000"
$c coords knight [lrange [$c coords [expr {1 + int(rand() * 64)}]] 0 1]
$c bind knight <ButtonPress-1> [namespace code [list DragStart %W %x %y]]
$c bind knight <Motion> [namespace code [list DragMotion %W %x %y]]
$c bind knight <ButtonRelease-1> [namespace code [list DragEnd %W %x %y]]
grid $c $f.txt $f.vs -sticky news
grid rowconfigure $f 0 -weight 1
grid columnconfigure $f 1 -weight 1
grid $f - - - - - -sticky news
set things [list $dlg.tf.ls $dlg.tf.sc $dlg.tf.cc $dlg.tf.b1]
if {![info exists ::widgetDemo]} {
lappend things $dlg.tf.b2
if {[tk windowingsystem] ne "aqua"} {
set things [linsert $things 0 [ttk::sizegrip $dlg.tf.sg]]
}
}
pack {*}$things -side right
if {[tk windowingsystem] eq "aqua"} {
pack configure {*}$things -padx {4 4} -pady {12 12}
pack configure [lindex $things 0] -padx {4 24}
pack configure [lindex $things end] -padx {16 4}
}
grid $dlg.tf - - - - - -sticky ew
if {[info exists ::widgetDemo]} {
grid [addSeeDismiss $dlg.buttons $dlg] - - - - - -sticky ew
}
grid rowconfigure $dlg 0 -weight 1
grid columnconfigure $dlg 0 -weight 1
bind $dlg <Control-F2> {console show}
bind $dlg <Return> [list $dlg.tf.b1 invoke]
bind $dlg <Escape> [list $dlg.tf.b2 invoke]
bind $dlg <Destroy> [namespace code [list Stop]]
wm protocol $dlg WM_DELETE_WINDOW [namespace code [list Exit $dlg]]
wm deiconify $dlg
tkwait window $dlg
}
if {![winfo exists .knightstour]} {
if {![info exists widgetDemo]} { wm withdraw . }
set r [catch [linsert $argv 0 CreateGUI] err]
if {$r} {
tk_messageBox -icon error -title "Error" -message $err
}
if {![info exists widgetDemo]} { exit $r }
}
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