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git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@14377 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2007-12-21 02:31:11 +00:00

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#!/usr/bin/env ruby
#
# The Computer Language Shootout
# http://shootout.alioth.debian.org
# contributed by Kevin Barnes (Ruby novice)
# PROGRAM: the main body is at the bottom.
# 1) read about the problem here: http://www-128.ibm.com/developerworks/java/library/j-javaopt/
# 2) see how I represent a board as a bitmask by reading the blank_board comments
# 3) read as your mental paths take you
def print *args
end
# class to represent all information about a particular rotation of a particular piece
class Rotation
# an array (by location) containing a bit mask for how the piece maps at the given location.
# if the rotation is invalid at that location the mask will contain false
attr_reader :start_masks
# maps a direction to a relative location. these differ depending on whether it is an even or
# odd row being mapped from
@@rotation_even_adder = { :west => -1, :east => 1, :nw => -7, :ne => -6, :sw => 5, :se => 6 }
@@rotation_odd_adder = { :west => -1, :east => 1, :nw => -6, :ne => -5, :sw => 6, :se => 7 }
def initialize( directions )
@even_offsets, @odd_offsets = normalize_offsets( get_values( directions ))
@even_mask = mask_for_offsets( @even_offsets)
@odd_mask = mask_for_offsets( @odd_offsets)
@start_masks = Array.new(60)
# create the rotational masks by placing the base mask at the location and seeing if
# 1) it overlaps the boundries and 2) it produces a prunable board. if either of these
# is true the piece cannot be placed
0.upto(59) do | offset |
mask = is_even(offset) ? (@even_mask << offset) : (@odd_mask << offset)
if (blank_board & mask == 0 && !prunable(blank_board | mask, 0, true)) then
imask = compute_required( mask, offset)
@start_masks[offset] = [ mask, imask, imask | mask ]
else
@start_masks[offset] = false
end
end
end
def compute_required( mask, offset )
board = blank_board
0.upto(offset) { | i | board |= 1 << i }
board |= mask
return 0 if (!prunable(board | mask, offset))
board = flood_fill(board,58)
count = 0
imask = 0
0.upto(59) do | i |
if (board[i] == 0) then
imask |= (1 << i)
count += 1
end
end
(count > 0 && count < 5) ? imask : 0
end
def flood_fill( board, location)
return board if (board[location] == 1)
board |= 1 << location
row, col = location.divmod(6)
board = flood_fill( board, location - 1) if (col > 0)
board = flood_fill( board, location + 1) if (col < 4)
if (row % 2 == 0) then
board = flood_fill( board, location - 7) if (col > 0 && row > 0)
board = flood_fill( board, location - 6) if (row > 0)
board = flood_fill( board, location + 6) if (row < 9)
board = flood_fill( board, location + 5) if (col > 0 && row < 9)
else
board = flood_fill( board, location - 5) if (col < 4 && row > 0)
board = flood_fill( board, location - 6) if (row > 0)
board = flood_fill( board, location + 6) if (row < 9)
board = flood_fill( board, location + 7) if (col < 4 && row < 9)
end
board
end
# given a location, produces a list of relative locations covered by the piece at this rotation
def offsets( location)
if is_even( location) then
@even_offsets.collect { | value | value + location }
else
@odd_offsets.collect { | value | value + location }
end
end
# returns a set of offsets relative to the top-left most piece of the rotation (by even or odd rows)
# this is hard to explain. imagine we have this partial board:
# 0 0 0 0 0 x [positions 0-5]
# 0 0 1 1 0 x [positions 6-11]
# 0 0 1 0 0 x [positions 12-17]
# 0 1 0 0 0 x [positions 18-23]
# 0 1 0 0 0 x [positions 24-29]
# 0 0 0 0 0 x [positions 30-35]
# ...
# The top-left of the piece is at position 8, the
# board would be passed as a set of positions (values array) containing [8,9,14,19,25] not necessarily in that
# sorted order. Since that array starts on an odd row, the offsets for an odd row are: [0,1,6,11,17] obtained
# by subtracting 8 from everything. Now imagine the piece shifted up and to the right so it's on an even row:
# 0 0 0 1 1 x [positions 0-5]
# 0 0 1 0 0 x [positions 6-11]
# 0 0 1 0 0 x [positions 12-17]
# 0 1 0 0 0 x [positions 18-23]
# 0 0 0 0 0 x [positions 24-29]
# 0 0 0 0 0 x [positions 30-35]
# ...
# Now the positions are [3,4,8,14,19] which after subtracting the lowest value (3) gives [0,1,5,11,16] thus, the
# offsets for this particular piece are (in even, odd order) [0,1,5,11,16],[0,1,6,11,17] which is what
# this function would return
def normalize_offsets( values)
min = values.min
even_min = is_even(min)
other_min = even_min ? min + 6 : min + 7
other_values = values.collect do | value |
if is_even(value) then
value + 6 - other_min
else
value + 7 - other_min
end
end
values.collect! { | value | value - min }
if even_min then
[values, other_values]
else
[other_values, values]
end
end
# produce a bitmask representation of an array of offset locations
def mask_for_offsets( offsets )
mask = 0
offsets.each { | value | mask = mask + ( 1 << value ) }
mask
end
# finds a "safe" position that a position as described by a list of directions can be placed
# without falling off any edge of the board. the values returned a location to place the first piece
# at so it will fit after making the described moves
def start_adjust( directions )
south = east = 0;
directions.each do | direction |
east += 1 if ( direction == :sw || direction == :nw || direction == :west )
south += 1 if ( direction == :nw || direction == :ne )
end
south * 6 + east
end
# given a set of directions places the piece (as defined by a set of directions) on the board at
# a location that will not take it off the edge
def get_values ( directions )
start = start_adjust(directions)
values = [ start ]
directions.each do | direction |
if (start % 12 >= 6) then
start += @@rotation_odd_adder[direction]
else
start += @@rotation_even_adder[direction]
end
values += [ start ]
end
# some moves take you back to an existing location, we'll strip duplicates
values.uniq
end
end
# describes a piece and caches information about its rotations to as to be efficient for iteration
# ATTRIBUTES:
# rotations -- all the rotations of the piece
# type -- a numeic "name" of the piece
# masks -- an array by location of all legal rotational masks (a n inner array) for that location
# placed -- the mask that this piece was last placed at (not a location, but the actual mask used)
class Piece
attr_reader :rotations, :type, :masks
attr_accessor :placed
# transform hashes that change one direction into another when you either flip or rotate a set of directions
@@flip_converter = { :west => :west, :east => :east, :nw => :sw, :ne => :se, :sw => :nw, :se => :ne }
@@rotate_converter = { :west => :nw, :east => :se, :nw => :ne, :ne => :east, :sw => :west, :se => :sw }
def initialize( directions, type )
@type = type
@rotations = Array.new();
@map = {}
generate_rotations( directions )
directions.collect! { | value | @@flip_converter[value] }
generate_rotations( directions )
# creates the masks AND a map that returns [location, rotation] for any given mask
# this is used when a board is found and we want to draw it, otherwise the map is unused
@masks = Array.new();
0.upto(59) do | i |
even = true
@masks[i] = @rotations.collect do | rotation |
mask = rotation.start_masks[i]
@map[mask[0]] = [ i, rotation ] if (mask)
mask || nil
end
@masks[i].compact!
end
end
# rotates a set of directions through all six angles and adds a Rotation to the list for each one
def generate_rotations( directions )
6.times do
rotations.push( Rotation.new(directions))
directions.collect! { | value | @@rotate_converter[value] }
end
end
# given a board string, adds this piece to the board at whatever location/rotation
# important: the outbound board string is 5 wide, the normal location notation is six wide (padded)
def fill_string( board_string)
location, rotation = @map[@placed]
rotation.offsets(location).each do | offset |
row, col = offset.divmod(6)
board_string[ row*5 + col, 1 ] = @type.to_s
end
end
end
# a blank bit board having this form:
#
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 0 0 0 0 0 1
# 1 1 1 1 1 1
#
# where left lest significant bit is the top left and the most significant is the lower right
# the actual board only consists of the 0 places, the 1 places are blockers to keep things from running
# off the edges or bottom
def blank_board
0b111111100000100000100000100000100000100000100000100000100000100000
end
def full_board
0b111111111111111111111111111111111111111111111111111111111111111111
end
# determines if a location (bit position) is in an even row
def is_even( location)
(location % 12) < 6
end
# support function that create three utility maps:
# $converter -- for each row an array that maps a five bit row (via array mapping)
# to the a a five bit representation of the bits below it
# $bit_count -- maps a five bit row (via array mapping) to the number of 1s in the row
# @@new_regions -- maps a five bit row (via array mapping) to an array of "region" arrays
# a region array has three values the first is a mask of bits in the region,
# the second is the count of those bits and the third is identical to the first
# examples:
# 0b10010 => [ 0b01100, 2, 0b01100 ], [ 0b00001, 1, 0b00001]
# 0b01010 => [ 0b10000, 1, 0b10000 ], [ 0b00100, 1, 0b00100 ], [ 0b00001, 1, 0b00001]
# 0b10001 => [ 0b01110, 3, 0b01110 ]
def create_collector_support
odd_map = [0b11, 0b110, 0b1100, 0b11000, 0b10000]
even_map = [0b1, 0b11, 0b110, 0b1100, 0b11000]
all_odds = Array.new(0b100000)
all_evens = Array.new(0b100000)
bit_counts = Array.new(0b100000)
new_regions = Array.new(0b100000)
0.upto(0b11111) do | i |
bit_count = odd = even = 0
0.upto(4) do | bit |
if (i[bit] == 1) then
bit_count += 1
odd |= odd_map[bit]
even |= even_map[bit]
end
end
all_odds[i] = odd
all_evens[i] = even
bit_counts[i] = bit_count
new_regions[i] = create_regions( i)
end
$converter = []
10.times { | row | $converter.push((row % 2 == 0) ? all_evens : all_odds) }
$bit_counts = bit_counts
$regions = new_regions.collect { | set | set.collect { | value | [ value, bit_counts[value], value] } }
end
# determines if a board is punable, meaning that there is no possibility that it
# can be filled up with pieces. A board is prunable if there is a grouping of unfilled spaces
# that are not a multiple of five. The following board is an example of a prunable board:
# 0 0 1 0 0
# 0 1 0 0 0
# 1 1 0 0 0
# 0 1 0 0 0
# 0 0 0 0 0
# ...
#
# This board is prunable because the top left corner is only 3 bits in area, no piece will ever fit it
# parameters:
# board -- an initial bit board (6 bit padded rows, see blank_board for format)
# location -- starting location, everything above and to the left is already full
# slotting -- set to true only when testing initial pieces, when filling normally
# additional assumptions are possible
#
# Algorithm:
# The algorithm starts at the top row (as determined by location) and iterates a row at a time
# maintainng counts of active open areas (kept in the collector array) each collector contains
# three values at the start of an iteration:
# 0: mask of bits that would be adjacent to the collector in this row
# 1: the number of bits collected so far
# 2: a scratch space starting as zero, but used during the computation to represent
# the empty bits in the new row that are adjacent (position 0)
# The exact procedure is described in-code
def prunable( board, location, slotting = false)
collectors = []
# loop accross the rows
(location / 6).to_i.upto(9) do | row_on |
# obtain a set of regions representing the bits of the curent row.
regions = $regions[(board >> (row_on * 6)) & 0b11111]
converter = $converter[row_on]
# track the number of collectors at the start of the cycle so that
# we don't compute against newly created collectors, only existing collectors
initial_collector_count = collectors.length
# loop against the regions. For each region of the row
# we will see if it connects to one or more existing collectors.
# if it connects to 1 collector, the bits from the region are added to the
# bits of the collector and the mask is placed in collector[2]
# If the region overlaps more than one collector then all the collectors
# it overlaps with are merged into the first one (the others are set to nil in the array)
# if NO collectors are found then the region is copied as a new collector
regions.each do | region |
collector_found = nil
region_mask = region[2]
initial_collector_count.times do | collector_num |
collector = collectors[collector_num]
if (collector) then
collector_mask = collector[0]
if (collector_mask & region_mask != 0) then
if (collector_found) then
collector_found[0] |= collector_mask
collector_found[1] += collector[1]
collector_found[2] |= collector[2]
collectors[collector_num] = nil
else
collector_found = collector
collector[1] += region[1]
collector[2] |= region_mask
end
end
end
end
if (collector_found == nil) then
collectors.push(Array.new(region))
end
end
# check the existing collectors, if any collector overlapped no bits in the region its [2] value will
# be zero. The size of any such reaason is tested if it is not a muliple of five true is returned since
# the board is prunable. if it is a multiple of five it is removed.
# Collector that are still active have a new adjacent value [0] set based n the matched bits
# and have [2] cleared out for the next cycle.
collectors.length.times do | collector_num |
collector = collectors[collector_num]
if (collector) then
if (collector[2] == 0) then
return true if (collector[1] % 5 != 0)
collectors[collector_num] = nil
else
# if a collector matches all bits in the row then we can return unprunable early for the
# follwing reasons:
# 1) there can be no more unavailable bits bince we fill from the top left downward
# 2) all previous regions have been closed or joined so only this region can fail
# 3) this region must be good since there can never be only 1 region that is nuot
# a multiple of five
# this rule only applies when filling normally, so we ignore the rule if we are "slotting"
# in pieces to see what configurations work for them (the only other time this algorithm is used).
return false if (collector[2] == 0b11111 && !slotting)
collector[0] = converter[collector[2]]
collector[2] = 0
end
end
end
# get rid of all the empty converters for the next round
collectors.compact!
end
return false if (collectors.length <= 1) # 1 collector or less and the region is fine
collectors.any? { | collector | (collector[1] % 5) != 0 } # more than 1 and we test them all for bad size
end
# creates a region given a row mask. see prunable for what a "region" is
def create_regions( value )
regions = []
cur_region = 0
5.times do | bit |
if (value[bit] == 0) then
cur_region |= 1 << bit
else
if (cur_region != 0 ) then
regions.push( cur_region)
cur_region = 0;
end
end
end
regions.push(cur_region) if (cur_region != 0)
regions
end
# find up to the counted number of solutions (or all solutions) and prints the final result
def find_all
find_top( 1)
find_top( 0)
print_results
end
# show the board
def print_results
print "#{@boards_found} solutions found\n\n"
print_full_board( @min_board)
print "\n"
print_full_board( @max_board)
print "\n"
end
# finds solutions. This special version of the main function is only used for the top level
# the reason for it is basically to force a particular ordering on how the rotations are tested for
# the first piece. It is called twice, first looking for placements of the odd rotations and then
# looking for placements of the even locations.
#
# WHY?
# Since any found solution has an inverse we want to maximize finding solutions that are not already found
# as an inverse. The inverse will ALWAYS be 3 one of the piece configurations that is exactly 3 rotations away
# (an odd number). Checking even vs odd then produces a higher probability of finding more pieces earlier
# in the cycle. We still need to keep checking all the permutations, but our probability of finding one will
# diminsh over time. Since we are TOLD how many to search for this lets us exit before checking all pieces
# this bennifit is very great when seeking small numbers of solutions and is 0 when looking for more than the
# maximum number
def find_top( rotation_skip)
board = blank_board
(@pieces.length-1).times do
piece = @pieces.shift
piece.masks[0].each do | mask, imask, cmask |
if ((rotation_skip += 1) % 2 == 0) then
piece.placed = mask
find( 1, 1, board | mask)
end
end
@pieces.push(piece)
end
piece = @pieces.shift
@pieces.push(piece)
end
# the normail find routine, iterates through the available pieces, checks all rotations at the current location
# and adds any boards found. depth is acheived via recursion. the overall approach is described
# here: http://www-128.ibm.com/developerworks/java/library/j-javaopt/
# parameters:
# start_location -- where to start looking for place for the next piece at
# placed -- number of pieces placed
# board -- current state of the board
#
# see in-code comments
def find( start_location, placed, board)
# find the next location to place a piece by looking for an empty bit
while board[start_location] == 1
start_location += 1
end
@pieces.length.times do
piece = @pieces.shift
piece.masks[start_location].each do | mask, imask, cmask |
if ( board & cmask == imask) then
piece.placed = mask
if (placed == 9) then
add_board
else
find( start_location + 1, placed + 1, board | mask)
end
end
end
@pieces.push(piece)
end
end
# print the board
def print_full_board( board_string)
10.times do | row |
print " " if (row % 2 == 1)
5.times do | col |
print "#{board_string[row*5 + col,1]} "
end
print "\n"
end
end
# when a board is found we "draw it" into a string and then flip that string, adding both to
# the list (hash) of solutions if they are unique.
def add_board
board_string = "99999999999999999999999999999999999999999999999999"
@all_pieces.each { | piece | piece.fill_string( board_string ) }
save( board_string)
save( board_string.reverse)
end
# adds a board string to the list (if new) and updates the current best/worst board
def save( board_string)
if (@all_boards[board_string] == nil) then
@min_board = board_string if (board_string < @min_board)
@max_board = board_string if (board_string > @max_board)
@all_boards.store(board_string,true)
@boards_found += 1
# the exit motif is a time saver. Ideally the function should return, but those tests
# take noticable time (performance).
if (@boards_found == @stop_count) then
print_results
exit(0)
end
end
end
##
## MAIN BODY :)
##
create_collector_support
@pieces = [
Piece.new( [ :nw, :ne, :east, :east ], 2),
Piece.new( [ :ne, :se, :east, :ne ], 7),
Piece.new( [ :ne, :east, :ne, :nw ], 1),
Piece.new( [ :east, :sw, :sw, :se ], 6),
Piece.new( [ :east, :ne, :se, :ne ], 5),
Piece.new( [ :east, :east, :east, :se ], 0),
Piece.new( [ :ne, :nw, :se, :east, :se ], 4),
Piece.new( [ :se, :se, :se, :west ], 9),
Piece.new( [ :se, :se, :east, :se ], 8),
Piece.new( [ :east, :east, :sw, :se ], 3)
];
@all_pieces = Array.new( @pieces)
@min_board = "99999999999999999999999999999999999999999999999999"
@max_board = "00000000000000000000000000000000000000000000000000"
@stop_count = ARGV[0].to_i || 2089
@all_boards = {}
@boards_found = 0
find_all ######## DO IT!!!
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