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#!/usr/bin/env python
#
# Copyright (c) 2007,2008,2009, Bjoern B. Brandenburg <bbb [at] cs.unc.edu>
#
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# * Neither the name of the copyright holder nor the
# names of its contributors may be used to endorse or promote products
# derived from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
"""
Simple bin-packing heuristics in Python.
Based on:
OPTIMIZATION THEORY
by Hubertus Th. Jongen, Klaus Meer, Eberhard Triesch
ISBN 1-4020-8099-9
KLUWER ACADEMIC PUBLISHERS
http://www.springerlink.com/content/h053786u87674865/
and:
http://york.cuny.edu/~malk/tidbits/tidbit-bin-packing.html
"""
id = lambda x: x
class DidNotFit(Exception):
def __init__(self, item):
self.item = item
def __str__(self):
return '%s could not be packed' % str(self.item)
def ignore(_):
pass
def report_failure(x):
raise DidNotFit(x)
def value(sets, weight=id):
return sum([sum([weight(x) for x in s]) for s in sets])
def next_fit(items, bins, capacity=1.0, weight=id, misfit=ignore,
empty_bin=list):
sets = [empty_bin() for _ in xrange(0, bins)]
cur = 0
sum = 0.0
for x in items:
c = weight(x)
while sum + c > capacity:
sum = 0.0
cur += 1
if cur == bins:
misfit(x)
return sets
sets[cur] += [x]
sum += c
return sets
def first_fit(items, bins, capacity=1.0, weight=id, misfit=ignore,
empty_bin=list):
sets = [empty_bin() for _ in xrange(0, bins)]
sums = [0.0 for _ in xrange(0, bins)]
for x in items:
c = weight(x)
for i in xrange(0, bins):
if sums[i] + c <= capacity:
sets[i] += [x]
sums[i] += c
break
else:
misfit(x)
return sets
def worst_fit(items, bins, capacity=1.0, weight=id, misfit=ignore,
empty_bin=list):
sets = [empty_bin() for _ in xrange(0, bins)]
sums = [0.0 for _ in xrange(0, bins)]
for x in items:
c = weight(x)
# pick the bin where the item will leave the most space
# after placing it, aka the bin with the least sum
candidates = [s for s in sums if s + c <= capacity]
if candidates:
# fits somewhere
i = sums.index(min(candidates))
sets[i] += [x]
sums[i] += c
else:
misfit(x)
return sets
def almost_worst_fit(items, bins, capacity=1.0, weight=id, misfit=ignore,
empty_bin=list):
sets = [empty_bin() for _ in xrange(0, bins)]
sums = [0.0 for _ in xrange(0, bins)]
for x in items:
c = weight(x)
# pick the bin where the item will leave almost the most space
# after placing it, aka the bin with the second to least sum
candidates = [s for s in sums if s + c <= capacity]
if candidates:
# fits somewhere
candidates.sort()
i = sums.index(candidates[1] if len(candidates) > 1 else candidates[0])
sets[i] += [x]
sums[i] += c
else:
misfit(x)
return sets
def best_fit(items, bins, capacity=1.0, weight=id, misfit=ignore,
empty_bin=list):
sets = [empty_bin() for _ in xrange(0, bins)]
sums = [0.0 for _ in xrange(0, bins)]
for x in items:
c = weight(x)
# find the first bin that is sufficiently large
idxs = range(0, bins)
idxs.sort(key=lambda i: sums[i], reverse=True)
for i in idxs:
if sums[i] + c <= capacity:
sets[i] += [x]
sums[i] += c
break
else:
misfit(x)
return sets
def any_fit(items, bins, capacity=1.0, weight=id, misfit=ignore,
empty_bin=list):
for h in [next_fit, first_fit, worst_fit, almost_worst_fit, best_fit]:
try:
sets = h(items, bins, capacity, weight, report_failure, empty_bin)
return sets
except DidNotFit as dnf:
pass
# if we get here, none of the heuristics worked
misfit(dnf.item)
# if we get here, misfit did not raise an exception => return something
return next_fit(items, bins, capacity, weight, misfit, empty_bin)
def decreasing(algorithm):
def alg_decreasing(items, bins, capacity=1.0, weight=id, *args, **kargs):
# don't clobber original items
items_sorted = list(items)
items_sorted.sort(key=weight, reverse=True)
return algorithm(items_sorted, bins, capacity, weight, *args, **kargs)
return alg_decreasing
next_fit_decreasing = decreasing(next_fit)
first_fit_decreasing = decreasing(first_fit)
worst_fit_decreasing = decreasing(worst_fit)
best_fit_decreasing = decreasing(best_fit)
almost_worst_fit_decreasing = decreasing(almost_worst_fit)
any_fit_decreasing = decreasing(any_fit)
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