def test_knapsack_unbounded(self):
# wikipedia example for _unbounded
i1 = Item(2, 1)
i2 = Item(10, 4)
i3 = Item(1, 1)
i4 = Item(2, 2)
i5 = Item(4, 12)
self.assertEqual((36,[3,3,0,0,0]), knapsack_unbounded([i1,i2,i3,i4,i5], 15))
def test_knapsack_01(self):
# wikipedia example for _01
# Item (Value, Weight)
i1 = Item(2, 1)
i2 = Item(10, 4)
i3 = Item(1, 1)
i4 = Item(2, 2)
i5 = Item(4, 12)
self.assertEqual((15, [1,1,1,1,0]), knapsack_01([i1,i2,i3,i4,i5], 15))
def test_other_example(self):
# http://www.cs.princeton.edu/~wayne/cs423/lectures/approx-alg-4up.pdf
# Item (Value, Weight)
i1 = Item(1, 1)
i2 = Item(6, 2)
i3 = Item(18,5)
i4 = Item(22,6)
i5 = Item(28,7)
self.assertEqual((40,[0,0,1,1,0]), knapsack_01([i1,i2,i3,i4,i5], 11))
def test_knapsack_unbounded_for_approx(self):
# http://math.stackexchange.com/questions/720001/
# Item (Value, Weight)
i1 = Item (90, 9)
i2 = Item (19, 2)
i3 = Item (1, 1)
self.assertEqual((95,[0,5,0]), knapsack_unbounded([i1,i2,i3], 10))
# approximation chooses this one
self.assertEqual((91,[1,0,1]), knapsack_approximate([i1,i2,i3], 10))
def trials():
"""Conduct timing trials for sample values of W."""
# 103 207 4 2 523
a = 103
b = 207
c = 4
d = 2
items = []
# Item (Value, Weight)
for i in range(a, b, c):
items.append(Item(i, i))
items.append(Item(d * i + 1, d * i + 1))
maxBestTotal = 0
print('W', 'KnapsackUnboundedTime', 'KnapsackApproximateTime',
'ActualAnswer', 'ApproximateAnswer')
diffTotal = 0
W = 10
numReps = 1
numTrials = 1
while W <= 65536:
itemSet = 'items=[]\n'
for item in items:
itemSet = itemSet + 'items.append(Item(' + str(
item.value) + ',' + str(item.weight) + '))\n'
setup = '''
from adk.knapsack import knapsack_unbounded, knapsack_01, knapsack_approximate, Item, record_best
import random\n''' + itemSet + '''
'''
executeUnbound = '''
record_best (knapsack_unbounded(items,''' + str(W) + ''')[0])
'''
totalUnbound = min(
timeit.Timer(executeUnbound,
setup=setup).repeat(numReps, numTrials))
executeApproximate = '''
record_best (knapsack_approximate(items,''' + str(W) + ''')[0])
'''
totalApproximate = min(
timeit.Timer(executeApproximate,
setup=setup).repeat(numReps, numTrials))
print(W, '{0:.5f}'.format(totalUnbound),
'{0:.5f}'.format(totalApproximate), record_best())
W = W * 2 + 1
if diffTotal > maxBestTotal:
print(a, b, c, d, diffTotal)
maxBestTotal = diffTotal
def reportOne():
"""
To see the generates matrices, modify the knapsack methods temporarily to
print out the matrices.
"""
items = [Item(4, 4), Item(8, 8), Item(9, 9), Item(10, 10)]
W = 33
print("Knapsack Unbounded")
w_un = knapsack_unbounded(items[:], W)
print(w_un)
print("Knapsack Approximate")
w_ap = knapsack_approximate(items[:], W)
print(w_ap)
print("Knapsack 0/1")
w_01 = knapsack_01(items[:], W)
print(w_01)
def trials():
"""
Locate knapsack items that has different results for :
1) knapsack_unbounded
2) knapsack_01
3) knapsack_approximate
Found this nice example:
W = 33
(33, [6, 0, 0, 1]) (32, [8, 0, 0, 0]) (31, [1, 1, 1, 1])
(val= 4 , weight= 4
(val= 8 , weight= 8
(val= 10 , weight= 10
(val= 9 , weight= 9
"""
# 103 207 4 2 523
for t in range(10000):
items = []
# Item (Value, Weight)
for _ in range(5):
i = random.randint(3, 11)
items.append(Item(i, i))
W = 33
w_un = knapsack_unbounded(items[:], W)
w_ap = knapsack_approximate(items[:], W)
w_01 = knapsack_01(items[:], W)
if w_un[0] != w_ap[0] and w_ap[0] != w_01[0] and w_un[0] != w_01[0]:
print(w_un, w_ap, w_01)
for i in items:
print('(val=', i.value, ', weight=', i.weight)
return
def trials():
"""
Search small space to determine input set to knapsack that offers greatest
difference between dynamic programming and approximate. Once computed, use
these values in adk.book.chapter11.py
"""
# 83 250 4 2 457
# 103 207 4 2 523
a = 23
b = 56
c = 8
d = 5
maxBestTotal = 0
for a in range(23, 113, 10):
for b2 in range(1, 8):
b = a * b2 + 1
for c in [4, 8, 16, 32, 64]:
for d in range(2, 7):
diffTotal = 0
W = 10
numReps = 1
numTrials = 1
while W <= 65536:
items = []
# Item (Value, Weight)
for i in range(a, b, c):
items.append(Item(i, i))
items.append(Item(d * i + 1, d * i + 1))
itemSet = 'items=[]\n'
for item in items:
itemSet = itemSet + 'items.append(Item(' + str(
item.value) + ',' + str(item.weight) + '))\n'
#itemSet = itemSet + 'items.append(Item(' + str(W//4) + "," + str(W//4) + '))\n'
setup = '''
from adk.knapsack import knapsack_unbounded, knapsack_01, knapsack_approximate, Item, record_best
import random\n''' + itemSet + '''
'''
executeUnbound = '''
record_best (knapsack_unbounded(items,''' + str(W) + ''')[0])
'''
totalUnbound = min(
timeit.Timer(executeUnbound, setup=setup).repeat(
numReps, numTrials))
executeApproximate = '''
record_best (knapsack_approximate(items,''' + str(W) + ''')[0])
'''
totalApproximate = min(
timeit.Timer(executeApproximate,
setup=setup).repeat(
numReps, numTrials))
#print (W, totalUnbound, totalApproximate, record_best())
best2 = record_best()
if len(best2) > 0:
diffTotal += best2[0] - best2[1]
W = W * 2 + 1
if diffTotal > maxBestTotal:
print(a, b, c, d, diffTotal)
maxBestTotal = diffTotal