def test_Mix3(self):
"""Three Levels."""
frequencies = PartiallySortedArray([8] * 8 + [255, 1024])
frequencies, externals, internals = INITIALIZE(frequencies)
self.assertEqual(nodeListToWeightList(internals), [16])
self.assertEqual(nodeListToWeightList(externals),
[8] * 6 + [255, 1024])
frequencies, externals, internals = GroupExternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [16] * 4)
self.assertEqual(nodeListToWeightList(externals), [255, 1024])
frequencies, externals, internals = DockInternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [64])
self.assertEqual(nodeListToWeightList(externals), [255, 1024])
frequencies, externals, internals = MixInternalWithExternal(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [319])
self.assertEqual(nodeListToWeightList(externals), [1024])
frequencies, externals, internals = GroupExternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [319])
self.assertEqual(nodeListToWeightList(externals), [1024])
frequencies, externals, internals = DockInternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [319])
self.assertEqual(nodeListToWeightList(externals), [1024])
frequencies, externals, internals = MixInternalWithExternal(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [1343])
self.assertEqual(nodeListToWeightList(externals), [])
def test_TREE7(self):
"""Alpha Equal One. Three Equal Weights."""
W = PartiallySortedArray([10] * 3)
T = gdmCodeTree(W)
self.assertEqual(str(T), "(30,[10],(20,[select(0)],[select(1)]))")
L = T.depths()
self.assertEqual(L, [1, 2, 2])
def test_TREE5(self):
"""Alpha Equal One. Sixteen Equal Weights."""
W = PartiallySortedArray([10] * 16)
T = gdmCodeTree(W)
self.assertEqual(T.weight(), W.rangeSum(0, len(W)))
L = T.depths()
self.assertEqual(L, [4] * 16)
def test_TREE3(self):
"""Alpha Equal One. Two Weights."""
W = PartiallySortedArray([10, 10])
T = gdmCodeTree(W)
self.assertEqual(str(T), "(20,[select(0)],[select(1)])")
L = T.depths()
self.assertEqual(L, [1] * 2)
def test_TREE10(self):
"""Exponential Sequence."""
W = PartiallySortedArray([1, 2, 4])
T = dvlCodeTree(W)
self.assertEqual(str(T), '(7,(3,[select(0)],[select(1)]),[4])')
L = T.depths()
self.assertEqual(sorted(L), [1, 2, 2])
def test_TREE8(self):
"""Alpha Equal One. Three Similar Weights."""
W = PartiallySortedArray([12, 11, 10])
T = gdmCodeTree(W)
self.assertEqual(str(T), "(33,[12],(21,[select(0)],[select(1)]))")
L = T.depths()
self.assertEqual(L, [1, 2, 2])
def test_TREE10(self):
"""Exponential Sequence."""
W = PartiallySortedArray([1, 2, 4])
T = gdmCodeTree(W)
self.assertEqual(T.toStringWithAllWeightsCalculated(),
'(7,(3,[1],[2]),[4])')
L = T.depths()
self.assertEqual(sorted(L), [1, 2, 2])
def test_INIT1(self):
"""Alpha Equal One. Two Weights."""
frequencies = PartiallySortedArray([10, 10])
frequencies, externals, internals = INITIALIZE(frequencies)
self.assertEqual(nodeListToString(internals),
'[(rangeSum(0,2),[select(0)],[select(1)])]')
self.assertEqual(nodeListToWeightList(internals), [20])
self.assertEqual(nodeListToWeightList(externals), [])
def test_TREE4(self):
"""Alpha Equal One. Four Equal Weights."""
W = PartiallySortedArray([10] * 4)
T = gdmCodeTree(W)
self.assertEqual(T.toStringWithAllWeightsCalculated(),
'(40,(20,[10],[10]),(20,[10],[10]))')
L = T.depths()
self.assertEqual(L, [2] * 4)
def test_INIT3(self):
"""Exponential Sequence."""
frequencies = PartiallySortedArray(
[10, 20, 40, 80, 160, 320, 640, 1280, 2560])
frequencies, externals, internals = INITIALIZE(frequencies)
self.assertEqual(nodeListToString(internals),
'[(rangeSum(0,2),[select(0)],[select(1)])]')
self.assertEqual(nodeListToWeightList(internals), [30])
self.assertEqual(nodeListToWeightList(externals),
[40, 80, 160, 320, 640, 1280, 2560])
def test_TREE12(self):
"""Exponential Sequence."""
W = PartiallySortedArray([1, 2, 4, 8, 16, 32, 64, 128, 256])
T = gdmCodeTree(W)
self.assertEqual(
T.toStringWithAllWeightsCalculated(),
'(511,(255,(127,(63,(31,(15,(7,(3,[1],[2]),[4]),[8]),[16]),[32]),[64]),[128]),[256])'
)
L = T.depths()
self.assertEqual(sorted(L), [1, 2, 3, 4, 5, 6, 7, 8, 8])
def test_DockInternals1(self):
"""Number of nodes to dock equal to a power of three."""
frequencies = PartiallySortedArray([8] * 4 + [32])
frequencies, externals, internals = INITIALIZE(frequencies)
frequencies, externals, internals = GroupExternals(
frequencies, externals, internals)
frequencies, externals, internals = DockInternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [32])
self.assertEqual(nodeListToWeightList(externals), [32])
def test_DockInternals2(self):
"""Number of nodes to dock is a power of two minus one."""
frequencies = PartiallySortedArray([14, 13, 12, 11, 10, 9, 8, 256])
frequencies, externals, internals = INITIALIZE(frequencies)
frequencies, externals, internals = GroupExternals(
frequencies, externals, internals)
frequencies, externals, internals = DockInternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [77])
self.assertEqual(nodeListToWeightList(externals), [256])
def test_TREE4(self):
"""Alpha Equal One. Four Equal Weights."""
W = PartiallySortedArray([10] * 4)
T = dvlCodeTree(W)
self.assertEqual(
str(T),
'(40,(20,[select(0)],[select(1)]),(rangeSum(2,4),[select(2)],[select(3)]))'
)
L = T.depths()
self.assertEqual(L, [2] * 4)
def test_GroupExternals1(self):
"""Basic Example.
"""
frequencies = PartiallySortedArray([10, 10, 11, 13, 14, 15, 20, 30])
frequencies, externals, internals = INITIALIZE(frequencies)
self.assertEqual(nodeListToWeightList(internals), [20])
self.assertEqual(nodeListToWeightList(externals),
[11, 13, 14, 15, 20, 30])
frequencies, externals, internals = GroupExternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [24, 29, 40])
self.assertEqual(nodeListToWeightList(externals), [30])
def initialize(self, weights, D):
self.weights = PartiallySortedArray(weights)
self.D = D
self.N = len(weights)
n0 = (self.N - 2) % (self.D - 1) + 2 # 2 <= n0 <= D
self.externals = [
ExternalNode(self.weights, i)
for i in range(n0, len(self.weights))
] # N - n0 external nodes
self.internals = [
InternalNode(self.weights,
[ExternalNode(self.weights, i) for i in range(0, n0)])
] #internal with n0 external nodes
def gdm(frequencies):
"""Given a sorted list of weights, return an array with the code lengths of an optimal prefix free code according to the GDM algorithm.
>>> print(gdm([1]*4+[8]*3))
[4, 4, 4, 4, 2, 2, 2]
"""
# Degenerated cases
if len(frequencies) == 0 :
return []
elif len(frequencies)==1:
return [0]
elif len(frequencies)==2:
return [1,1]
codeTree = gdmCodeTree(PartiallySortedArray(frequencies))
codeLengths = codeTree.depths()
return codeLengths
def dvl(frequencies):
"""Given a sorted list of weights, return an array with the code lengths of an optimal prefix free code according to the Deferred van Leeuwen's algorithm.
>>> print(dvl([1,1,1,1]))
[2, 2, 2, 2]
"""
# Degenerated cases
if len(frequencies) == 0:
return []
elif len(frequencies) == 1:
return [0]
elif len(frequencies) == 2:
return [1, 1]
codeTree = dvlCodeTree(PartiallySortedArray(frequencies))
codeLengths = codeTree.depths()
return codeLengths
def test_Mix1(self):
"""All weights equal."""
frequencies = PartiallySortedArray([8] * 8)
frequencies, externals, internals = INITIALIZE(frequencies)
self.assertEqual(nodeListToWeightList(internals), [16])
self.assertEqual(nodeListToWeightList(externals), [8] * 6)
frequencies, externals, internals = GroupExternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [16] * 4)
self.assertEqual(nodeListToWeightList(externals), [])
frequencies, externals, internals = DockInternals(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [16] * 4)
self.assertEqual(nodeListToWeightList(externals), [])
frequencies, externals, internals = MixInternalWithExternal(
frequencies, externals, internals)
self.assertEqual(nodeListToWeightList(internals), [16] * 4)
self.assertEqual(nodeListToWeightList(externals), [])
def test_TREE1(self):
"""Empty input."""
frequencies = PartiallySortedArray([])
self.assertEqual(dvlCodeTree(frequencies), None)
def test_TREE6(self):
"""Alpha Equal One. Eight Similar Weights."""
W = PartiallySortedArray([10, 11, 12, 13, 14, 15, 16, 17])
T = gdmCodeTree(W)
L = T.depths()
self.assertEqual(L, [3] * 8)
def test_TREE2(self):
"""Alpha Equal One. Singleton input."""
frequencies = PartiallySortedArray([10])
self.assertEqual(dvlCodeTree(frequencies),
ExternalNode(frequencies, 0))
def test_TREE9(self):
"""Alpha Equal Two. Single very small weight."""
W = PartiallySortedArray([1] + [8] * 3)
T = gdmCodeTree(W)
L = T.depths()
self.assertEqual(L, [2] * 4)