def test_get_codes(self, d):
"""the sum of len(code) * freq_dict[code] is optimal, so it
must be invariant under permutation of the dictionary"""
# NB: this also tests huffman_tree indirectly
t = huffman_tree(d)
c1 = get_codes(t)
d2 = list(d.items())
shuffle(d2)
d2 = dict(d2)
t2 = huffman_tree(d2)
c2 = get_codes(t2)
self.assertEqual(sum([d[k] * len(c1[k]) for k in d]),
sum([d2[k] * len(c2[k]) for k in d2]))
def test_avg_length(self, d):
"""avg_length should return a float in the
interval [0, 8]"""
t = huffman_tree(d)
f = avg_length(t, d)
self.assertTrue(isinstance(f, float))
self.assertTrue(0 <= f <= 8.0)
def test_round_trip(self, b):
"""test inverting generate_compressed and generate_uncompressed"""
orig_text = b
freq = make_freq_dict(orig_text)
assume(len(freq) > 1)
tree = huffman_tree(freq)
codes = get_codes(tree)
compressed = generate_compressed(orig_text, codes)
uncompressed = generate_uncompressed(tree, compressed, len(orig_text))
assert orig_text == uncompressed
def test_number_nodes(self, d):
"""if the root is an interior node, it must be numbered
two less than the number of symbols"""
# a complete tree has one fewer interior nodes than
# it has leaves, and we are numbering from 0
# NB: this also tests huffman_tree indirectly
t = huffman_tree(d)
assume(not t.is_leaf())
count = len(d)
number_nodes(t)
self.assertEqual(count, t.number + 2)
def test_num_nodes_to_bytes(self, b):
"""num_nodes_to_bytes returns a bytes object that
has length 1 (since the number of internal nodes cannot
exceed 256)"""
# NB: also indirectly tests make_freq_dict and huffman_tree
d = make_freq_dict(b)
assume(len(d) > 1)
t = huffman_tree(d)
number_nodes(t)
n = num_nodes_to_bytes(t)
self.assertTrue(isinstance(n, bytes))
self.assertEqual(len(n), 1)
def test_generate_compressed(self, b):
"""generate_compressed should return a bytes
object that is no longer than the input bytes, and
the size of the compressed object should be
invariant under permuting the input"""
# NB: this also indirectly tests make_freq_dict, huffman_tree,
# and get_codes
d = make_freq_dict(b)
t = huffman_tree(d)
c = get_codes(t)
compressed = generate_compressed(b, c)
self.assertTrue(isinstance(compressed, bytes))
self.assertTrue(len(compressed) <= len(b))
l = list(b)
shuffle(l)
b = bytes(l)
d = make_freq_dict(b)
t = huffman_tree(d)
c = get_codes(t)
compressed2 = generate_compressed(b, c)
self.assertEqual(len(compressed2), len(compressed))
def test_tree_to_bytes(self, b):
"""tree_to_bytes generates a bytes representation of
a post-order traversal of a trees internal nodes"""
# Since each internal node requires 4 bytes to represent,
# and there are 1 fewer internal node than distinct symbols,
# the length of the bytes produced should be 4 times the
# length of the frequency dictionary, minus 4"""
# NB: also indirectly tests make_freq_dict, huffman_tree, and
# number_nodes
d = make_freq_dict(b)
assume(len(d) > 1)
t = huffman_tree(d)
number_nodes(t)
output_bytes = tree_to_bytes(t)
dictionary_length = len(d)
leaf_count = dictionary_length
self.assertEqual(4 * (leaf_count - 1), len(output_bytes))
def test_huffman_tree(self, d):
"""huffman_tree returns a non-leaf HuffmanNode"""
t = huffman_tree(d)
self.assertTrue(isinstance(t, HuffmanNode))
self.assertTrue(not t.is_leaf())