def extract(self):
"""
Extract root element of the Heap.
Returns
=======
root_element : TreeNode
The TreeNode at the root of the heap,
if the heap is not empty.
None
If the heap is empty.
"""
if self._last_pos_filled == -1:
return None
else:
element_to_be_extracted = TreeNode(self.heap[0].key,
self.heap[0].data)
self._swap(0, self._last_pos_filled)
self.heap[self._last_pos_filled] = TreeNode(
float('inf') if self.heap_property == 'min' else float('-inf'),
None)
self._heapify(0)
self.heap.pop()
self._last_pos_filled -= 1
return element_to_be_extracted
def insert(self, key, data=None):
"""
Insert a new element to the heap according to heap property.
Parameters
==========
key
The key for comparison.
data
The data to be inserted.
Returns
=======
None
"""
new_node = TreeNode(key, data)
self.heap.append(new_node)
self._last_pos_filled += 1
i = self._last_pos_filled
self.heap[i]._leftmost, self.heap[
i]._rightmost = self.d * i + 1, self.d * i + self.d
while True:
parent = (i - 1) // self.d
if i == 0 or self._comp(self.heap[parent].key, self.heap[i].key):
break
else:
self._swap(i, parent)
i = parent
def test_BinaryHeap():
max_heap = BinaryHeap(heap_property="max")
assert max_heap.extract() is None
max_heap.insert(100, 100)
max_heap.insert(19, 19)
max_heap.insert(36, 36)
max_heap.insert(17, 17)
max_heap.insert(3, 3)
max_heap.insert(25, 25)
max_heap.insert(1, 1)
max_heap.insert(2, 2)
max_heap.insert(7, 7)
assert str(max_heap) == \
("[(1, 100, 100, 2), (3, 19, 19, 4), "
"(5, 36, 36, 6), (7, 17, 17, 8), "
"(None, 3, 3, None), (None, 25, 25, None), "
"(None, 1, 1, None), (None, 2, 2, None), (None, 7, 7, None)]")
expected_extracted_element = max_heap.heap[0].key
assert max_heap.extract().key == expected_extracted_element
expected_sorted_elements = [36, 25, 19, 17, 7, 3, 2, 1]
sorted_elements = []
for _ in range(8):
sorted_elements.append(max_heap.extract().key)
assert expected_sorted_elements == sorted_elements
elements = [
TreeNode(7, 7),
TreeNode(25, 25),
TreeNode(100, 100),
TreeNode(1, 1),
TreeNode(2, 2),
TreeNode(3, 3),
TreeNode(17, 17),
TreeNode(19, 19),
TreeNode(36, 36)
]
min_heap = BinaryHeap(elements=elements, heap_property="min")
expected_extracted_element = min_heap.heap[0].key
assert min_heap.extract().key == expected_extracted_element
expected_sorted_elements = [2, 3, 7, 17, 19, 25, 36, 100]
sorted_elements = [min_heap.extract().key for _ in range(8)]
assert expected_sorted_elements == sorted_elements
def test_TernaryHeap():
max_heap = TernaryHeap(heap_property="max")
assert raises(IndexError, lambda: max_heap.extract())
max_heap.insert(100, 100)
max_heap.insert(19, 19)
max_heap.insert(36, 36)
max_heap.insert(17, 17)
max_heap.insert(3, 3)
max_heap.insert(25, 25)
max_heap.insert(1, 1)
max_heap.insert(2, 2)
max_heap.insert(7, 7)
assert str(max_heap) == \
('[(100, 100, [1, 2, 3]), (25, 25, [4, 5, 6]), '
'(36, 36, [7, 8]), (17, 17, []), '
'(3, 3, []), (19, 19, []), (1, 1, []), '
'(2, 2, []), (7, 7, [])]')
assert max_heap.extract().key == 100
expected_sorted_elements = [36, 25, 19, 17, 7, 3, 2, 1]
sorted_elements = []
for _ in range(8):
sorted_elements.append(max_heap.extract().key)
assert expected_sorted_elements == sorted_elements
elements = [
TreeNode(7, 7),
TreeNode(25, 25),
TreeNode(100, 100),
TreeNode(1, 1),
TreeNode(2, 2),
TreeNode(3, 3),
TreeNode(17, 17),
TreeNode(19, 19),
TreeNode(36, 36)
]
min_heap = TernaryHeap(elements=DynamicOneDimensionalArray(
TreeNode, 9, elements),
heap_property="min")
expected_extracted_element = min_heap.heap[0].key
assert min_heap.extract().key == expected_extracted_element
expected_sorted_elements = [2, 3, 7, 17, 19, 25, 36, 100]
sorted_elements = [min_heap.extract().key for _ in range(8)]
assert expected_sorted_elements == sorted_elements
def test_DHeap():
assert raises(ValueError, lambda: DHeap(heap_property="none", d=4))
max_heap = DHeap(heap_property="max", d=5)
assert max_heap.extract() is None
max_heap.insert(100, 100)
max_heap.insert(19, 19)
max_heap.insert(36, 36)
max_heap.insert(17, 17)
max_heap.insert(3, 3)
max_heap.insert(25, 25)
max_heap.insert(1, 1)
max_heap = DHeap(max_heap.heap, heap_property="max", d=4)
max_heap.insert(2, 2)
max_heap.insert(7, 7)
assert str(max_heap) == \
('[(100, 100, [1, 2, 3, 4]), (25, 25, [5, 6, 7, 8]), '
'(36, 36, []), (17, 17, []), (3, 3, []), (19, 19, []), '
'(1, 1, []), (2, 2, []), (7, 7, [])]')
assert max_heap.extract().key == 100
expected_sorted_elements = [36, 25, 19, 17, 7, 3, 2, 1]
sorted_elements = []
for _ in range(8):
sorted_elements.append(max_heap.extract().key)
assert expected_sorted_elements == sorted_elements
elements = [
TreeNode(7, 7),
TreeNode(25, 25),
TreeNode(100, 100),
TreeNode(1, 1),
TreeNode(2, 2),
TreeNode(3, 3),
TreeNode(17, 17),
TreeNode(19, 19),
TreeNode(36, 36)
]
min_heap = DHeap(elements=DynamicOneDimensionalArray(
TreeNode, 9, elements),
heap_property="min")
assert min_heap.extract().key == 1
expected_sorted_elements = [2, 3, 7, 17, 19, 25, 36, 100]
sorted_elements = [min_heap.extract().key for _ in range(8)]
assert expected_sorted_elements == sorted_elements
def extract(self):
"""
Extract root element of the Heap.
Returns
=======
root_element : TreeNode
The TreeNode at the root of the heap,
if the heap is not empty.
None
If the heap is empty.
"""
if self._last_pos_filled == -1:
raise IndexError("Heap is empty.")
else:
element_to_be_extracted = TreeNode(self.heap[0].key,
self.heap[0].data)
self._swap(0, self._last_pos_filled)
self.heap.delete(self._last_pos_filled)
self._last_pos_filled -= 1
self._heapify(0)
return element_to_be_extracted
def test_AVLTree():
a = AVLTree('M', 'M')
a.insert('N', 'N')
a.insert('O', 'O')
a.insert('L', 'L')
a.insert('K', 'K')
a.insert('Q', 'Q')
a.insert('P', 'P')
a.insert('H', 'H')
a.insert('I', 'I')
a.insert('A', 'A')
assert str(a) == ("[(None, 'M', 'M', None), (8, 'N', 'N', 6), "
"(None, 'O', 'O', None), (4, 'L', 'L', 0), "
"(None, 'K', 'K', None), (None, 'Q', 'Q', None), "
"(2, 'P', 'P', 5), (9, 'H', 'H', None), "
"(7, 'I', 'I', 3), (None, 'A', 'A', None)]")
assert [a.balance_factor(n) for n in a.tree if n is not None] == \
[0, -1, 0, 0, 0, 0, 0, -1, 0, 0]
a1 = AVLTree(1, 1)
a1.insert(2, 2)
a1.insert(3, 3)
a1.insert(4, 4)
a1.insert(5, 5)
assert str(a1) == (
"[(None, 1, 1, None), (0, 2, 2, 3), (None, 3, 3, None), "
"(2, 4, 4, 4), (None, 5, 5, None)]")
a3 = AVLTree(-1, 1)
a3.insert(-2, 2)
a3.insert(-3, 3)
a3.insert(-4, 4)
a3.insert(-5, 5)
assert str(a3) == ("[(None, -1, 1, None), (3, -2, 2, 0), "
"(None, -3, 3, None), (4, -4, 4, 2), "
"(None, -5, 5, None)]")
a2 = AVLTree()
a2.insert(1, 1)
a2.insert(1, 1)
assert str(a2) == "[(None, 1, 1, None)]"
a3 = AVLTree()
a3.tree = ArrayForTrees(TreeNode, 0)
for i in range(7):
a3.tree.append(TreeNode(i, i))
a3.tree[0].left = 1
a3.tree[0].right = 6
a3.tree[1].left = 5
a3.tree[1].right = 2
a3.tree[2].left = 3
a3.tree[2].right = 4
a3._left_right_rotate(0, 1)
assert str(a3) == ("[(4, 0, 0, 6), (5, 1, 1, 3), (1, 2, 2, 0), "
"(None, 3, 3, None), (None, 4, 4, None), "
"(None, 5, 5, None), (None, 6, 6, None)]")
a4 = AVLTree()
a4.tree = ArrayForTrees(TreeNode, 0)
for i in range(7):
a4.tree.append(TreeNode(i, i))
a4.tree[0].left = 1
a4.tree[0].right = 2
a4.tree[2].left = 3
a4.tree[2].right = 4
a4.tree[3].left = 5
a4.tree[3].right = 6
a4._right_left_rotate(0, 2)
assert str(a4) == ("[(1, 0, 0, 5), (None, 1, 1, None), (6, 2, 2, 4), "
"(0, 3, 3, 2), (None, 4, 4, None), (None, 5, 5, None), "
"(None, 6, 6, None)]")
a5 = AVLTree(is_order_statistic=True)
a5.tree = ArrayForTrees(TreeNode, [
TreeNode(10, 10),
TreeNode(5, 5),
TreeNode(17, 17),
TreeNode(2, 2),
TreeNode(9, 9),
TreeNode(12, 12),
TreeNode(20, 20),
TreeNode(3, 3),
TreeNode(11, 11),
TreeNode(15, 15),
TreeNode(18, 18),
TreeNode(30, 30),
TreeNode(13, 13),
TreeNode(33, 33)
])
a5.tree[0].left, a5.tree[0].right, a5.tree[0].parent, a5.tree[0].height = \
1, 2, None, 4
a5.tree[1].left, a5.tree[1].right, a5.tree[1].parent, a5.tree[1].height = \
3, 4, 0, 2
a5.tree[2].left, a5.tree[2].right, a5.tree[2].parent, a5.tree[2].height = \
5, 6, 0, 3
a5.tree[3].left, a5.tree[3].right, a5.tree[3].parent, a5.tree[3].height = \
None, 7, 1, 1
a5.tree[4].left, a5.tree[4].right, a5.tree[4].parent, a5.tree[4].height = \
None, None, 1, 0
a5.tree[5].left, a5.tree[5].right, a5.tree[5].parent, a5.tree[5].height = \
8, 9, 2, 2
a5.tree[6].left, a5.tree[6].right, a5.tree[6].parent, a5.tree[6].height = \
10, 11, 2, 2
a5.tree[7].left, a5.tree[7].right, a5.tree[7].parent, a5.tree[7].height = \
None, None, 3, 0
a5.tree[8].left, a5.tree[8].right, a5.tree[8].parent, a5.tree[8].height = \
None, None, 5, 0
a5.tree[9].left, a5.tree[9].right, a5.tree[9].parent, a5.tree[9].height = \
12, None, 5, 1
a5.tree[10].left, a5.tree[10].right, a5.tree[10].parent, a5.tree[10].height = \
None, None, 6, 0
a5.tree[11].left, a5.tree[11].right, a5.tree[11].parent, a5.tree[11].height = \
None, 13, 6, 1
a5.tree[12].left, a5.tree[12].right, a5.tree[12].parent, a5.tree[12].height = \
None, None, 9, 0
a5.tree[13].left, a5.tree[13].right, a5.tree[13].parent, a5.tree[13].height = \
None, None, 11, 0
# testing order statistics
a5.tree[0].size = 14
a5.tree[1].size = 4
a5.tree[2].size = 9
a5.tree[3].size = 2
a5.tree[4].size = 1
a5.tree[5].size = 4
a5.tree[6].size = 4
a5.tree[7].size = 1
a5.tree[8].size = 1
a5.tree[9].size = 2
a5.tree[10].size = 1
a5.tree[11].size = 2
a5.tree[12].size = 1
a5.tree[13].size = 1
assert raises(ValueError, lambda: a5.select(0))
assert raises(ValueError, lambda: a5.select(15))
assert a5.rank(-1) is None
def test_select_rank(expected_output):
output = []
for i in range(len(expected_output)):
output.append(a5.select(i + 1).key)
assert output == expected_output
output = []
expected_ranks = [i + 1 for i in range(len(expected_output))]
for i in range(len(expected_output)):
output.append(a5.rank(expected_output[i]))
assert output == expected_ranks
test_select_rank([2, 3, 5, 9, 10, 11, 12, 13, 15, 17, 18, 20, 30, 33])
a5.delete(9)
a5.delete(13)
a5.delete(20)
assert str(a5) == ("[(7, 10, 10, 5), (None, 5, 5, None), "
"(0, 17, 17, 6), (None, 2, 2, None), '', "
"(8, 12, 12, 9), (10, 30, 30, 13), (3, 3, 3, 1), "
"(None, 11, 11, None), (None, 15, 15, None), "
"(None, 18, 18, None), '', '', (None, 33, 33, None)]")
test_select_rank([2, 3, 5, 10, 11, 12, 15, 17, 18, 30, 33])
a5.delete(10)
a5.delete(17)
test_select_rank([2, 3, 5, 11, 12, 15, 18, 30, 33])
a5.delete(11)
a5.delete(30)
test_select_rank([2, 3, 5, 12, 15, 18, 33])
a5.delete(12)
test_select_rank([2, 3, 5, 15, 18, 33])
a5.delete(15)
test_select_rank([2, 3, 5, 18, 33])
a5.delete(18)
test_select_rank([2, 3, 5, 33])
a5.delete(33)
test_select_rank([2, 3, 5])
a5.delete(5)
test_select_rank([2, 3])
a5.delete(3)
test_select_rank([2])
a5.delete(2)
test_select_rank([])
def test_BinaryHeap():
max_heap = BinaryHeap(heap_property="max")
assert raises(IndexError, lambda: max_heap.extract())
max_heap.insert(100, 100)
max_heap.insert(19, 19)
max_heap.insert(36, 36)
max_heap.insert(17, 17)
max_heap.insert(3, 3)
max_heap.insert(25, 25)
max_heap.insert(1, 1)
max_heap.insert(2, 2)
max_heap.insert(7, 7)
assert str(max_heap) == \
("[(100, 100, [1, 2]), (19, 19, [3, 4]), "
"(36, 36, [5, 6]), (17, 17, [7, 8]), "
"(3, 3, []), (25, 25, []), (1, 1, []), "
"(2, 2, []), (7, 7, [])]")
assert max_heap.extract().key == 100
expected_sorted_elements = [36, 25, 19, 17, 7, 3, 2, 1]
l = max_heap.heap[0].left
l = max_heap.heap[0].right
sorted_elements = []
for _ in range(8):
sorted_elements.append(max_heap.extract().key)
assert expected_sorted_elements == sorted_elements
elements = [
TreeNode(7, 7),
TreeNode(25, 25),
TreeNode(100, 100),
TreeNode(1, 1),
TreeNode(2, 2),
TreeNode(3, 3),
TreeNode(17, 17),
TreeNode(19, 19),
TreeNode(36, 36)
]
min_heap = BinaryHeap(elements=DynamicOneDimensionalArray(
TreeNode, 9, elements),
heap_property="min")
assert min_heap.extract().key == 1
expected_sorted_elements = [2, 3, 7, 17, 19, 25, 36, 100]
sorted_elements = [min_heap.extract().key for _ in range(8)]
assert expected_sorted_elements == sorted_elements
non_TreeNode_elements = [(7, 7),
TreeNode(25, 25),
TreeNode(100, 100),
TreeNode(1, 1), (2, 2),
TreeNode(3, 3),
TreeNode(17, 17),
TreeNode(19, 19),
TreeNode(36, 36)]
assert raises(
ValueError, lambda: BinaryHeap(elements=non_TreeNode_elements,
heap_property='min'))
def test_AVLTree():
a = AVLTree('M', 'M')
a.insert('N', 'N')
a.insert('O', 'O')
a.insert('L', 'L')
a.insert('K', 'K')
a.insert('Q', 'Q')
a.insert('P', 'P')
a.insert('H', 'H')
a.insert('I', 'I')
a.insert('A', 'A')
trav = BinaryTreeTraversal(a)
in_order = trav.depth_first_search(order='in_order')
pre_order = trav.depth_first_search(order='pre_order')
assert [node.key for node in in_order
] == ['A', 'H', 'I', 'K', 'L', 'M', 'N', 'O', 'P', 'Q']
assert [node.key for node in pre_order
] == ['N', 'I', 'H', 'A', 'L', 'K', 'M', 'P', 'O', 'Q']
assert [a.balance_factor(n) for n in a.tree if n is not None] == \
[0, -1, 0, 0, 0, 0, 0, -1, 0, 0]
a1 = AVLTree(1, 1)
a1.insert(2, 2)
a1.insert(3, 3)
a1.insert(4, 4)
a1.insert(5, 5)
trav = BinaryTreeTraversal(a1)
in_order = trav.depth_first_search(order='in_order')
pre_order = trav.depth_first_search(order='pre_order')
assert [node.key for node in in_order] == [1, 2, 3, 4, 5]
assert [node.key for node in pre_order] == [2, 1, 4, 3, 5]
a3 = AVLTree(-1, 1)
a3.insert(-2, 2)
a3.insert(-3, 3)
a3.insert(-4, 4)
a3.insert(-5, 5)
trav = BinaryTreeTraversal(a3)
in_order = trav.depth_first_search(order='in_order')
pre_order = trav.depth_first_search(order='pre_order')
assert [node.key for node in in_order] == [-5, -4, -3, -2, -1]
assert [node.key for node in pre_order] == [-2, -4, -5, -3, -1]
a2 = AVLTree()
a2.insert(1, 1)
a2.insert(1, 1)
trav = BinaryTreeTraversal(a2)
in_order = trav.depth_first_search(order='in_order')
pre_order = trav.depth_first_search(order='pre_order')
assert [node.key for node in in_order] == [1]
assert [node.key for node in pre_order] == [1]
a3 = AVLTree()
a3.tree = ArrayForTrees(TreeNode, 0)
for i in range(7):
a3.tree.append(TreeNode(i, i))
a3.tree[0].left = 1
a3.tree[0].right = 6
a3.tree[1].left = 5
a3.tree[1].right = 2
a3.tree[2].left = 3
a3.tree[2].right = 4
a3._left_right_rotate(0, 1)
trav = BinaryTreeTraversal(a3)
in_order = trav.depth_first_search(order='in_order')
pre_order = trav.depth_first_search(order='pre_order')
assert [node.key for node in in_order] == [5, 1, 3, 2, 4, 0, 6]
assert [node.key for node in pre_order] == [2, 1, 5, 3, 0, 4, 6]
a4 = AVLTree()
a4.tree = ArrayForTrees(TreeNode, 0)
for i in range(7):
a4.tree.append(TreeNode(i, i))
a4.tree[0].left = 1
a4.tree[0].right = 2
a4.tree[2].left = 3
a4.tree[2].right = 4
a4.tree[3].left = 5
a4.tree[3].right = 6
a4._right_left_rotate(0, 2)
trav = BinaryTreeTraversal(a4)
in_order = trav.depth_first_search(order='in_order')
pre_order = trav.depth_first_search(order='pre_order')
assert [node.key for node in in_order] == [1, 0, 5, 3, 6, 2, 4]
assert [node.key for node in pre_order] == [3, 0, 1, 5, 2, 6, 4]
a5 = AVLTree(is_order_statistic=True)
a5.tree = ArrayForTrees(TreeNode, [
TreeNode(10, 10),
TreeNode(5, 5),
TreeNode(17, 17),
TreeNode(2, 2),
TreeNode(9, 9),
TreeNode(12, 12),
TreeNode(20, 20),
TreeNode(3, 3),
TreeNode(11, 11),
TreeNode(15, 15),
TreeNode(18, 18),
TreeNode(30, 30),
TreeNode(13, 13),
TreeNode(33, 33)
])
a5.tree[0].left, a5.tree[0].right, a5.tree[0].parent, a5.tree[0].height = \
1, 2, None, 4
a5.tree[1].left, a5.tree[1].right, a5.tree[1].parent, a5.tree[1].height = \
3, 4, 0, 2
a5.tree[2].left, a5.tree[2].right, a5.tree[2].parent, a5.tree[2].height = \
5, 6, 0, 3
a5.tree[3].left, a5.tree[3].right, a5.tree[3].parent, a5.tree[3].height = \
None, 7, 1, 1
a5.tree[4].left, a5.tree[4].right, a5.tree[4].parent, a5.tree[4].height = \
None, None, 1, 0
a5.tree[5].left, a5.tree[5].right, a5.tree[5].parent, a5.tree[5].height = \
8, 9, 2, 2
a5.tree[6].left, a5.tree[6].right, a5.tree[6].parent, a5.tree[6].height = \
10, 11, 2, 2
a5.tree[7].left, a5.tree[7].right, a5.tree[7].parent, a5.tree[7].height = \
None, None, 3, 0
a5.tree[8].left, a5.tree[8].right, a5.tree[8].parent, a5.tree[8].height = \
None, None, 5, 0
a5.tree[9].left, a5.tree[9].right, a5.tree[9].parent, a5.tree[9].height = \
12, None, 5, 1
a5.tree[10].left, a5.tree[10].right, a5.tree[10].parent, a5.tree[10].height = \
None, None, 6, 0
a5.tree[11].left, a5.tree[11].right, a5.tree[11].parent, a5.tree[11].height = \
None, 13, 6, 1
a5.tree[12].left, a5.tree[12].right, a5.tree[12].parent, a5.tree[12].height = \
None, None, 9, 0
a5.tree[13].left, a5.tree[13].right, a5.tree[13].parent, a5.tree[13].height = \
None, None, 11, 0
# testing order statistics
a5.tree[0].size = 14
a5.tree[1].size = 4
a5.tree[2].size = 9
a5.tree[3].size = 2
a5.tree[4].size = 1
a5.tree[5].size = 4
a5.tree[6].size = 4
a5.tree[7].size = 1
a5.tree[8].size = 1
a5.tree[9].size = 2
a5.tree[10].size = 1
a5.tree[11].size = 2
a5.tree[12].size = 1
a5.tree[13].size = 1
assert raises(ValueError, lambda: a5.select(0))
assert raises(ValueError, lambda: a5.select(15))
assert a5.rank(-1) is None
def test_select_rank(expected_output):
output = []
for i in range(len(expected_output)):
output.append(a5.select(i + 1).key)
assert output == expected_output
output = []
expected_ranks = [i + 1 for i in range(len(expected_output))]
for i in range(len(expected_output)):
output.append(a5.rank(expected_output[i]))
assert output == expected_ranks
test_select_rank([2, 3, 5, 9, 10, 11, 12, 13, 15, 17, 18, 20, 30, 33])
a5.delete(9)
a5.delete(13)
a5.delete(20)
trav = BinaryTreeTraversal(a5)
in_order = trav.depth_first_search(order='in_order')
pre_order = trav.depth_first_search(order='pre_order')
assert [node.key
for node in in_order] == [2, 3, 5, 10, 11, 12, 15, 17, 18, 30, 33]
assert [node.key for node in pre_order
] == [17, 10, 3, 2, 5, 12, 11, 15, 30, 18, 33]
test_select_rank([2, 3, 5, 10, 11, 12, 15, 17, 18, 30, 33])
a5.delete(10)
a5.delete(17)
test_select_rank([2, 3, 5, 11, 12, 15, 18, 30, 33])
a5.delete(11)
a5.delete(30)
test_select_rank([2, 3, 5, 12, 15, 18, 33])
a5.delete(12)
test_select_rank([2, 3, 5, 15, 18, 33])
a5.delete(15)
test_select_rank([2, 3, 5, 18, 33])
a5.delete(18)
test_select_rank([2, 3, 5, 33])
a5.delete(33)
test_select_rank([2, 3, 5])
a5.delete(5)
test_select_rank([2, 3])
a5.delete(3)
test_select_rank([2])
a5.delete(2)
test_select_rank([])
