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"""
Based on "Skip Lists: A Probabilistic Alternative to Balanced Trees" by William Pugh
https://epaperpress.com/sortsearch/download/skiplist.pdf
"""
from random import random
from typing import Generic, List, Optional, Tuple, TypeVar
KT = TypeVar("KT")
VT = TypeVar("VT")
class Node(Generic[KT, VT]):
def __init__(self, key: KT, value: VT):
self.key = key
self.value = value
self.forward: List[Node[KT, VT]] = []
def __repr__(self) -> str:
"""
:return: Visual representation of Node
>>> node = Node("Key", 2)
>>> repr(node)
'Node(Key: 2)'
"""
return f"Node({self.key}: {self.value})"
@property
def level(self) -> int:
"""
:return: Number of forward references
>>> node = Node("Key", 2)
>>> node.level
0
>>> node.forward.append(Node("Key2", 4))
>>> node.level
1
>>> node.forward.append(Node("Key3", 6))
>>> node.level
2
"""
return len(self.forward)
class SkipList(Generic[KT, VT]):
def __init__(self, p: float = 0.5, max_level: int = 16):
self.head = Node("root", None)
self.level = 0
self.p = p
self.max_level = max_level
def __str__(self) -> str:
"""
:return: Visual representation of SkipList
>>> skip_list = SkipList()
>>> print(skip_list)
SkipList(level=0)
>>> skip_list.insert("Key1", "Value")
>>> print(skip_list) # doctest: +ELLIPSIS
SkipList(level=...
[root]--...
[Key1]--Key1...
None *...
>>> skip_list.insert("Key2", "OtherValue")
>>> print(skip_list) # doctest: +ELLIPSIS
SkipList(level=...
[root]--...
[Key1]--Key1...
[Key2]--Key2...
None *...
"""
items = list(self)
if len(items) == 0:
return f"SkipList(level={self.level})"
label_size = max((len(str(item)) for item in items), default=4)
label_size = max(label_size, 4) + 4
node = self.head
lines = []
forwards = node.forward.copy()
lines.append(f"[{node.key}]".ljust(label_size, "-") + "* " * len(forwards))
lines.append(" " * label_size + "| " * len(forwards))
while len(node.forward) != 0:
node = node.forward[0]
lines.append(
f"[{node.key}]".ljust(label_size, "-")
+ " ".join(str(n.key) if n.key == node.key else "|" for n in forwards)
)
lines.append(" " * label_size + "| " * len(forwards))
forwards[: node.level] = node.forward
lines.append("None".ljust(label_size) + "* " * len(forwards))
return f"SkipList(level={self.level})\n" + "\n".join(lines)
def __iter__(self):
node = self.head
while len(node.forward) != 0:
yield node.forward[0].key
node = node.forward[0]
def random_level(self) -> int:
"""
:return: Random level from [1, self.max_level] interval.
Higher values are less likely.
"""
level = 1
while random() < self.p and level < self.max_level:
level += 1
return level
def _locate_node(self, key) -> Tuple[Optional[Node[KT, VT]], List[Node[KT, VT]]]:
"""
:param key: Searched key,
:return: Tuple with searched node (or None if given key is not present)
and list of nodes that refer (if key is present) of should refer to
given node.
"""
# Nodes with refer or should refer to output node
update_vector = []
node = self.head
for i in reversed(range(self.level)):
# i < node.level - When node level is lesser than `i` decrement `i`.
# node.forward[i].key < key - Jumping to node with key value higher
# or equal to searched key would result
# in skipping searched key.
while i < node.level and node.forward[i].key < key:
node = node.forward[i]
# Each leftmost node (relative to searched node) will potentially have to
# be updated.
update_vector.append(node)
update_vector.reverse() # Note that we were inserting values in reverse order.
# len(node.forward) != 0 - If current node doesn't contain any further
# references then searched key is not present.
# node.forward[0].key == key - Next node key should be equal to search key
# if key is present.
if len(node.forward) != 0 and node.forward[0].key == key:
return node.forward[0], update_vector
else:
return None, update_vector
def delete(self, key: KT):
"""
:param key: Key to remove from list.
>>> skip_list = SkipList()
>>> skip_list.insert(2, "Two")
>>> skip_list.insert(1, "One")
>>> skip_list.insert(3, "Three")
>>> list(skip_list)
[1, 2, 3]
>>> skip_list.delete(2)
>>> list(skip_list)
[1, 3]
"""
node, update_vector = self._locate_node(key)
if node is not None:
for i, update_node in enumerate(update_vector):
# Remove or replace all references to removed node.
if update_node.level > i and update_node.forward[i].key == key:
if node.level > i:
update_node.forward[i] = node.forward[i]
else:
update_node.forward = update_node.forward[:i]
def insert(self, key: KT, value: VT):
"""
:param key: Key to insert.
:param value: Value associated with given key.
>>> skip_list = SkipList()
>>> skip_list.insert(2, "Two")
>>> skip_list.find(2)
'Two'
>>> list(skip_list)
[2]
"""
node, update_vector = self._locate_node(key)
if node is not None:
node.value = value
else:
level = self.random_level()
if level > self.level:
# After level increase we have to add additional nodes to head.
for i in range(self.level - 1, level):
update_vector.append(self.head)
self.level = level
new_node = Node(key, value)
for i, update_node in enumerate(update_vector[:level]):
# Change references to pass through new node.
if update_node.level > i:
new_node.forward.append(update_node.forward[i])
if update_node.level < i + 1:
update_node.forward.append(new_node)
else:
update_node.forward[i] = new_node
def find(self, key: VT) -> Optional[VT]:
"""
:param key: Search key.
:return: Value associated with given key or None if given key is not present.
>>> skip_list = SkipList()
>>> skip_list.find(2)
>>> skip_list.insert(2, "Two")
>>> skip_list.find(2)
'Two'
>>> skip_list.insert(2, "Three")
>>> skip_list.find(2)
'Three'
"""
node, _ = self._locate_node(key)
if node is not None:
return node.value
return None
def test_insert():
skip_list = SkipList()
skip_list.insert("Key1", 3)
skip_list.insert("Key2", 12)
skip_list.insert("Key3", 41)
skip_list.insert("Key4", -19)
node = skip_list.head
all_values = {}
while node.level != 0:
node = node.forward[0]
all_values[node.key] = node.value
assert len(all_values) == 4
assert all_values["Key1"] == 3
assert all_values["Key2"] == 12
assert all_values["Key3"] == 41
assert all_values["Key4"] == -19
def test_insert_overrides_existing_value():
skip_list = SkipList()
skip_list.insert("Key1", 10)
skip_list.insert("Key1", 12)
skip_list.insert("Key5", 7)
skip_list.insert("Key7", 10)
skip_list.insert("Key10", 5)
skip_list.insert("Key7", 7)
skip_list.insert("Key5", 5)
skip_list.insert("Key10", 10)
node = skip_list.head
all_values = {}
while node.level != 0:
node = node.forward[0]
all_values[node.key] = node.value
if len(all_values) != 4:
print()
assert len(all_values) == 4
assert all_values["Key1"] == 12
assert all_values["Key7"] == 7
assert all_values["Key5"] == 5
assert all_values["Key10"] == 10
def test_searching_empty_list_returns_none():
skip_list = SkipList()
assert skip_list.find("Some key") is None
def test_search():
skip_list = SkipList()
skip_list.insert("Key2", 20)
assert skip_list.find("Key2") == 20
skip_list.insert("Some Key", 10)
skip_list.insert("Key2", 8)
skip_list.insert("V", 13)
assert skip_list.find("Y") is None
assert skip_list.find("Key2") == 8
assert skip_list.find("Some Key") == 10
assert skip_list.find("V") == 13
def test_deleting_item_from_empty_list_do_nothing():
skip_list = SkipList()
skip_list.delete("Some key")
assert len(skip_list.head.forward) == 0
def test_deleted_items_are_not_founded_by_find_method():
skip_list = SkipList()
skip_list.insert("Key1", 12)
skip_list.insert("V", 13)
skip_list.insert("X", 14)
skip_list.insert("Key2", 15)
skip_list.delete("V")
skip_list.delete("Key2")
assert skip_list.find("V") is None
assert skip_list.find("Key2") is None
def test_delete_removes_only_given_key():
skip_list = SkipList()
skip_list.insert("Key1", 12)
skip_list.insert("V", 13)
skip_list.insert("X", 14)
skip_list.insert("Key2", 15)
skip_list.delete("V")
assert skip_list.find("V") is None
assert skip_list.find("X") == 14
assert skip_list.find("Key1") == 12
assert skip_list.find("Key2") == 15
skip_list.delete("X")
assert skip_list.find("V") is None
assert skip_list.find("X") is None
assert skip_list.find("Key1") == 12
assert skip_list.find("Key2") == 15
skip_list.delete("Key1")
assert skip_list.find("V") is None
assert skip_list.find("X") is None
assert skip_list.find("Key1") is None
assert skip_list.find("Key2") == 15
skip_list.delete("Key2")
assert skip_list.find("V") is None
assert skip_list.find("X") is None
assert skip_list.find("Key1") is None
assert skip_list.find("Key2") is None
def test_delete_doesnt_leave_dead_nodes():
skip_list = SkipList()
skip_list.insert("Key1", 12)
skip_list.insert("V", 13)
skip_list.insert("X", 142)
skip_list.insert("Key2", 15)
skip_list.delete("X")
def traverse_keys(node):
yield node.key
for forward_node in node.forward:
yield from traverse_keys(forward_node)
assert len(set(traverse_keys(skip_list.head))) == 4
def test_iter_always_yields_sorted_values():
def is_sorted(lst):
for item, next_item in zip(lst, lst[1:]):
if next_item < item:
return False
return True
skip_list = SkipList()
for i in range(10):
skip_list.insert(i, i)
assert is_sorted(list(skip_list))
skip_list.delete(5)
skip_list.delete(8)
skip_list.delete(2)
assert is_sorted(list(skip_list))
skip_list.insert(-12, -12)
skip_list.insert(77, 77)
assert is_sorted(list(skip_list))
def pytests():
for i in range(100):
# Repeat test 100 times due to the probabilistic nature of skip list
# random values == random bugs
test_insert()
test_insert_overrides_existing_value()
test_searching_empty_list_returns_none()
test_search()
test_deleting_item_from_empty_list_do_nothing()
test_deleted_items_are_not_founded_by_find_method()
test_delete_removes_only_given_key()
test_delete_doesnt_leave_dead_nodes()
test_iter_always_yields_sorted_values()
def main():
"""
>>> pytests()
"""
skip_list = SkipList()
skip_list.insert(2, "2")
skip_list.insert(4, "4")
skip_list.insert(6, "4")
skip_list.insert(4, "5")
skip_list.insert(8, "4")
skip_list.insert(9, "4")
skip_list.delete(4)
print(skip_list)
if __name__ == "__main__":
main()
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