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"""
Min-heaps.
"""
from heapq import heappop, heappush
from itertools import count
import networkx as nx
__all__ = ["MinHeap", "PairingHeap", "BinaryHeap"]
class MinHeap:
"""Base class for min-heaps.
A MinHeap stores a collection of key-value pairs ordered by their values.
It supports querying the minimum pair, inserting a new pair, decreasing the
value in an existing pair and deleting the minimum pair.
"""
class _Item:
"""Used by subclassess to represent a key-value pair."""
__slots__ = ("key", "value")
def __init__(self, key, value):
self.key = key
self.value = value
def __repr__(self):
return repr((self.key, self.value))
def __init__(self):
"""Initialize a new min-heap."""
self._dict = {}
def min(self):
"""Query the minimum key-value pair.
Returns
-------
key, value : tuple
The key-value pair with the minimum value in the heap.
Raises
------
NetworkXError
If the heap is empty.
"""
raise NotImplementedError
def pop(self):
"""Delete the minimum pair in the heap.
Returns
-------
key, value : tuple
The key-value pair with the minimum value in the heap.
Raises
------
NetworkXError
If the heap is empty.
"""
raise NotImplementedError
def get(self, key, default=None):
"""Returns the value associated with a key.
Parameters
----------
key : hashable object
The key to be looked up.
default : object
Default value to return if the key is not present in the heap.
Default value: None.
Returns
-------
value : object.
The value associated with the key.
"""
raise NotImplementedError
def insert(self, key, value, allow_increase=False):
"""Insert a new key-value pair or modify the value in an existing
pair.
Parameters
----------
key : hashable object
The key.
value : object comparable with existing values.
The value.
allow_increase : bool
Whether the value is allowed to increase. If False, attempts to
increase an existing value have no effect. Default value: False.
Returns
-------
decreased : bool
True if a pair is inserted or the existing value is decreased.
"""
raise NotImplementedError
def __nonzero__(self):
"""Returns whether the heap if empty."""
return bool(self._dict)
def __bool__(self):
"""Returns whether the heap if empty."""
return bool(self._dict)
def __len__(self):
"""Returns the number of key-value pairs in the heap."""
return len(self._dict)
def __contains__(self, key):
"""Returns whether a key exists in the heap.
Parameters
----------
key : any hashable object.
The key to be looked up.
"""
return key in self._dict
class PairingHeap(MinHeap):
"""A pairing heap."""
class _Node(MinHeap._Item):
"""A node in a pairing heap.
A tree in a pairing heap is stored using the left-child, right-sibling
representation.
"""
__slots__ = ("left", "next", "prev", "parent")
def __init__(self, key, value):
super().__init__(key, value)
# The leftmost child.
self.left = None
# The next sibling.
self.next = None
# The previous sibling.
self.prev = None
# The parent.
self.parent = None
def __init__(self):
"""Initialize a pairing heap."""
super().__init__()
self._root = None
def min(self):
if self._root is None:
raise nx.NetworkXError("heap is empty.")
return (self._root.key, self._root.value)
def pop(self):
if self._root is None:
raise nx.NetworkXError("heap is empty.")
min_node = self._root
self._root = self._merge_children(self._root)
del self._dict[min_node.key]
return (min_node.key, min_node.value)
def get(self, key, default=None):
node = self._dict.get(key)
return node.value if node is not None else default
def insert(self, key, value, allow_increase=False):
node = self._dict.get(key)
root = self._root
if node is not None:
if value < node.value:
node.value = value
if node is not root and value < node.parent.value:
self._cut(node)
self._root = self._link(root, node)
return True
elif allow_increase and value > node.value:
node.value = value
child = self._merge_children(node)
# Nonstandard step: Link the merged subtree with the root. See
# below for the standard step.
if child is not None:
self._root = self._link(self._root, child)
# Standard step: Perform a decrease followed by a pop as if the
# value were the smallest in the heap. Then insert the new
# value into the heap.
# if node is not root:
# self._cut(node)
# if child is not None:
# root = self._link(root, child)
# self._root = self._link(root, node)
# else:
# self._root = (self._link(node, child)
# if child is not None else node)
return False
else:
# Insert a new key.
node = self._Node(key, value)
self._dict[key] = node
self._root = self._link(root, node) if root is not None else node
return True
def _link(self, root, other):
"""Link two nodes, making the one with the smaller value the parent of
the other.
"""
if other.value < root.value:
root, other = other, root
next = root.left
other.next = next
if next is not None:
next.prev = other
other.prev = None
root.left = other
other.parent = root
return root
def _merge_children(self, root):
"""Merge the subtrees of the root using the standard two-pass method.
The resulting subtree is detached from the root.
"""
node = root.left
root.left = None
if node is not None:
link = self._link
# Pass 1: Merge pairs of consecutive subtrees from left to right.
# At the end of the pass, only the prev pointers of the resulting
# subtrees have meaningful values. The other pointers will be fixed
# in pass 2.
prev = None
while True:
next = node.next
if next is None:
node.prev = prev
break
next_next = next.next
node = link(node, next)
node.prev = prev
prev = node
if next_next is None:
break
node = next_next
# Pass 2: Successively merge the subtrees produced by pass 1 from
# right to left with the rightmost one.
prev = node.prev
while prev is not None:
prev_prev = prev.prev
node = link(prev, node)
prev = prev_prev
# Now node can become the new root. Its has no parent nor siblings.
node.prev = None
node.next = None
node.parent = None
return node
def _cut(self, node):
"""Cut a node from its parent."""
prev = node.prev
next = node.next
if prev is not None:
prev.next = next
else:
node.parent.left = next
node.prev = None
if next is not None:
next.prev = prev
node.next = None
node.parent = None
class BinaryHeap(MinHeap):
"""A binary heap."""
def __init__(self):
"""Initialize a binary heap."""
super().__init__()
self._heap = []
self._count = count()
def min(self):
dict = self._dict
if not dict:
raise nx.NetworkXError("heap is empty")
heap = self._heap
pop = heappop
# Repeatedly remove stale key-value pairs until a up-to-date one is
# met.
while True:
value, _, key = heap[0]
if key in dict and value == dict[key]:
break
pop(heap)
return (key, value)
def pop(self):
dict = self._dict
if not dict:
raise nx.NetworkXError("heap is empty")
heap = self._heap
pop = heappop
# Repeatedly remove stale key-value pairs until a up-to-date one is
# met.
while True:
value, _, key = heap[0]
pop(heap)
if key in dict and value == dict[key]:
break
del dict[key]
return (key, value)
def get(self, key, default=None):
return self._dict.get(key, default)
def insert(self, key, value, allow_increase=False):
dict = self._dict
if key in dict:
old_value = dict[key]
if value < old_value or (allow_increase and value > old_value):
# Since there is no way to efficiently obtain the location of a
# key-value pair in the heap, insert a new pair even if ones
# with the same key may already be present. Deem the old ones
# as stale and skip them when the minimum pair is queried.
dict[key] = value
heappush(self._heap, (value, next(self._count), key))
return value < old_value
return False
else:
dict[key] = value
heappush(self._heap, (value, next(self._count), key))
return True
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