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