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import sys
__author__ = "Johannes Koester"
class Interval:
""" Container for an interval with start and end point. """
def __init__(self, start, end):
self.start = start
self.end = end
def is_overlap(self, other):
""" Return True if this interval overlaps with the given interval. """
return (self.start - other.end <= 0 and self.end - other.start >= 0) or (self.end - other.start >= 0 and self.start - other.end <= 0)
def __repr__(self):
return "({},{})".format(self.start, self.end)
class IntervalNode:
"""
Node in the IntervalTree.
"""
def __init__(self, interval, obj, tree):
self.interval = interval
self.obj = obj
self.right = None
self.left = None
self.maxend = self.interval.end
self.height = 0
self.tree = tree
def recalc_maxend(self):
self.maxend = self.interval.end
if child in (self.left, self.right):
if child:
self.maxend = max(child.maxend, self.maxend)
def __repr__(self):
return str(self.interval)
class IntervalTree:
"""
Interval tree as proposed by Cormen et al.
"""
def __init__(self):
self.root = None
def insert(self, *args, obj = None):
"""
Insert a new interval into the tree. *args can be a start and endpoint given as ints, or a single object with the attributes start and end.
"""
node = self._convert_args(*args, obj = obj, node = True)
self._insert(self.root, node)
# balance the tree to avoid degeneration
self._rotate()
def find(self, *args):
"""
Find all intervals in the tree that intersect with the given interval. *args can be a start and endpoint given as ints, or a single object with the attributes start and end.
"""
for interval in self._find(self.root, self._convert_args(*args)):
yield interval
def _insert(self, root, node):
if not root:
self.root = node
return
maxend = None
if node.interval.start < root.interval.start:
if root.left:
maxend = self._insert(root.left, node)
else:
root.left = node
else:
if root.right:
maxend = self._insert(root.right, node)
else:
root.right = node
root.height += 1
if not maxend:
maxend = node.interval.end
root.maxend = max(maxend, root.maxend)
return root.maxend
def _find(self, root, interval):
if not root:
return
if interval.start > root.maxend:
return
if root.interval.is_overlap(interval):
yield root.interval
if interval.start < root.interval.start:
for i in self._find(root.left, interval):
yield i
elif not interval.end < root.interval.start:
for i in self._find(root.right, interval):
yield i
def _rotate(self):
if self.root.right and self.root.left:
heightdiff = self.root.right.height - self.root.left.height
if heightdiff > 1:
# perform a left rotation
p = self.root
q = self.root.right
self.root = q
p.right = q.left
q.left = p
q.height += 1
p.height -= 1
p.recalc_maxend()
q.recalc_maxend()
elif heightdiff < -1:
# perform a right rotation
p = self.root
q = self.root.left
self.root = q
p.left = q.right
q.right = p
q.height += 1
p.height -= 1
p.recalc_maxend()
q.recalc_maxend()
def _inorder(self, root):
if not root:
return
for i in self._inorder(root.left):
yield i
yield root
for i in self._inorder(root.right):
yield i
def __iter__(self):
for i in self._inorder(self.root):
yield i
def __repr__(self):
return ", ".join(map(str, self))
def _convert_args(self, *args, obj = None, node = False):
""" Convert args into an interval. *args can be a start and endpoint given as ints, or a single object with the attributes start and end. """
if len(args) == 2:
interval = Interval(*args)
else:
interval = Interval(args[0].start, args[0].end)
if node:
if not obj and len(args) == 1:
obj = args[0]
return IntervalNode(interval, obj, self)
return interval
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