alex-r-bigelow / intervaltree

A mutable, self-balancing interval tree. Queries may be by point, by range overlap, or by range containment.

intervaltree

A mutable, self-balancing interval tree for Python 3. Queries may be by point, by range overlap, or by range envelopment.

This library was designed to allow tagging text and time intervals, where the intervals include the lower bound but not the upper bound.

Fork details

Note: this fork adds a little bit of O(n log n) bloat for specific use cases, namely:

• efficient histogram computation
• iterative results for overlap queries (instead of collecting all the results in memory before returning)

If this isn't what you're looking for, I suggest you stick with the main repository.

Installing

pip install git+https://github.com/alex-r-bigelow/intervaltree.git

Features

• Supports Python 3.4+ (Tested under 3.6.7)

• Initializing

  • blank tree = IntervalTree()
  • from an iterable of Interval objects (tree = IntervalTree(intervals))
  • from an iterable of tuples (tree = IntervalTree.from_tuples(interval_tuples))

• Insertions

  • tree[begin:end] = data
  • tree.add(interval)
  • tree.addi(begin, end, data)

• Deletions

  • tree.remove(interval) (raises ValueError if not present)
  • tree.discard(interval) (quiet if not present)
  • tree.removei(begin, end, data) (short for tree.remove(Interval(begin, end, data)))
  • tree.discardi(begin, end, data) (short for tree.discard(Interval(begin, end, data)))
  • tree.remove_overlap(point)
  • tree.remove_overlap(begin, end) (removes all overlapping the range)
  • tree.remove_envelop(begin, end) (removes all enveloped in the range)

• Point queries

  • tree[point]
  • tree.at(point) (same as previous)

• Overlap queries

  • tree[begin:end]
  • tree.overlap(begin, end) (same as previous)
  • tree.iterOverlap(begin, end) (same as previous, except returns an iterator that yields Intervals immediately)

• Envelop queries

  • tree.envelop(begin, end)

• Membership queries

  • interval_obj in tree (this is fastest, O(1))
  • tree.containsi(begin, end, data)
  • tree.overlaps(point)
  • tree.overlaps(begin, end)

• Iterable

  • for interval_obj in tree:
  • tree.items()

• Sizing

  • len(tree)
  • tree.is_empty()
  • not tree
  • tree.begin() (the begin coordinate of the leftmost interval)
  • tree.end() (the end coordinate of the rightmost interval)

• Set-like operations

  • union

    • result_tree = tree.union(iterable)
    • result_tree = tree1 | tree2
    • tree.update(iterable)
    • tree |= other_tree

  • difference

    • result_tree = tree.difference(iterable)
    • result_tree = tree1 - tree2
    • tree.difference_update(iterable)
    • tree -= other_tree

  • intersection

    • result_tree = tree.intersection(iterable)
    • result_tree = tree1 & tree2
    • tree.intersection_update(iterable)
    • tree &= other_tree

  • symmetric difference

    • result_tree = tree.symmetric_difference(iterable)
    • result_tree = tree1 ^ tree2
    • tree.symmetric_difference_update(iterable)
    • tree ^= other_tree

  • comparison

    • tree1.issubset(tree2) or tree1 <= tree2
    • tree1 <= tree2
    • tree1.issuperset(tree2) or tree1 > tree2
    • tree1 >= tree2
    • tree1 == tree2

• Restructuring

  • chop(begin, end) (slice intervals and remove everything between begin and end, optionally modifying the data fields of the chopped-up intervals)
  • slice(point) (slice intervals at point)
  • split_overlaps() (slice at all interval boundaries, optionally modifying the data field)
  • merge_overlaps() (joins overlapping intervals into a single interval, optionally merging the data fields)
  • merge_equals() (joins intervals with matching ranges into a single interval, optionally merging the data fields)

• Copying and typecasting

  • IntervalTree(tree) (Interval objects are same as those in tree)
  • tree.copy() (Interval objects are shallow copies of those in tree)
  • set(tree) (can later be fed into IntervalTree())
  • list(tree) (ditto)

• Pickle-friendly

• Automatic AVL balancing

• Histogram computation

  • tree.computeCountHistogram(bins) (returns a list of evenly-spaced Interval objects of length bins, with counts for the number of Intervals that intersect each bin)
  • tree.computeUtilizationHistogram(bins) (returns a list of evenly-spaced Interval objects of length bins, with the percentage of each bin that contains an interval. Note that this will be higher than 1.0 if multiple intervals within the bin overlap each other; i.e. two intervals covering the entire bin would result in 2.0, or a 200% utilization rate)

Examples

• Getting started

  >>> from intervaltree import Interval, IntervalTree
  >>> t = IntervalTree()
  >>> t
  IntervalTree()

• Adding intervals - any object works!

  >>> t[1:2] = "1-2"
  >>> t[4:7] = (4, 7)
  >>> t[5:9] = {5: 9}

• Query by point

  The result of a query is a set object, so if ordering is important, you must sort it first.

  >>> sorted(t[6])
  [Interval(4, 7, (4, 7)), Interval(5, 9, {5: 9})]
  >>> sorted(t[6])[0]
  Interval(4, 7, (4, 7))

• Query by range

  Note that ranges are inclusive of the lower limit, but non-inclusive of the upper limit. So:

  >>> sorted(t[2:4])
  []

  Since our search was over 2 ≤ x < 4, neither Interval(1, 2) nor Interval(4, 7) was included. The first interval, 1 ≤ x < 2 does not include x = 2. The second interval, 4 ≤ x < 7, does include x = 4, but our search interval excludes it. So, there were no overlapping intervals. However:

  >>> sorted(t[1:5])
  [Interval(1, 2, '1-2'), Interval(4, 7, (4, 7))]

  To only return intervals that are completely enveloped by the search range:

  >>> sorted(t.envelop(1, 5))
  [Interval(1, 2, '1-2')]

• Accessing an Interval object

  >>> iv = Interval(4, 7, (4, 7))
  >>> iv.begin
  4
  >>> iv.end
  7
  >>> iv.data
  (4, 7)
  
  >>> begin, end, data = iv
  >>> begin
  4
  >>> end
  7
  >>> data
  (4, 7)

• Constructing from lists of intervals

  We could have made a similar tree this way:

  >>> ivs = [(1, 2), (4, 7), (5, 9)]
  >>> t = IntervalTree(
  ...    Interval(begin, end, "%d-%d" % (begin, end)) for begin, end in ivs
  ... )

  Or, if we don't need the data fields:

  >>> t2 = IntervalTree(Interval(*iv) for iv in ivs)

  Or even:

  >>> t2 = IntervalTree.from_tuples(ivs)

• Removing intervals

  >>> t.remove(Interval(1, 2, "1-2"))
  >>> sorted(t)
  [Interval(4, 7, '4-7'), Interval(5, 9, '5-9')]
  
  >>> t.remove(Interval(500, 1000, "Doesn't exist"))  # raises ValueError
  Traceback (most recent call last):
  ValueError
  
  >>> t.discard(Interval(500, 1000, "Doesn't exist"))  # quietly does nothing
  
  >>> del t[5]  # same as t.remove_overlap(5)
  >>> t
  IntervalTree()

  We could also empty a tree entirely:

  >>> t2.clear()
  >>> t2
  IntervalTree()

  Or remove intervals that overlap a range:

  >>> t = IntervalTree([
  ...     Interval(0, 10),
  ...     Interval(10, 20),
  ...     Interval(20, 30),
  ...     Interval(30, 40)])
  >>> t.remove_overlap(25, 35)
  >>> sorted(t)
  [Interval(0, 10), Interval(10, 20)]

  We can also remove only those intervals completely enveloped in a range:

  >>> t.remove_envelop(5, 20)
  >>> sorted(t)
  [Interval(0, 10)]

• Chopping

  We could also chop out parts of the tree:

  >>> t = IntervalTree([Interval(0, 10)])
  >>> t.chop(3, 7)
  >>> sorted(t)
  [Interval(0, 3), Interval(7, 10)]

  To modify the new intervals' data fields based on which side of the interval is being chopped:

  >>> def datafunc(iv, islower):
  ...     oldlimit = iv[islower]
  ...     return "oldlimit: {0}, islower: {1}".format(oldlimit, islower)
  >>> t = IntervalTree([Interval(0, 10)])
  >>> t.chop(3, 7, datafunc)
  >>> sorted(t)[0]
  Interval(0, 3, 'oldlimit: 10, islower: True')
  >>> sorted(t)[1]
  Interval(7, 10, 'oldlimit: 0, islower: False')

• Slicing

  You can also slice intervals in the tree without removing them:

  >>> t = IntervalTree([Interval(0, 10), Interval(5, 15)])
  >>> t.slice(3)
  >>> sorted(t)
  [Interval(0, 3), Interval(3, 10), Interval(5, 15)]

  You can also set the data fields, for example, re-using datafunc() from above:

  >>> t = IntervalTree([Interval(5, 15)])
  >>> t.slice(10, datafunc)
  >>> sorted(t)[0]
  Interval(5, 10, 'oldlimit: 15, islower: True')
  >>> sorted(t)[1]
  Interval(10, 15, 'oldlimit: 5, islower: False')

Future improvements

See the issue tracker on GitHub.

Based on

• Eternally Confuzzled's AVL tree
• Wikipedia's Interval Tree
• Heavily modified from Tyler Kahn's Interval Tree implementation in Python (GitHub project)
• Incorporates contributions from:
  • konstantint/Konstantin Tretyakov of the University of Tartu (Estonia)
  • siniG/Avi Gabay
  • lmcarril/Luis M. Carril of the Karlsruhe Institute for Technology (Germany)

Copyright

• Chaim Leib Halbert, 2013-2018
• Modifications, Konstantin Tretyakov, 2014

Licensed under the Apache License, version 2.0.

The source code for this project is at https://github.com/chaimleib/intervaltree