A mutable, self-balancing interval tree for Python 2 and 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.

This means that 0-length intervals are null and overlap nothing. If you see errors about null intervals, make sure end is strictly greater than begin. Our Intervals are like string ranges: 'hello'[0:0] == '', but 'hello'[0:1] == 'h'.

Version 3 changes!

• The search(begin, end, strict) method no longer exists. Instead, use one of these:
  • at(point)
  • overlap(begin, end)
  • envelop(begin, end)
• The extend(items) method no longer exists. Instead, use update(items).
• Methods like merge_overlaps() which took a strict argument consistently default to strict=True. Before, some methods defaulted to True and others to False.

pip install intervaltree

• Supports Python 2.7 and Python 3.5+ (Tested under 2.7, and 3.5 thru 3.14)

• 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)

• 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)
  • merge_neighbors() (joins adjacent intervals into a single interval if the distance between their range terminals is less than or equal to a given distance. Optionally merges overlapping intervals. Can also merge 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

• 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')

See the issue tracker on GitHub.

• 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)
  • depristo/MarkDePristo

• Chaim Leib Halbert, 2013-2025
• 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