intervaltree

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.

Features

• Supports Python 2.6+ and Python 3.2+

• Initialize blank or from an iterable of Intervals in O(n * log n).

• Insertions

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

• 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)

• Overlap queries:

  • tree[point]
  • tree[begin, end]
  • tree.search(point)
  • tree.search(begin, end)

• Envelop queries:

  • tree.search(begin, end, strict=True)

• 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)

• Restructuring

  • split_overlaps()

• Copy- and typecast-able:

  • 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)

• Equal-able

• Pickle-friendly

• Automatic AVL balancing

Examples

• Getting started

    from intervaltree import Interval, 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

    ivs = t[6]            # set([Interval(4, 7, (4, 7)), Interval(5, 9, {5: 9})])
    iv = sorted(ivs)[0]   # Interval(4, 7, (4, 7))
  

• Accessing an Interval object

    iv.begin  # 4
    iv.end    # 7
    iv.data   # (4, 7)
  

• Query by range

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

    t[2:4]    # set()
  

  But:

    t[1:5]    # set([Interval(1, 2, '1-2'), Interval(4, 7, (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:

    t = IntervalTree(Interval(*iv) for iv in ivs)
  

• Removing intervals

    t.remove( Interval(1, 2, "1-2") )
    list(t)     # [Interval(4, 7, '4-7'), Interval(5, 9, '5-9')]
    
    t.remove( Interval(500, 1000, "Doesn't exist")) # raises ValueError
    t.discard(Interval(500, 1000, "Doesn't exist")) # quietly does nothing
    
    t.remove_overlap(5)   
    list(t)     # []
  

  We could also empty a tree by removing all intervals, from the lowest bound to the highest bound of the IntervalTree:

    t.remove_overlap(t.begin(), t.end())
  

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 modifications by konstantint

Copyright

• Chaim-Leib Halbert, 2014