Editable interval tree data structure for Python 2 and 3

## 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.

### Installing

pip install intervaltree

### Features

- Supports Python 2.6+ and Python 3.2+
- Initializing
- blank
`tree = IntervalTree()` - from an iterable of
`Interval`objects (`tree = IntervalTree(intervals)`) - from an iterable of tuples
(
`tree = IntervalTree.from_tuples(interval_tuples)`)

- blank
- 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)

- 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)

- 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`

- union
- Restructuring
`chop(begin, end)`(slice intervals and remove everything between`begin`and`end`)`slice(point)`(slice intervals at`point`)`split_overlaps()`(slice at all interval boundaries)

- 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

### 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]) []

But:

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

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)

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, 2013-2015
- 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

## Change log

### Version 2.1.0

- Added:
`merge_overlaps()`method and tests`merge_equals()`method and tests`range()`method`span()`method, for returning the difference between`end()`and`begin()`

- Fixes:
- Development version numbering is changing to be compliant with PEP440. Version numbering now contains major, minor and micro release numbers, plus the number of builds following the stable release version, e.g. 2.0.4b34
- Speed improvement:
`begin()`and`end()`methods used iterative`min()`and`max()`builtins instead of the more efficient`iloc`member available to`SortedDict` `overlaps()`method used to return`True`even if provided null test interval

- Maintainers:
- Added coverage test (
`make coverage`) with html report (`htmlcov/index.html`) - Tests run slightly faster

- Added coverage test (

### Version 2.0.4

- Fix: Issue #27: README incorrectly showed using a comma instead of a
colon when querying the
`IntervalTree`: it showed`tree[begin, end]`instead of`tree[begin:end]`

### Version 2.0.3

- Fix: README showed using + operator for setlike union instead of the correct | operator
- Removed tests from release package to speed up installation; to get the tests, download from GitHub

### Version 2.0.2

- Fix: Issue #20: performance enhancement for large trees.
`IntervalTree.search()`made a copy of the entire`boundary_table`resulting in linear search time. The`sortedcollections`package is now the sole install dependency

### Version 2.0.1

- Fix: Issue #26: failed to prune empty
`Node`after a rotation promoted contents of`s_center`

### Version 2.0.0

`IntervalTree`now supports the full`collections.MutableSet`API- Added:
`__delitem__`to`IntervalTree``Interval`comparison methods`lt()`,`gt()`,`le()`and`ge()`to`Interval`, as an alternative to the comparison operators, which are designed for sorting`IntervalTree.from_tuples(iterable)``IntervalTree.clear()``IntervalTree.difference(iterable)``IntervalTree.difference_update(iterable)``IntervalTree.union(iterable)``IntervalTree.intersection(iterable)``IntervalTree.intersection_update(iterable)``IntervalTree.symmetric_difference(iterable)``IntervalTree.symmetric_difference_update(iterable)``IntervalTree.chop(a, b)``IntervalTree.slice(point)`

- Deprecated
`IntervalTree.extend()`– use`update()`instead - Internal improvements:
- More verbose tests with progress bars
- More tests for comparison and sorting behavior
- Code in the README is included in the unit tests

- Fixes
- BACKWARD INCOMPATIBLE: On ranged queries where
`begin >= end`, the query operated on the overlaps of`begin`. This behavior was documented as expected in 1.x; it is now changed to be more consistent with the definition of`Interval`s, which are half-open. - Issue #25: pruning empty Nodes with staggered descendants could result in invalid trees
- Sorting
`Interval`s and numbers in the same list gathered all the numbers at the beginning and the`Interval`s at the end `IntervalTree.overlaps()`and friends returned`None`instead of`False`- Maintainers:
`make install-testpypi`failed because the`pip`was missing a`--pre`flag

- BACKWARD INCOMPATIBLE: On ranged queries where

### Version 1.1.1

- Removed requirement for pyandoc in order to run functionality tests.

### Version 1.1.0

- Added ability to use
`Interval.distance_to()`with points, not just`Intervals` - Added documentation on return types to
`IntervalTree`and`Interval` `Interval.__cmp__()`works with points too- Fix:
`IntervalTree.score()`returned maximum score of 0.5 instead of 1.0. Now returns max of subscores instead of avg - Internal improvements:
- Development version numbering scheme, based on
`git describe`the “building towards” release is appended after a hyphen, eg. 1.0.2-37-g2da2ef0-1.10. The previous tagged release is 1.0.2, and there have been 37 commits since then, current tag is g2da2ef0, and we are getting ready for a 1.1.0 release - Optimality tests added
`Interval`overlap tests for ranges,`Interval`s and points added

- Development version numbering scheme, based on

### Version 1.0.2

`Node.depth_score_helper()`raised

`AttributeError`

### Version 1.0.1

- Fix: pip install failure because of failure to generate README.rst

### Version 1.0.0

- Renamed from PyIntervalTree to intervaltree
- Speed improvements for adding and removing Intervals (~70% faster than 0.4)
- Bug fixes:
- BACKWARD INCOMPATIBLE:
`len()`of an`Interval`is always 3, reverting to default behavior for`namedtuples`. In Python 3,`len`returning a non-integer raises an exception. Instead, use`Interval.length()`, which returns 0 for null intervals and`end - begin`otherwise. Also, if the`len() === 0`, then`not iv`is`True`. - When inserting an
`Interval`via`__setitem__`and improper parameters given, all errors were transformed to`IndexError` `split_overlaps`did not update the`boundary_table`counts

- BACKWARD INCOMPATIBLE:
- Internal improvements:
- More robust local testing tools
- Long series of interdependent tests have been separated into sections

### Version 0.4

- Faster balancing (~80% faster)
- Bug fixes:
- Double rotations were performed in place of a single rotation when presented an unbalanced Node with a balanced child.
- During single rotation, kept referencing an unrotated Node instead of the new, rotated one

### Version 0.3.3

- Made IntervalTree crash if inited with a null Interval (end <= begin)
- IntervalTree raises ValueError instead of AssertionError when a null Interval is inserted

### Version 0.3.2

- Support for Python 3.2+ and 2.6+
- Changed license from LGPL to more permissive Apache license
- Merged changes from https://github.com/konstantint/PyIntervalTree to
https://github.com/chaimleib/PyIntervalTree
- Interval now inherits from a namedtuple. Benefits: should be faster. Drawbacks: slight behavioural change (Intervals not mutable anymore).
- Added float tests
- Use setup.py for tests
- Automatic testing via travis-ci
- Removed dependency on six

- Interval improvements:
- Intervals without data have a cleaner string representation
- Intervals without data are pickled more compactly
- Better hashing
- Intervals are ordered by begin, then end, then by data. If data is not orderable, sorts by type(data)

- Bug fixes:
- Fixed crash when querying empty tree
- Fixed missing close parenthesis in examples
- Made IntervalTree crash earlier if a null Interval is added

- Internals:
- New test directory
- Nicer display of data structures for debugging, using custom test/pprint.py (Python 2.6, 2.7)
- More sensitive exception handling
- Local script to test in all supported versions of Python
- Added IntervalTree.score() to measure how optimally a tree is structured

### Version 0.2.3

- Slight changes for inclusion in PyPI.
- Some documentation changes
- Added tests
- Bug fix: interval addition via [] was broken in Python 2.7 (see http://bugs.python.org/issue21785)
- Added intervaltree.bio subpackage, adding some utilities for use in bioinformatics

### Version 0.2.2b

- Forked from https://github.com/MusashiAharon/PyIntervalTree

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