inversion list

(data structure)

Definition: A set of non-overlapping numeric ranges, stored in an array in increasing order. Items in odd indexes begin ranges, and items in even indexes are the first number after the ends.

Use a form of binary search to determine if a number is in any of the ranges. If the search ends on an odd index (a beginning), the number is in the set. If the search ends on an even index (a just-after-end) or outside the array, it is not in the set.

Generalization (I am a kind of ...)

Aggregate child (... is a part of or used in me.)
array, binary search.

See also inverted index.

Note: For example, to represent the ranges 10-14, 25, and 37-42, the inversion list would be: 10 15 25 26 37 43

There are linear algorithms for union, intersection, set difference, negation, etc.

The term inversion list is also used to refer to storing a sequence of bits as the numeric position of each switch between 0 and 1 bits. See Teodor Ziatanov's InversionList in Perl. Some authors refer to inverted index as inversion list.

Author: JH


prototype code with tests (Perl), NQP implementation (Perl).

More information

Definition adapted from Inversion list [Wikipedia]. More explanation and code in Richard Gillam, A Practical Programmer's Guide to the Encoding Standard, chapter 13, page 504ff, Addison-Wesley Professional, 2002.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 25 March 2016.
HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:
Jarkko Hietaniemi, "inversion list", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 25 March 2016. (accessed TODAY) Available from: