**Packages**- mtl
- containers

An efficient implementation of maps from integer keys to values (dictionaries).
API of this module is strict in the keys, but lazy in the values. If you need value-strict maps, use Data.IntMap.Strict instead. The IntMap type itself is shared between the lazy and strict modules, meaning that the same IntMap value can be passed to functions in both modules (although that is rarely needed).
These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.
> import Data.IntMap.Lazy (IntMap)
> import qualified Data.IntMap.Lazy as IntMap
The implementation is based on *big-endian patricia trees*. This data structure performs especially well on binary operations like union and intersection. However, my benchmarks show that it is also (much) faster on insertions and deletions when compared to a generic size-balanced map implementation (see Data.Map).
* Chris Okasaki and Andy Gill, "*Fast Mergeable Integer Maps*", Workshop on ML, September 1998, pages 77-86, http://citeseer.ist.psu.edu/okasaki98fast.html
* D.R. Morrison, "/PATRICIA -- Practical Algorithm To Retrieve Information Coded In Alphanumeric/", Journal of the ACM, 15(4), October 1968, pages 514-534.
Operation comments contain the operation time complexity in the Big-O notation http://en.wikipedia.org/wiki/Big_O_notation. Many operations have a worst-case complexity of *O(min(n,W))*. This means that the operation can become linear in the number of elements with a maximum of *W* -- the number of bits in an Int (32 or 64).

An efficient implementation of ordered maps from keys to values (dictionaries).
API of this module is strict in the keys, but lazy in the values. If you need value-strict maps, use Data.Map.Strict instead. The Map type itself is shared between the lazy and strict modules, meaning that the same Map value can be passed to functions in both modules (although that is rarely needed).
These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.
> import qualified Data.Map.Lazy as Map
The implementation of Map is based on *size balanced* binary trees (or trees of *bounded balance*) as described by:
* Stephen Adams, "*Efficient sets: a balancing act*", Journal of Functional Programming 3(4):553-562, October 1993, http://www.swiss.ai.mit.edu/~adams/BB/.
* J. Nievergelt and E.M. Reingold, "*Binary search trees of bounded balance*", SIAM journal of computing 2(1), March 1973.
Note that the implementation is *left-biased* -- the elements of a first argument are always preferred to the second, for example in union or insert.
Operation comments contain the operation time complexity in the Big-O notation (http://en.wikipedia.org/wiki/Big_O_notation).