**Packages**- containers

An efficient implementation of maps from integer keys to values (dictionaries).
This module re-exports the value lazy Data.IntMap.Lazy API, plus several deprecated value strict functions. Please note that these functions have different strictness properties than those in Data.IntMap.Strict: they only evaluate the result of the combining function. For example, the default value to insertWith' is only evaluated if the combining function is called and uses it.
These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.
> import Data.IntMap (IntMap)
> import qualified Data.IntMap 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 integer sets.
These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.
> import Data.IntSet (IntSet)
> import qualified Data.IntSet as IntSet
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 set implementation (see Data.Set).
* 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.
Additionally, this implementation places bitmaps in the leaves of the tree. Their size is the natural size of a machine word (32 or 64 bits) and greatly reduce memory footprint and execution times for dense sets, e.g. sets other. The asymptotics are not affected by this optimization.
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).

A map of integers to values a.

A set of integers.