Module
Map

*Note:* You should use Data.Map.Strict instead of this module if:

- You will eventually need all the values stored.
- The stored values don't represent large virtual data structures to be lazily computed.

An efficient implementation of ordered maps from keys to values (dictionaries).

These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.

import qualified Data.Map 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).

map
:: (a -> b) -> Map k a -> Map k b

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (a -> b) -> Map k a -> Map k b

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (a -> b) -> IntMap a -> IntMap b

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (a -> b) -> IntMap a -> IntMap b

containers - Data.IntMap.Strict

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (Key -> Key) -> IntSet -> IntSet

*O(n*min(n,W))*.

is the set obtained by applying `map`

f s`f`

to each element of `s`

.

It's worth noting that the size of the result may be smaller if,
for some `(x,y)`

, `x /= y && f x == f y`

map
:: (a -> b) -> Set a -> Set b

*O(n*log n)*.

is the set obtained by applying `map`

f s`f`

to each element of `s`

.

It's worth noting that the size of the result may be smaller if,
for some `(x,y)`

, `x /= y && f x == f y`

Data
Map

A Map from keys `k`

to values `a`

.

Data
Map

A Map from keys `k`

to values `a`

.

Module
Strict

An efficient implementation of ordered maps from keys to values (dictionaries).

API of this module is strict in both the keys and the values.
If you need value-lazy maps, use Data.Map.Lazy instead.
The `Map`

type 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.Strict 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).

Be aware that the `Functor`

, `Traversable`

and `Data`

instances
are the same as for the Data.Map.Lazy module, so if they are used
on strict maps, the resulting maps will be lazy.

Module
Lazy

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).

showTreeWith
:: (k -> a -> String) -> Bool -> Bool -> Map k a -> String

*O(n)*. The expression (

) shows
the tree that implements the map. Elements are shown using the `showTreeWith`

showelem hang wide map`showElem`

function. If `hang`

is
`True`

, a *hanging* tree is shown otherwise a rotated tree is shown. If
`wide`

is `True`

, an extra wide version is shown.

Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]] Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t (4,()) +--(2,()) | +--(1,()) | +--(3,()) +--(5,()) Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t (4,()) | +--(2,()) | | | +--(1,()) | | | +--(3,()) | +--(5,()) Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t +--(5,()) | (4,()) | | +--(3,()) | | +--(2,()) | +--(1,())

showTreeWith
:: (k -> a -> String) -> Bool -> Bool -> Map k a -> String

*O(n)*. The expression (

) shows
the tree that implements the map. Elements are shown using the `showTreeWith`

showelem hang wide map`showElem`

function. If `hang`

is
`True`

, a *hanging* tree is shown otherwise a rotated tree is shown. If
`wide`

is `True`

, an extra wide version is shown.

Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]] Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t (4,()) +--(2,()) | +--(1,()) | +--(3,()) +--(5,()) Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t (4,()) | +--(2,()) | | | +--(1,()) | | | +--(3,()) | +--(5,()) Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t +--(5,()) | (4,()) | | +--(3,()) | | +--(2,()) | +--(1,())

foldlWithKey
:: (a -> k -> b -> a) -> a -> Map k b -> a

*O(n)*. Fold the keys and values in the map using the given left-associative
binary operator, such that

.
`foldlWithKey`

f z == `foldl`

(\z' (kx, x) -> f z' kx x) z . `toAscList`

For example,

keys = reverse . foldlWithKey (\ks k x -> k:ks) []

let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"

foldlWithKey
:: (a -> k -> b -> a) -> a -> Map k b -> a

*O(n)*. Fold the keys and values in the map using the given left-associative
binary operator, such that

.
`foldlWithKey`

f z == `foldl`

(\z' (kx, x) -> f z' kx x) z . `toAscList`

For example,

keys = reverse . foldlWithKey (\ks k x -> k:ks) []

let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"

foldrWithKey
:: (k -> a -> b -> b) -> b -> Map k a -> b

*O(n)*. Fold the keys and values in the map using the given right-associative
binary operator, such that

.
`foldrWithKey`

f z == `foldr`

(`uncurry`

f) z . `toAscList`

For example,

keys map = foldrWithKey (\k x ks -> k:ks) [] map

let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"

foldrWithKey
:: (k -> a -> b -> b) -> b -> Map k a -> b

*O(n)*. Fold the keys and values in the map using the given right-associative
binary operator, such that

.
`foldrWithKey`

f z == `foldr`

(`uncurry`

f) z . `toAscList`

For example,

keys map = foldrWithKey (\k x ks -> k:ks) [] map

let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"

null
:: Map k a -> Bool

containers - Data.Map.Lazy Data.Map.Strict

*O(1)*. Is the map empty?

Data.Map.null (empty) == True Data.Map.null (singleton 1 'a') == False

foldlWithKey
:: (a -> Key -> b -> a) -> a -> IntMap b -> a

*O(n)*. Fold the keys and values in the map using the given left-associative
binary operator, such that

.
`foldlWithKey`

f z == `foldl`

(\z' (kx, x) -> f z' kx x) z . `toAscList`

For example,

keys = reverse . foldlWithKey (\ks k x -> k:ks) []

let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"

foldrWithKey
:: (Key -> a -> b -> b) -> b -> IntMap a -> b

containers - Data.IntMap.Strict

*O(n)*. Fold the keys and values in the map using the given right-associative
binary operator, such that

.
`foldrWithKey`

f z == `foldr`

(`uncurry`

f) z . `toAscList`

For example,

keys map = foldrWithKey (\k x ks -> k:ks) [] map

let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"