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# map

## Map

* An intermediary operation
* it keeps all the elements
  * the cardinalty of inputs/domain equals the cardinality of outputs/range
* similar to the data structure (objects that store key value pairs)
  * it is a noun
* One set of things is being mapped to a differnt set of things
* It is a verb
  * a function maps an array of values to another array of values.
* Say you have a function f and an array of values A = \[a1, a2, a3, a4]. To map f over A means applying f to every element in A:
  * a1 → f (a1) = a1’
  * a2 → f (a2) = a2’
  * a3 → f (a3) = a3’
  * a4 → f (a4) = a4’
  * then assembling an array of the results in the same order as the inputs:
    * A’ = map( f, A ) = \[a1’, a2’, a3’, a4’]
* A way of removing loops
  * use of streams in java and fluent interfaces to implement actions on elements in a data structure

## Flatmap

* It is doing two opertaions
  * flatten
    * turn array of array into one array
  * map