Clarify wording in Chapter 4 problem descriptions (#207)

* rename factorizations function and clarify problem

Rename the function factorizations to factorize.

Clarify the problem description (in chapter 4) to make it clear that
the solution must find the prime factorization.

* clarify what components means in exercise (chapter 4)

Author: a-robu

exercises/chapter4/test/Main.purs

@@ -109,13 +109,13 @@ Note to reader: Delete this line to expand comment block -}
           Assert.equal (sort [ [ 3, 4, 5 ], [ 5, 12, 13 ], [ 6, 8, 10 ] ])
             $ sort
             $ triples 13
-      suite "Exercise - factorizations" do
+      suite "Exercise - factorize" do
         test "Test small non-prime number" do
           Assert.equal [ 3, 2 ]
-            $ factorizations 6
+            $ factorize 6
         test "Test number that uses the prime numbers less than 10" do
           Assert.equal [ 7, 5, 3, 2 ]
-            $ factorizations 210
+            $ factorize 210
     suite "Exercise Group - Folds and Tail Recursion" do
       test "Exercise - allTrue" do
         assert "all elements true"

exercises/chapter4/test/no-peeking/Solutions.purs

@@ -58,20 +58,20 @@ triples n = do
   pure [ i, j, k ]
 
 -- | Provide the prime numbers that, multiplied together, make the argument.
-factorizations :: Int -> Array Int
-factorizations n = factorizations' 2 n []
+factorize :: Int -> Array Int
+factorize n = factorize' 2 n []
   where
-  factorizations' :: Int -> Int -> Array Int -> Array Int
-  factorizations' _ 1 result = result
+  factorize' :: Int -> Int -> Array Int -> Array Int
+  factorize' _ 1 result = result
 
-  factorizations' divisor dividend result =
+  factorize' divisor dividend result =
     let
       remainder = rem dividend divisor
     in
       if remainder == 0 then
-        factorizations' (divisor) (quot dividend divisor) (cons divisor result)
+        factorize' (divisor) (quot dividend divisor) (cons divisor result)
       else
-        factorizations' (divisor + 1) dividend result
+        factorize' (divisor + 1) dividend result
 
 allTrue :: Array Boolean -> Boolean
 allTrue bools = foldl (\acc bool -> acc && bool) true bools

text/chapter4.md

@@ -384,8 +384,8 @@ This means that if the guard fails, then the current branch of the array compreh
 
  1. (Easy) Write a function `isPrime` which tests if its integer argument is prime or not. _Hint_: Use the `factors` function.
  1. (Medium) Write a function `cartesianProduct` which uses do notation to find the _cartesian product_ of two arrays, i.e. the set of all pairs of elements `a`, `b`, where `a` is an element of the first array, and `b` is an element of the second.
- 1. (Medium) Write a function `triples :: Int -> Array (Array Int)` which takes a number `n` and calculates all Pythagorean triples whose components are less than or equal to `n`. A _Pythagorean triple_ is an array of numbers `[a, b, c]` such that `a² + b² = c²`. _Hint_: Use the `guard` function in an array comprehension.
- 1. (Difficult) Write a function `factorizations` which produces all _factorizations_ of an integer `n`, i.e. arrays of integers whose product is `n`. _Hint_: for an integer greater than 1, break the problem down into two subproblems: finding the first factor, and finding the remaining factors.
+ 1. (Medium) Write a function `triples :: Int -> Array (Array Int)` which takes a number `n` and returns all Pythagorean triples whose components (the `a`, `b` and `c` values) are each less than or equal to `n`. A _Pythagorean triple_ is an array of numbers `[a, b, c]` such that `a² + b² = c²`. _Hint_: Use the `guard` function in an array comprehension.
+ 1. (Difficult) Write a function `factorize` which produces the [prime factorization](https://www.mathsisfun.com/prime-factorization.html) of `n`, i.e. the array of prime integers whose product is `n`. _Hint_: for an integer greater than 1, break the problem down into two subproblems: finding the first factor, and finding the remaining factors.
 
 ## Folds