Merge pull request #9 from DanielSherlock/permutations

Fixed and tidied `combinatorics.list_permutation` function

src/gleam_community/maths/combinatorics.gleam

@@ -319,6 +319,18 @@ fn do_list_combination(arr: List(a), k: Int, prefix: List(a)) -> List(List(a)) {
 ///
 /// Generate all permutations of a given list.
 ///
+/// Repeated elements are treated as distinct for the
+/// purpose of permutations, so two identical elements
+/// for example will appear "both ways round". This
+/// means lists with repeated elements return the same
+/// number of permutations as ones without.
+///
+/// N.B. The output of this function is a list of size
+/// factorial in the size of the input list. Caution is
+/// advised on input lists longer than ~11 elements, which
+/// may cause the VM to use unholy amounts of memory for
+/// the output.
+///
 /// <details>
 ///     <summary>Example:</summary>
 ///
@@ -338,6 +350,10 @@ fn do_list_combination(arr: List(a), k: Int, prefix: List(a)) -> List(List(a)) {
 ///         [2, 3, 1],
 ///         [3, 2, 1],
 ///       ]))
+///
+///       [1.0, 1.0]
+///       |> combinatorics.list_permutation()
+///       |> should.equal([[1.0, 1.0], [1.0, 1.0]])
 ///     }
 /// </details>
 ///
@@ -350,30 +366,16 @@ fn do_list_combination(arr: List(a), k: Int, prefix: List(a)) -> List(List(a)) {
 pub fn list_permutation(arr: List(a)) -> List(List(a)) {
   case arr {
     [] -> [[]]
-    _ ->
-      flat_map(
-        arr,
-        fn(x) {
-          let remaining = list.filter(arr, fn(y) { x != y })
-          list.map(list_permutation(remaining), fn(perm) { [x, ..perm] })
-        },
-      )
+    _ -> {
+      use x <- list.flat_map(arr)
+      // `x` is drawn from the list `arr` above,
+      // so Ok(...) can be safely asserted as the result of `list.pop` below
+      let assert Ok(#(_, remaining)) = list.pop(arr, fn(y) { x == y })
+      list.map(list_permutation(remaining), fn(perm) { [x, ..perm] })
+    }
   }
 }
 
-/// Flat map function
-fn flat_map(list: List(a), f: fn(a) -> List(b)) -> List(b) {
-  list
-  |> list.map(f)
-  |> concat()
-}
-
-/// Concatenate a list of lists
-fn concat(lists: List(List(a))) -> List(a) {
-  lists
-  |> list.fold([], list.append)
-}
-
 /// <div style="text-align: right;">
 ///     <a href="https://github.com/gleam-community/maths/issues">
 ///         <small>Spot a typo? Open an issue!</small>

test/gleam/gleam_community_maths_combinatorics.gleam

@@ -1,5 +1,6 @@
 import gleam_community/maths/combinatorics
 import gleam/set
+import gleam/list
 import gleeunit
 import gleeunit/should
 
@@ -103,15 +104,22 @@ pub fn list_cartesian_product_test() {
 }
 
 pub fn list_permutation_test() {
-  // An empty lists returns an empty list
+  // An empty lists returns one (empty) permutation
   []
   |> combinatorics.list_permutation()
   |> should.equal([[]])
 
+  // Singleton returns one (singleton) permutation
+  // Also works regardless of type of list elements
+  ["a"]
+  |> combinatorics.list_permutation()
+  |> should.equal([["a"]])
+
   // Test with some arbitrary inputs
   [1, 2]
   |> combinatorics.list_permutation()
-  |> should.equal([[1, 2], [2, 1]])
+  |> set.from_list()
+  |> should.equal(set.from_list([[1, 2], [2, 1]]))
 
   // Test with some arbitrary inputs
   [1, 2, 3]
@@ -125,6 +133,20 @@ pub fn list_permutation_test() {
     [2, 3, 1],
     [3, 2, 1],
   ]))
+
+  // Repeated elements are treated as distinct for the
+  // purpose of permutations, so two identical elements
+  // will appear "both ways round"
+  [1.0, 1.0]
+  |> combinatorics.list_permutation()
+  |> should.equal([[1.0, 1.0], [1.0, 1.0]])
+
+  // This means lists with repeated elements return the
+  // same number of permutations as ones without
+  ["l", "e", "t", "t", "e", "r", "s"]
+  |> combinatorics.list_permutation()
+  |> list.length()
+  |> should.equal(5040)
 }
 
 pub fn list_combination_test() {