Add saddle-points exercise

config.json

@@ -616,6 +616,14 @@
         "prerequisites": [],
         "difficulty": 4
       },
+      {
+        "slug": "saddle-points",
+        "name": "Saddle Points",
+        "uuid": "c3244c98-8419-4178-9a94-80374d2ebd3f",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
+      },
       {
         "slug": "sieve",
         "name": "Sieve",

exercises/practice/saddle-points/.docs/instructions.md

@@ -0,0 +1,27 @@
+# Instructions
+
+Your task is to find the potential trees where you could build your tree house.
+
+The data company provides the data as grids that show the heights of the trees.
+The rows of the grid represent the east-west direction, and the columns represent the north-south direction.
+
+An acceptable tree will be the largest in its row, while being the smallest in its column.
+
+A grid might not have any good trees at all.
+Or it might have one, or even several.
+
+Here is a grid that has exactly one candidate tree.
+
+```text
+      ↓
+      1  2  3  4
+    |-----------
+  1 | 9  8  7  8
+→ 2 |[5] 3  2  4
+  3 | 6  6  7  1
+```
+
+- Row 2 has values 5, 3, 2, and 4. The largest value is 5.
+- Column 1 has values 9, 5, and 6. The smallest value is 5.
+
+So the point at `[2, 1]` (row: 2, column: 1) is a great spot for a tree house.

exercises/practice/saddle-points/.docs/introduction.md

@@ -0,0 +1,11 @@
+# Introduction
+
+You plan to build a tree house in the woods near your house so that you can watch the sun rise and set.
+
+You've obtained data from a local survey company that show the height of every tree in each rectangular section of the map.
+You need to analyze each grid on the map to find good trees for your tree house.
+
+A good tree is both:
+
+- taller than every tree to the east and west, so that you have the best possible view of the sunrises and sunsets.
+- shorter than every tree to the north and south, to minimize the amount of tree climbing.

exercises/practice/saddle-points/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "saddle-points.sml"
+    ],
+    "test": [
+      "test.sml"
+    ],
+    "example": [
+      ".meta/example.sml"
+    ]
+  },
+  "blurb": "Detect saddle points in a matrix.",
+  "source": "J Dalbey's Programming Practice problems",
+  "source_url": "https://users.csc.calpoly.edu/~jdalbey/103/Projects/ProgrammingPractice.html"
+}

exercises/practice/saddle-points/.meta/example.sml

@@ -0,0 +1,29 @@
+type point = {row: int, column: int};
+
+fun saddlePoints ([] : int list list): point list = []
+  | saddlePoints ([] :: _): point list = []
+  | saddlePoints (matrix: int list list): point list =
+  let
+        fun rowMax (row: int list): int = foldl Int.max (hd row) (tl row)
+        val rowMaximums = Vector.fromList (map rowMax matrix)
+
+        fun transpose ([] :: _) = []
+          | transpose rows = map hd rows :: transpose (map tl rows)
+        fun colMin (col: int list): int = foldl Int.min (hd col) (tl col)
+        val columnMinimums = Vector.fromList (map colMin (transpose matrix))
+
+        fun checkCol rowIdx (element, (colIdx, acc)) =
+          (colIdx + 1,
+           if element = Vector.sub (rowMaximums, rowIdx)
+              andalso element = Vector.sub (columnMinimums, colIdx)
+           then {row = rowIdx + 1, column = colIdx + 1} :: acc
+           else acc)
+
+        fun check (row, rowIdx, acc) =
+          #2 (foldl (checkCol rowIdx) (0, acc) row)
+
+        fun checkRow (row, (rowIdx, acc)) =
+          (rowIdx + 1, check (row, rowIdx, acc))
+    in
+      rev (#2 (foldl checkRow (0, []) matrix))
+    end

exercises/practice/saddle-points/.meta/tests.toml

@@ -0,0 +1,37 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[3e374e63-a2e0-4530-a39a-d53c560382bd]
+description = "Can identify single saddle point"
+
+[6b501e2b-6c1f-491f-b1bb-7f278f760534]
+description = "Can identify that empty matrix has no saddle points"
+
+[8c27cc64-e573-4fcb-a099-f0ae863fb02f]
+description = "Can identify lack of saddle points when there are none"
+
+[6d1399bd-e105-40fd-a2c9-c6609507d7a3]
+description = "Can identify multiple saddle points in a column"
+
+[3e81dce9-53b3-44e6-bf26-e328885fd5d1]
+description = "Can identify multiple saddle points in a row"
+
+[88868621-b6f4-4837-bb8b-3fad8b25d46b]
+description = "Can identify saddle point in bottom right corner"
+
+[5b9499ca-fcea-4195-830a-9c4584a0ee79]
+description = "Can identify saddle points in a non square matrix"
+
+[ee99ccd2-a1f1-4283-ad39-f8c70f0cf594]
+description = "Can identify that saddle points in a single column matrix are those with the minimum value"
+
+[63abf709-a84b-407f-a1b3-456638689713]
+description = "Can identify that saddle points in a single row matrix are those with the maximum value"

exercises/practice/saddle-points/saddle-points.sml

@@ -0,0 +1,4 @@
+type point = {row: int, column: int};
+
+fun saddlePoints (matrix: int list list): point list =
+  raise Fail "'saddlePoints' is not implemented"

exercises/practice/saddle-points/test.sml

@@ -0,0 +1,84 @@
+(* version 1.0.0 *)
+
+use "testlib.sml";
+use "saddle-points.sml";
+
+infixr |>
+fun x |> f = f x
+
+val testsuite =
+  describe "saddle-points" [
+    test "Can identify single saddle point"
+      (fn _ => let
+        val matrix = [[9, 8, 7], [5, 3, 2], [6, 6, 7]]
+        val expected = [{row = 2, column = 1}]
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify that empty matrix has no saddle points"
+      (fn _ => let
+        val matrix = [[]]
+        val expected = []
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify lack of saddle points when there are none"
+      (fn _ => let
+        val matrix = [[1, 2, 3], [3, 1, 2], [2, 3, 1]]
+        val expected = []
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify multiple saddle points in a column"
+      (fn _ => let
+        val matrix = [[4, 5, 4], [3, 5, 5], [1, 5, 4]]
+        val expected = [{row = 1, column = 2}, {row = 2, column = 2}, {row = 3, column = 2}]
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify multiple saddle points in a row"
+      (fn _ => let
+        val matrix = [[6, 7, 8], [5, 5, 5], [7, 5, 6]]
+        val expected = [{row = 2, column = 1}, {row = 2, column = 2}, {row = 2, column = 3}]
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify saddle point in bottom right corner"
+      (fn _ => let
+        val matrix = [[8, 7, 9], [6, 7, 6], [3, 2, 5]]
+        val expected = [{row = 3, column = 3}]
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify saddle points in a non square matrix"
+      (fn _ => let
+        val matrix = [[3, 1, 3], [3, 2, 4]]
+        val expected = [{row = 1, column = 1}, {row = 1, column = 3}]
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify that saddle points in a single column matrix are those with the minimum value"
+      (fn _ => let
+        val matrix = [[2], [1], [4], [1]]
+        val expected = [{row = 2, column = 1}, {row = 4, column = 1}]
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end),
+
+    test "Can identify that saddle points in a single row matrix are those with the maximum value"
+      (fn _ => let
+        val matrix = [[2, 5, 3, 5]]
+        val expected = [{row = 1, column = 2}, {row = 1, column = 4}]
+      in
+        saddlePoints matrix |> Expect.equalTo expected
+      end)
+  ]
+
+val _ = Test.run testsuite

exercises/practice/saddle-points/testlib.sml

@@ -0,0 +1,160 @@
+structure Expect =
+struct
+  datatype expectation = Pass | Fail of string * string
+
+  local
+    fun failEq b a =
+      Fail ("Expected: " ^ b, "Got: " ^ a)
+
+    fun failExn b a =
+      Fail ("Expected: " ^ b, "Raised: " ^ a)
+
+    fun exnName (e: exn): string = General.exnName e
+  in
+    fun truthy a =
+      if a
+      then Pass
+      else failEq "true" "false"
+
+    fun falsy a =
+      if a
+      then failEq "false" "true"
+      else Pass
+
+    fun equalTo b a = 
+      if a = b
+      then Pass
+      else failEq (PolyML.makestring b) (PolyML.makestring a)
+
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
+      then Pass
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
+
+    fun anyError f =
+      (
+        f ();
+        failExn "an exception" "Nothing"
+      ) handle _ => Pass
+
+    fun error e f =
+      (
+        f ();
+        failExn (exnName e) "Nothing"
+      ) handle e' => if exnMessage e' = exnMessage e
+                     then Pass
+                     else failExn (exnMessage e) (exnMessage e')
+  end
+end
+
+structure TermColor =
+struct
+  datatype color = Red | Green | Yellow | Normal
+
+  fun f Red    = "\027[31m"
+    | f Green  = "\027[32m"
+    | f Yellow = "\027[33m"
+    | f Normal = "\027[0m"
+
+  fun colorize color s = (f color) ^ s ^ (f Normal)
+
+  val redit = colorize Red
+
+  val greenit = colorize Green
+
+  val yellowit = colorize Yellow
+end
+
+structure Test =
+struct
+  datatype testnode = TestGroup of string * testnode list
+                    | Test of string * (unit -> Expect.expectation)
+
+  local
+    datatype evaluation = Success of string
+                        | Failure of string * string * string
+                        | Error of string * string
+
+    fun indent n s = (implode (List.tabulate (n, fn _ => #" "))) ^ s
+
+    fun fmt indentlvl ev =
+      let
+        val check = TermColor.greenit "\226\156\148 " (* ✔ *)
+        val cross = TermColor.redit "\226\156\150 "   (* ✖ *)
+        val indentlvl = indentlvl * 2
+      in
+      case ev of
+        Success descr => indent indentlvl (check ^ descr)
+      | Failure (descr, exp, got) =>
+          String.concatWith "\n" [indent indentlvl (cross ^ descr),
+                                  indent (indentlvl + 2) exp,
+                                  indent (indentlvl + 2) got]
+      | Error (descr, reason) =>
+          String.concatWith "\n" [indent indentlvl (cross ^ descr),
+                                  indent (indentlvl + 2) (TermColor.redit reason)]
+      end
+
+    fun eval (TestGroup _) = raise Fail "Only a 'Test' can be evaluated"
+      | eval (Test (descr, thunk)) =
+          (
+            case thunk () of
+              Expect.Pass   => ((1, 0, 0), Success descr)
+            | Expect.Fail (s, s') => ((0, 1, 0), Failure (descr, s, s'))
+          )
+          handle e => ((0, 0, 1), Error (descr, "Unexpected error: " ^ exnMessage e))
+
+    fun flatten depth testnode =
+      let
+        fun sum (x, y, z) (a, b, c) = (x + a, y + b, z + c)
+
+        fun aux (t, (counter, acc)) =
+          let
+            val (counter', texts) = flatten (depth + 1) t
+          in
+            (sum counter' counter, texts :: acc)
+          end
+      in
+        case testnode of
+          TestGroup (descr, ts) =>
+            let
+              val (counter, texts) = foldr aux ((0, 0, 0), []) ts
+            in
+              (counter, (indent (depth * 2) descr) :: List.concat texts)
+            end
+        | Test _ =>
+            let
+              val (counter, evaluation) = eval testnode
+            in
+              (counter, [fmt depth evaluation])
+            end
+      end
+
+    fun println s = print (s ^ "\n")
+  in
+    fun run suite =
+      let
+        val ((succeeded, failed, errored), texts) = flatten 0 suite
+
+        val summary = String.concatWith ", " [
+          TermColor.greenit ((Int.toString succeeded) ^ " passed"),
+          TermColor.redit ((Int.toString failed) ^ " failed"),
+          TermColor.redit ((Int.toString errored) ^ " errored"),
+          (Int.toString (succeeded + failed + errored)) ^ " total"
+        ]
+
+        val status = if failed = 0 andalso errored = 0
+                     then OS.Process.success
+                     else OS.Process.failure
+
+      in
+        List.app println texts;
+        println "";
+        println ("Tests: " ^ summary);
+        OS.Process.exit status
+      end
+  end
+end
+
+fun describe description tests = Test.TestGroup (description, tests)
+fun test description thunk = Test.Test (description, thunk)