Add saddle-points exercise (#64)

Author: keiravillekode

config.json

@@ -313,6 +313,14 @@
         "prerequisites": [],
         "difficulty": 4
       },
+      {
+        "slug": "saddle-points",
+        "name": "Saddle Points",
+        "uuid": "63af24ea-4dc9-485a-8977-223fe2ee0751",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
+      },
       {
         "slug": "triangle",
         "name": "Triangle",

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.fut"
+    ],
+    "test": [
+      "test.fut"
+    ],
+    "example": [
+      ".meta/example.fut"
+    ]
+  },
+  "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.fut

@@ -0,0 +1,21 @@
+def saddle_points [m] [n] (matrix: [m][n]i32): [][2]i32 =
+  let row_maximums = loop row_maximums = replicate m 0 for i < m do
+    let greatest = loop greatest = i32.lowest for j < n do
+      i32.max greatest matrix[i][j]
+    in
+      row_maximums with [i] = greatest
+  in
+    let column_minimums = loop column_minimums = replicate n 0 for j < n do
+      let least = loop least = i32.highest for i < m do
+        i32.min least matrix[i][j]
+      in
+        column_minimums with [j] = least
+    in
+      let result = loop result = [] for i < m do
+        let result = loop result = result for j < n do
+          if matrix[i][j] != row_maximums[i] || matrix[i][j] != column_minimums[j] then result else
+          result ++ [[1 + i32.i64 i, 1 + i32.i64 j]]
+        in
+          result
+      in
+        result

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.fut

@@ -0,0 +1 @@
+def saddle_points [m] [n] (matrix: [m][n]i32): [][2]i32 = ???

exercises/practice/saddle-points/test.fut

@@ -0,0 +1,49 @@
+import "saddle_points"
+
+-- Can identify single saddle point
+-- ==
+-- input  { [[9, 8, 7], [5, 3, 2], [6, 6, 7]] }
+-- output { [[2, 1]] }
+
+-- Can identify that empty matrix has no saddle points
+-- ==
+-- input  { [empty([0]i32)] }
+-- output { empty([0][2]i32) }
+
+-- Can identify lack of saddle points when there are none
+-- ==
+-- input  { [[1, 2, 3], [3, 1, 2], [2, 3, 1]] }
+-- output { empty([0][2]i32) }
+
+-- Can identify multiple saddle points in a column
+-- ==
+-- input  { [[4, 5, 4], [3, 5, 5], [1, 5, 4]] }
+-- output { [[1, 2], [2, 2], [3, 2]] }
+
+-- Can identify multiple saddle points in a row
+-- ==
+-- input  { [[6, 7, 8], [5, 5, 5], [7, 5, 6]] }
+-- output { [[2, 1], [2, 2], [2, 3]] }
+
+-- Can identify saddle point in bottom right corner
+-- ==
+-- input  { [[8, 7, 9], [6, 7, 6], [3, 2, 5]] }
+-- output { [[3, 3]] }
+
+-- Can identify saddle points in a non square matrix
+-- ==
+-- input  { [[3, 1, 3], [3, 2, 4]] }
+-- output { [[1, 1], [1, 3]] }
+
+-- Can identify that saddle points in a single column matrix are those with the minimum value
+-- ==
+-- input  { [[2], [1], [4], [1]] }
+-- output { [[2, 1], [4, 1]] }
+
+-- Can identify that saddle points in a single row matrix are those with the maximum value
+-- ==
+-- input  { [[2, 5, 3, 5]] }
+-- output { [[1, 2], [1, 4]] }
+
+let main [m] [n] (matrix: [m][n]i32): [][2]i32 =
+  saddle_points matrix