saddle-points

config.json

@@ -390,6 +390,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 4
+      },
+      {
+        "slug": "saddle-points",
+        "name": "Saddle Points",
+        "uuid": "cbffab05-8db3-438f-bf16-490d19a403a7",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
       }
     ]
   },

exercises/practice/saddle-points/.busted

@@ -0,0 +1,5 @@
+return {
+  default = {
+    ROOT = { '.' }
+  }
+}

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": [
+    "glennj"
+  ],
+  "files": {
+    "solution": [
+      "saddle_points.moon"
+    ],
+    "test": [
+      "saddle_points_spec.moon"
+    ],
+    "example": [
+      ".meta/example.moon"
+    ]
+  },
+  "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.moon

@@ -0,0 +1,20 @@
+{
+  saddle_points: (mtx) ->
+    nrow, ncol = #mtx, #mtx[1]
+
+    row_max = [math.mininteger for _ = 1, nrow]
+    col_min = [math.maxinteger for _ = 1, ncol]
+
+    for r = 1, nrow
+      for c = 1, ncol
+        row_max[r] = math.max row_max[r], mtx[r][c]
+        col_min[c] = math.min col_min[c], mtx[r][c]
+
+    results = {}
+    for r = 1, nrow
+      for c = 1, ncol
+        if row_max[r] == mtx[r][c] and col_min[c] == mtx[r][c]
+          table.insert results, {row: r, column: c}
+
+    results
+}

exercises/practice/saddle-points/.meta/spec_generator.moon

@@ -0,0 +1,33 @@
+int_list = (list) -> "{#{table.concat list, ', '}}"
+
+int_lists = (lists, level) ->
+  if #lists == 1
+    "{#{int_list lists[1]}}"
+  else
+    rows = [indent int_list(row) .. ',', level + 1 for row in *lists]
+    table.insert rows, 1, '{'
+    table.insert rows, indent '}', level
+    table.concat rows, '\n'
+
+result_obj = (obj) -> "{row: #{obj.row}, column: #{obj.column}}"
+result_list = (list) -> "{#{table.concat [result_obj obj for obj in *list], ', '}}"
+
+{
+  module_imports: {'saddle_points'},
+
+  test_helpers: [[
+  cmp_saddle_points = (a, b) ->
+    a.row < b.row or (a.row == b.row and a.column < b.column)
+]]
+
+  generate_test: (case, level) ->
+    lines = {
+      "matrix = #{int_lists case.input.matrix, level}",
+      "result = saddle_points matrix"
+      "expected = #{result_list case.expected}",
+      "table.sort result, cmp_saddle_points",
+      "table.sort expected, cmp_saddle_points",
+      "assert.are.same expected, result"
+    }
+    table.concat [indent line, level for line in *lines], '\n'
+}

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.moon

@@ -0,0 +1,4 @@
+{
+  saddle_points: (mtx) ->
+    error 'Implement me'
+}

exercises/practice/saddle-points/saddle_points_spec.moon

@@ -0,0 +1,105 @@
+import saddle_points from require 'saddle_points'
+
+describe 'saddle-points', ->
+  cmp_saddle_points = (a, b) ->
+    a.row < b.row or (a.row == b.row and a.column < b.column)
+
+  it 'Can identify single saddle point', ->
+    matrix = {
+      {9, 8, 7},
+      {5, 3, 2},
+      {6, 6, 7},
+    }
+    result = saddle_points matrix
+    expected = {{row: 2, column: 1}}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify that empty matrix has no saddle points', ->
+    matrix = {{}}
+    result = saddle_points matrix
+    expected = {}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify lack of saddle points when there are none', ->
+    matrix = {
+      {1, 2, 3},
+      {3, 1, 2},
+      {2, 3, 1},
+    }
+    result = saddle_points matrix
+    expected = {}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify multiple saddle points in a column', ->
+    matrix = {
+      {4, 5, 4},
+      {3, 5, 5},
+      {1, 5, 4},
+    }
+    result = saddle_points matrix
+    expected = {{row: 1, column: 2}, {row: 2, column: 2}, {row: 3, column: 2}}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify multiple saddle points in a row', ->
+    matrix = {
+      {6, 7, 8},
+      {5, 5, 5},
+      {7, 5, 6},
+    }
+    result = saddle_points matrix
+    expected = {{row: 2, column: 1}, {row: 2, column: 2}, {row: 2, column: 3}}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify saddle point in bottom right corner', ->
+    matrix = {
+      {8, 7, 9},
+      {6, 7, 6},
+      {3, 2, 5},
+    }
+    result = saddle_points matrix
+    expected = {{row: 3, column: 3}}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify saddle points in a non square matrix', ->
+    matrix = {
+      {3, 1, 3},
+      {3, 2, 4},
+    }
+    result = saddle_points matrix
+    expected = {{row: 1, column: 3}, {row: 1, column: 1}}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify that saddle points in a single column matrix are those with the minimum value', ->
+    matrix = {
+      {2},
+      {1},
+      {4},
+      {1},
+    }
+    result = saddle_points matrix
+    expected = {{row: 2, column: 1}, {row: 4, column: 1}}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result
+
+  pending 'Can identify that saddle points in a single row matrix are those with the maximum value', ->
+    matrix = {{2, 5, 3, 5}}
+    result = saddle_points matrix
+    expected = {{row: 1, column: 2}, {row: 1, column: 4}}
+    table.sort result, cmp_saddle_points
+    table.sort expected, cmp_saddle_points
+    assert.are.same expected, result