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Add Saddle Points (#121)
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‎config.json‎

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"prerequisites": [],
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"difficulty": 1
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},
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{
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"slug": "saddle-points",
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"name": "Saddle Points",
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"uuid": "04348df7-d82a-406b-8527-64e82a835fcd",
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"practices": [],
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"prerequisites": [],
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"difficulty": 5
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},
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{
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"slug": "scrabble-score",
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"name": "Scrabble Score",

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

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

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

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

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

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

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let
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inherit (import <nixpkgs/lib>)
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cartesianProduct
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min
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max
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range
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;
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transpose =
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matrix:
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let
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colTotal = builtins.length (builtins.head matrix);
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in
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builtins.genList (i: map (row: builtins.elemAt row i) matrix) colTotal;
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minimum = xs: builtins.foldl' min (builtins.head xs) xs;
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maximum = xs: builtins.foldl' max (builtins.head xs) xs;
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in
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{
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saddlePoints =
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matrix:
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let
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maxPerRow = map maximum matrix;
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minPerCol = map minimum (transpose matrix);
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indices = cartesianProduct {
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row = range 1 (builtins.length matrix);
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column = range 1 (builtins.length (builtins.head matrix));
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};
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in
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builtins.filter (
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{ row, column }:
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let
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maxInRow = builtins.elemAt maxPerRow (row - 1);
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minInCol = builtins.elemAt minPerCol (column - 1);
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element = builtins.elemAt (builtins.elemAt matrix (row - 1)) (column - 1);
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in
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element == maxInRow && element == minInCol
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) indices;
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}

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

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

‎exercises/practice/saddle-points/saddle-points-test.nix‎

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let
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inherit (import ./saddle-points.nix) saddlePoints;
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in
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{
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"test can identify single saddle point" = {
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expr = saddlePoints [
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[
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9
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8
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7
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]
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[
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5
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3
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2
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]
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[
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6
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6
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7
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]
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];
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expected = [
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{
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row = 2;
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column = 1;
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}
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];
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};
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"test can identify that empty matrix has no saddle points" = {
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expr = saddlePoints [
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[ ]
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];
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expected = [ ];
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};
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"test can identify lack of saddle points when there are none" = {
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expr = saddlePoints [
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[
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1
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2
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3
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]
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[
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3
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1
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2
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]
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[
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2
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3
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1
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]
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];
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expected = [ ];
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};
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"test can identify multiple saddle points in a column" = {
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expr = saddlePoints [
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[
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4
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5
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4
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]
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[
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3
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5
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5
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]
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[
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1
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5
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4
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]
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];
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expected = [
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{
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row = 1;
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column = 2;
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}
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{
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row = 2;
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column = 2;
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}
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{
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row = 3;
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column = 2;
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}
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];
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};
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"test can identify multiple saddle points in a row" = {
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expr = saddlePoints [
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[
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6
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7
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8
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]
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[
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5
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5
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5
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]
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[
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7
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5
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6
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]
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];
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expected = [
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{
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row = 2;
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column = 1;
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}
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{
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row = 2;
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column = 2;
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}
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{
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row = 2;
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column = 3;
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}
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];
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};
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"test can identify saddle point in bottom right corner" = {
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expr = saddlePoints [
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[
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8
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7
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9
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]
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[
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6
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7
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6
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]
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[
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3
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2
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5
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]
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];
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expected = [
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{
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row = 3;
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column = 3;
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}
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];
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};
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"test can identify saddle points in a non square matrix" = {
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expr = saddlePoints [
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[
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3
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1
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3
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]
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[
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3
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2
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4
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]
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];
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expected = [
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{
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row = 1;
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column = 1;
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}
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{
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row = 1;
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column = 3;
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}
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];
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};
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"test can identify that saddle points in a single column matrix are those with the minimum value" =
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{
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expr = saddlePoints [
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[ 2 ]
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[ 1 ]
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[ 4 ]
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[ 1 ]
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];
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expected = [
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{
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row = 2;
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column = 1;
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}
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{
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row = 4;
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column = 1;
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}
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];
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};
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"test can identify that saddle points in a single row matrix are those with the maximum value" = {
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expr = saddlePoints [
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[
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2
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5
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3
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5
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]
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];
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expected = [
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{
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row = 1;
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column = 2;
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}
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{
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row = 1;
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column = 4;
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}
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];
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};
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}

‎exercises/practice/saddle-points/saddle-points.nix‎

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{
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saddlePoints = matrix: throw "You need to implement this function.";
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}

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