[New Exercise]: Saddle Points

config.json

@@ -649,6 +649,14 @@
         "prerequisites": [],
         "difficulty": 3
       },
+      {
+        "slug": "saddle-points",
+        "name": "Saddle Points",
+        "uuid": "512f0d92-57c1-403c-a96a-82b5066fd047",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 3
+      },
       {
         "slug": "clock",
         "name": "Clock",

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

@@ -0,0 +1,26 @@
+# 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  <--- potential tree house at row 2, column 1, for tree with height 5
+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/SaddlePoints.example.ps1

@@ -0,0 +1,91 @@
+<#
+.DESCRIPTION
+    A helper class act as a data structure for the saddle point.
+    It has a two properties: Row and Column, their indexes should be offset by 1 to reflect normal counting.
+    It also has an Equals method for comparison in tests.
+    Please don't delete or change this class.
+#>
+Class SaddlePoint {
+    [int]$Row
+    [int]$Column
+
+    SaddlePoint($row, $col) {
+        $this.Row = $row
+        $this.Column = $col
+    }
+
+    [bool] Equals($other) {
+        return $this.Row -eq $other.Row -and $this.Column -eq $other.Column
+    }
+}
+
+Function Get-SaddlePoints() {
+    <#
+    .SYNOPSIS
+    Find all the available saddle points in a given matrix.
+
+    .DESCRIPTION
+    Given a matrix (jagged arrays), return all the available saddle points found.
+    The matrix can have a different number of rows and columns (non square), and it may have zero or more saddle points.
+
+    It's called a "saddle point" because it is greater than or equal to every element in its row and less than or equal to every element in its column.
+
+    Your code should be able to provide the (possibly empty) list of all the saddle points for any given matrix.
+
+    .PARAMETER Matrix
+    An array of arrays, each inner array contains number that could be a saddle point.
+
+    .EXAMPLE
+    Get-SaddlePoints -Matrix @( ,@(1, 2, 3))
+    Returns: [SaddlePoint]::new(1, 3)
+    #>
+    [CmdletBinding()]
+    Param(
+        [int[][]]$Matrix
+    )
+    #check for valid matrix
+    $lenCount = ($Matrix | Select-Object {$_.Count} -Unique).Count
+    if ($lenCount -gt 1) { Throw "Irregular matrix"}
+
+    #got total rows and column
+    $rows = $Matrix.Count
+    $columns = $Matrix[0].Count
+
+    $maxValues, $minValues = Get-MaxMinValues $Matrix $rows $columns
+
+    #saddle found when max of row is the same as min of column
+    $saddlePoints = @()
+    for ($row = 0; $row -lt $rows; $row++) {
+        for ($col = 0; $col -lt $columns; $col++) {
+            $value =  $Matrix[$row][$col]
+            if ($maxValues[$row] -eq $value -and $minValues[$col] -eq $value) {
+                $saddlePoints += [SaddlePoint]::new($row+1, $col+1)
+            }
+
+        }
+    }
+    $saddlePoints
+}
+
+function Get-MaxMinValues($matrix, $rows, $columns) {
+    <#
+    .DESCRIPTION
+    Helper function to find max value for each row and min value for each col
+    #>
+    $maxValues = @([int]::MinValue) * $rows  
+    $minValues = @([int]::MaxValue) * $columns
+
+    for ($row = 0; $row -lt $rows; $row++) {
+        for ($col = 0; $col -lt $columns; $col++) {
+            $value =  $Matrix[$row][$col]
+            if ($value -ge $maxValues[$row]) {
+                $maxValues[$row] = $value
+            }
+
+            if ($value -le $minValues[$col]) {
+                $minValues[$col] = $value
+            }
+        }
+    }
+    $maxValues, $minValues
+}

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

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glaxxie"
+  ],
+  "files": {
+    "solution": [
+      "SaddlePoints.ps1"
+    ],
+    "test": [
+      "SaddlePoints.tests.ps1"
+    ],
+    "example": [
+      ".meta/SaddlePoints.example.ps1"
+    ]
+  },
+  "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/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/SaddlePoints.ps1

@@ -0,0 +1,48 @@
+<#
+.DESCRIPTION
+    A helper class act as a data structure for the saddle point.
+    It has a two properties: Row and Column, their indexes should be offset by 1 to reflect normal counting.
+    It also has an Equals method for comparison in tests.
+    Please don't delete or change this class.
+#>
+Class SaddlePoint {
+    [int]$Row
+    [int]$Column
+
+    SaddlePoint($row, $col) {
+        $this.Row = $row
+        $this.Column = $col
+    }
+
+    [bool] Equals($other) {
+        return $this.Row -eq $other.Row -and $this.Column -eq $other.Column
+    }
+}
+
+Function Get-SaddlePoints() {
+    <#
+    .SYNOPSIS
+    Find all the available saddle points in a given matrix.
+
+    .DESCRIPTION
+    Given a matrix (jagged arrays), return all the available saddle points found.
+    The matrix can have a different number of rows and columns (non square), and it may have zero or more saddle points.
+
+    It's called a "saddle point" because it is greater than or equal to every element in its row and less than or equal to every element in its column.
+
+    Your code should be able to provide the (possibly empty) list of all the saddle points for any given matrix.
+
+    .PARAMETER Matrix
+    An array of arrays, each inner array contains number that could be a saddle point.
+
+    .EXAMPLE
+    Get-SaddlePoints -Matrix @( ,@(1, 2, 3))
+    Returns: [SaddlePoint]::new(1, 3)
+    #>
+    [CmdletBinding()]
+    Param(
+        [int[][]]$Matrix
+    )
+
+    Throw "Please implement this function"
+}

exercises/practice/saddle-points/SaddlePoints.tests.ps1

@@ -0,0 +1,114 @@
+BeforeAll {
+    . "./SaddlePoints.ps1"
+}
+
+Describe "SaddlePoints test cases" {
+    Context "Can identify saddle" {
+        It "single saddle point" {
+            $got  = Get-SaddlePoints -Matrix @( 
+                @(9, 8, 7), 
+                @(5, 3, 2), 
+                @(6, 6, 7)
+            )
+            $want = @([SaddlePoint]::new(2, 1))
+
+            $got | Should -BeExactly $want
+        }
+
+        It "empty matrix has no saddle points" {
+            $got  = Get-SaddlePoints -Matrix @()
+
+            $got | Should -BeNullOrEmpty
+        }
+
+        It "lack of saddle points when there are none" {
+            $got  = Get-SaddlePoints -Matrix @(
+                @(1, 2, 3), 
+                @(3, 1, 2), 
+                @(2, 3, 1)
+            )
+
+            $got | Should -BeNullOrEmpty
+        }
+
+        It "multiple saddle points in a column" {
+            $got  = Get-SaddlePoints -Matrix @(
+                @(4, 5, 4), 
+                @(3, 5, 5), 
+                @(1, 5, 4)
+            )
+            $want = @(
+                [SaddlePoint]::new(1, 2),
+                [SaddlePoint]::new(2, 2),
+                [SaddlePoint]::new(3, 2)
+            )
+
+            $got | Should -BeExactly $want
+        }
+
+        It "multiple saddle points in a row" {
+            $got  = Get-SaddlePoints -Matrix @(
+                @(6, 7, 8), 
+                @(5, 5, 5), 
+                @(7, 5, 6)
+            )
+            $want = @(
+                [SaddlePoint]::new(2, 1),
+                [SaddlePoint]::new(2, 2),
+                [SaddlePoint]::new(2, 3)
+            )
+
+            $got | Should -BeExactly $want
+        }
+
+        It "saddle point in bottom right corner" {
+            $got  = Get-SaddlePoints -Matrix @(
+                @(8, 7, 9), 
+                @(6, 7, 6), 
+                @(3, 2, 5)
+            )
+            $want = @([SaddlePoint]::new(3, 3))
+
+            $got | Should -BeExactly $want
+        }
+
+        It "saddle points in a non square matrix" {
+            $got  = Get-SaddlePoints -Matrix @(
+                @(3, 1, 3), 
+                @(3, 2, 4)
+            )
+            $want = @([SaddlePoint]::new(1, 1), [SaddlePoint]::new(1, 3))
+
+            $got | Should -BeExactly $want
+        }
+
+        It "saddle points in a single column matrix are those with the minimum value" {
+            $got  = Get-SaddlePoints -Matrix @(
+                @(2), 
+                @(1),
+                @(4),
+                @(1)
+            )
+            $want = @([SaddlePoint]::new(2, 1), [SaddlePoint]::new(4, 1))
+
+            $got | Should -BeExactly $want
+        }
+
+        It "saddle points in a single row matrix are those with the maximum value" {
+            $got  = Get-SaddlePoints -Matrix @( ,@(2, 5, 3, 5))
+            $want = @([SaddlePoint]::new(1, 2), [SaddlePoint]::new(1, 4))
+
+            $got | Should -BeExactly $want
+        }
+    }
+
+    Context "invalid input" {
+        It "irregular_matrix" {
+            {Get-SaddlePoints -Matrix @( 
+                @(3, 2, 1),
+                @(0, 1),
+                @(2, 1, 0)
+            )} | Should -Throw "Irregular matrix"
+        }
+    }
+}