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[New Exercise]: Piecing It Together (#425)
Add exercise `piecing it together`
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‎config.json‎

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"prerequisites": [],
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"difficulty": 5
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},
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{
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"slug": "piecing-it-together",
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"name": "Piecing It Together",
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"uuid": "23b80d70-283c-44be-a360-8a23a42773f4",
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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": "rectangles",
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"name": "Rectangles",

‎exercises/practice/piecing-it-together/.docs/instructions.md‎

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# Instructions
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Given partial information about a jigsaw puzzle, add the missing pieces.
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If the information is insufficient to complete the details, or if given parts are in contradiction, the user should be notified.
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The full information about the jigsaw puzzle contains the following parts:
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- `pieces`: Total number of pieces
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- `border`: Number of border pieces
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- `inside`: Number of inside (non-border) pieces
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- `rows`: Number of rows
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- `columns`: Number of columns
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- `aspectRatio`: Aspect ratio of columns to rows
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- `format`: Puzzle format, which can be `portrait`, `square`, or `landscape`
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For this exercise, you may assume square pieces, so that the format can be derived from the aspect ratio:
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- If the aspect ratio is less than 1, it's `portrait`
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- If it is equal to 1, it's `square`
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- If it is greater than 1, it's `landscape`
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## Three examples
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### Portrait
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A portrait jigsaw puzzle with 6 pieces, all of which are border pieces and none are inside pieces. It has 3 rows and 2 columns. The aspect ratio is 1.5 (3/2).
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![A 2 by 3 jigsaw puzzle](https://assets.exercism.org/images/exercises/piecing-it-together/jigsaw-puzzle-2x3.svg)
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### Square
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A square jigsaw puzzle with 9 pieces, all of which are border pieces except for the one in the center, which is an inside piece. It has 3 rows and 3 columns. The aspect ratio is 1 (3/3).
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![A 3 by 3 jigsaw puzzle](https://assets.exercism.org/images/exercises/piecing-it-together/jigsaw-puzzle-3x3.svg)
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### Landscape
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A landscape jigsaw puzzle with 12 pieces, 10 of which are border pieces and 2 are inside pieces. It has 3 rows and 4 columns. The aspect ratio is 1.333333... (4/3).
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![A 4 by 3 jigsaw puzzle](https://assets.exercism.org/images/exercises/piecing-it-together/jigsaw-puzzle-4x3.svg)

‎exercises/practice/piecing-it-together/.docs/introduction.md‎

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# Introduction
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Your best friend has started collecting jigsaw puzzles and wants to build a detailed catalog of their collection — recording information such as the total number of pieces, the number of rows and columns, the number of border and inside pieces, aspect ratio, and puzzle format.
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Even with your powers combined, it takes multiple hours to solve a single jigsaw puzzle with one thousand pieces — and then you still need to count the rows and columns and calculate the remaining numbers manually.
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The even larger puzzles with thousands of pieces look quite daunting now.
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"There has to be a better way!" you exclaim and sit down in front of your computer to solve the problem.

‎exercises/practice/piecing-it-together/.meta/PiecingItTogether.example.ps1‎

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<#
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.SYNOPSIS
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Given partial information about a jigsaw puzzle, add the missing pieces.
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.DESCRIPTION
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Calculate properties of a jigsaw puzzle with given information if possible.
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If not possible due to insufficient or incorrect information, the user should be notified.
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Read instructions for more information and example.
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#>
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enum Format {
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Unknown
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Portrait
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Square
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Landscape
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}
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class JigsawPuzzle {
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[int]$Pieces
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[int]$Border
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[int]$Inside
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[int]$Rows
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[int]$Columns
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[double]$AspectRatio
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[Format]$Format
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GetData([PSCustomObject]$partialData)
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{
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if ($partialData.PSObject.Properties.Name -contains "AspectRatio") {
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$this.ProcessDataFromRatio($partialData)
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} elseif ($partialData.PSObject.Properties.Name -contains "Format") {
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$this.ProcessDataFromFormat($partialData)
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} else {
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throw "insufficient data"
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}
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}
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FillFromRowsAndColumns()
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{
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$this.Pieces = $this.Rows * $this.Columns
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$this.Border = 2*$this.Rows + 2*$this.Columns - 4
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$this.Inside = $this.Pieces - $this.Border
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$this.AspectRatio = $this.Columns / $this.Rows
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}
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[int[]]FindRowsAndColumn() {
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$a, $b = 0, 0
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for ($i = 1; $i -le [Math]::Sqrt($this.Pieces); $i++) {
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if (($i * $i * $this.AspectRatio) -eq $this.Pieces) {
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$a, $b = $i, ($i * $this.AspectRatio)
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break
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}
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}
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return $this.Format -eq [Format]::Landscape ? [Math]::Min($a,$b), [Math]::Max($a,$b)
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: [Math]::Max($a,$b), [Math]::Min($a,$b)
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}
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ProcessDataFromRatio([PSCustomObject]$partialData)
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{
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$properties = $partialData.PSObject.Properties.Name
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$this.AspectRatio = $partialData.AspectRatio
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$this.Format = switch ($true) {
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($partialData.AspectRatio -gt 1) { [Format]::Landscape }
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($partialData.AspectRatio -lt 1) { [Format]::Portrait }
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Default {[Format]::Square}
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}
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if ($properties -contains "Pieces") {
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$this.Pieces = $partialData.Pieces
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$this.Rows, $this.Columns = $this.FindRowsAndColumn()
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} elseif ($properties -contains "Border") {
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$this.Border = $partialData.Border
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$this.Rows = ($this.Border + 4) / (2 * (1 + $this.AspectRatio))
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$this.Columns = $this.Rows * $this.AspectRatio
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} elseif ($properties -contains "Inside") {
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$this.Inside = $partialData.Inside
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$r = $this.AspectRatio
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$i = $this.Inside
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$discriminant = [Math]::Pow((2 * $r + 2), 2) - (16 * $r) + (4 * $r * $i)
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$rows1 = ((2 * $r + 2) + [Math]::Sqrt($discriminant)) / (2 * $r)
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$rows2 = ((2 * $r + 2) - [Math]::Sqrt($discriminant)) / (2 * $r)
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$this.Rows = @($rows1, $rows2) | Where-Object { $_ -gt 0 -and [Math]::Round($_) -eq $_ } | Select-Object -First 1
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$this.Columns = $r * $this.Rows
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} elseif ($properties -contains "Rows") {
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$this.Rows = $partialData.Rows
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$this.Columns = $this.AspectRatio * $this.Rows
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} elseif ($properties -contains "Columns") {
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$this.Columns = $partialData.Columns
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$this.Rows = $this.Columns / $this.AspectRatio
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}
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$this.FillFromRowsAndColumns()
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}
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ProcessDataFromFormat([PSCustomObject]$partialData)
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{
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$this.Format = $partialData.Format
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$properties = $partialData.PSObject.Properties.Name
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if ($this.Format -eq [Format]::Square) {
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$this.AspectRatio = 1.0
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if ($properties -contains "Pieces") {
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$this.Rows = $this.Columns = [Math]::Sqrt($partialData.Pieces)
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} elseif ($properties -contains "Rows") {
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$this.Rows = $partialData.Rows
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$this.Columns = $this.Rows
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} elseif ($properties -contains "Columns") {
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$this.Columns = $partialData.Columns
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$this.Rows = $this.Columns
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} elseif ($properties -contains "Border") {
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$this.Rows = $this.Columns = ($partialData.Border + 4) / 4
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} elseif ($properties -contains "Inside") {
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$this.Rows = $this.Columns = [Math]::Sqrt($partialData.Inside) + 2
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} else {
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throw "bad data"
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}
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} else {
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$otherProperties = ($properties | Where-Object { $_ -ne "Format"}).Count
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if ($otherProperties -lt 2) {
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throw "insufficient data"
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}
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$pairs = $this.GenerateRowsAndColumnsFromFormat([PSCustomObject]$partialData)
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foreach ($pair in $pairs) {
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$tempPieces = $pair[0] * $pair[1]
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$tempBorder = 2*$pair[0] + 2*$pair[1] - 4
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if ($tempPieces -eq $partialData.Pieces -and $tempBorder -eq $partialData.Border) {
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if ($partialData.Format -eq [Format]::Landscape) {
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$this.Rows = [Math]::Min($pair[0], $pair[1])
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$this.Columns = [Math]::Max($pair[0], $pair[1])
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} else {
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$this.Rows = [Math]::Max($pair[0], $pair[1])
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$this.Columns = [Math]::Min($pair[0], $pair[1])
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}
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}
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}
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}
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$this.FillFromRowsAndColumns()
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$this.ValidateGivenData($partialData)
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}
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[object[]]GenerateRowsAndColumnsFromFormat([PSCustomObject]$partialData) {
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$properties = $partialData.PSObject.Properties.Name
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$pairs = @()
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if ($properties -contains "Pieces") {
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$this.Pieces = $partialData.Pieces
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for ($r = 1; $r -le [Math]::Sqrt($this.Pieces); $r++) {
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for ($c = $r; $c -le $this.Pieces; $c++) {
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if ($r * $c -eq $this.Pieces) {
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$pairs += ,@($c, $r)
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}
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}
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}
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}elseif ($properties -contains "Border") {
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$this.Border = $partialData.Border
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$sum = ($this.Border + 4) / 2
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for ($c = 1; $c -lt ($sum - 1); $c++) {
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$pairs += ,@($c, ($sum - $c))
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}
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}
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return $pairs
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}
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ValidateGivenData([PSCustomObject]$partialData)
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{
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foreach ($property in $partialData.psobject.Properties) {
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if ($property.Value -ne $this.PSObject.Properties[$property.Name].Value) {
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throw "contradictory data"
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}
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}
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}
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}

‎exercises/practice/piecing-it-together/.meta/config.json‎

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{
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"authors": [
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"glaxxie"
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],
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"files": {
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"solution": [
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"PiecingItTogether.ps1"
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],
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"test": [
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"PiecingItTogether.tests.ps1"
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],
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"example": [
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".meta/PiecingItTogether.example.ps1"
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]
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},
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"blurb": "Fill in missing jigsaw puzzle details from partial data",
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"source": "atk just started another 1000-pieces jigsaw puzzle when this idea hit him",
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"source_url": "https://github.com/exercism/problem-specifications/pull/2554"
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}

‎exercises/practice/piecing-it-together/.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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[ad626f23-09a2-4f5f-ba22-eec0671fa2a9]
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description = "1000 pieces puzzle with 1.6 aspect ratio"
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[3e0c5919-3561-42f5-b9ed-26d70c20214e]
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description = "square puzzle with 32 rows"
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[1126f160-b094-4dc2-bf37-13e36e394867]
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description = "400 pieces square puzzle with only inside pieces and aspect ratio"
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[a9743178-5642-4cc0-8fdb-00d6b031c3a0]
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description = "1500 pieces landscape puzzle with 30 rows and 1.6 aspect ratio"
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[f6378369-989c-497f-a6e2-f30b1fa76cba]
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description = "300 pieces portrait puzzle with 70 border pieces"
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[f53f82ba-5663-4c7e-9e86-57fdbb3e53d2]
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description = "puzzle with insufficient data"
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[a3d5c31a-cc74-44bf-b4fc-9e4d65f1ac1a]
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description = "puzzle with contradictory data"

‎exercises/practice/piecing-it-together/PiecingItTogether.ps1‎

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<#
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.SYNOPSIS
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Given partial information about a jigsaw puzzle, add the missing pieces.
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.DESCRIPTION
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Calculate properties of a jigsaw puzzle with given information if possible.
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If not possible due to insufficient or incorrect information, the user should be notified.
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Read instructions for more information and example.
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#>
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enum Format {
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Portrait
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Square
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Landscape
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}
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class JigsawPuzzle {
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[int]$Pieces
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[int]$Border
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[int]$Inside
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[int]$Rows
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[int]$Columns
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[double]$AspectRatio
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[Format]$Format
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GetData([PSCustomObject]$partialData)
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{
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Throw "Please implement this function"
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}
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}

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