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Merge pull request #311 from exercism/killer-sudoku-helper
Add Killer Sudoku Helper exercise
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‎config.json

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"prerequisites": [],
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"difficulty": 4
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},
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{
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"slug": "killer-sudoku-helper",
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"name": "Killer Sudoku Helper",
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"uuid": "dcb58258-8510-4980-8e6f-6d8ff136eb83",
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"practices": [],
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"prerequisites": [],
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"difficulty": 4
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},
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{
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"slug": "kindergarten-garden",
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"name": "Kindergarten Garden",

‎exercises/practice/killer-sudoku-helper/.docs/instructions.md

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# Instructions
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A friend of yours is learning how to solve Killer Sudokus (rules below) but struggling to figure out which digits can go in a cage.
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They ask you to help them out by writing a small program that lists all valid combinations for a given cage, and any constraints that affect the cage.
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To make the output of your program easy to read, the combinations it returns must be sorted.
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## Killer Sudoku Rules
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- [Standard Sudoku rules][sudoku-rules] apply.
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- The digits in a cage, usually marked by a dotted line, add up to the small number given in the corner of the cage.
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- A digit may only occur once in a cage.
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For a more detailed explanation, check out [this guide][killer-guide].
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## Example 1: Cage with only 1 possible combination
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In a 3-digit cage with a sum of 7, there is only one valid combination: 124.
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- 1 + 2 + 4 = 7
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- Any other combination that adds up to 7, e.g. 232, would violate the rule of not repeating digits within a cage.
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![Sudoku grid, with three killer cages that are marked as grouped together.
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The first killer cage is in the 3×3 box in the top left corner of the grid.
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The middle column of that box forms the cage, with the followings cells from top to bottom: first cell contains a 1 and a pencil mark of 7, indicating a cage sum of 7, second cell contains a 2, third cell contains a 5.
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The numbers are highlighted in red to indicate a mistake.
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The second killer cage is in the central 3×3 box of the grid.
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The middle column of that box forms the cage, with the followings cells from top to bottom: first cell contains a 1 and a pencil mark of 7, indicating a cage sum of 7, second cell contains a 2, third cell contains a 4.
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None of the numbers in this cage are highlighted and therefore don't contain any mistakes.
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The third killer cage follows the outside corner of the central 3×3 box of the grid.
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It is made up of the following three cells: the top left cell of the cage contains a 2, highlighted in red, and a cage sum of 7.
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The top right cell of the cage contains a 3.
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The bottom right cell of the cage contains a 2, highlighted in red. All other cells are empty.][one-solution-img]
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## Example 2: Cage with several combinations
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In a 2-digit cage with a sum 10, there are 4 possible combinations:
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- 19
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- 28
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- 37
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- 46
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![Sudoku grid, all squares empty except for the middle column, column 5, which has 8 rows filled.
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Each continguous two rows form a killer cage and are marked as grouped together.
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From top to bottom: first group is a cell with value 1 and a pencil mark indicating a cage sum of 10, cell with value 9.
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Second group is a cell with value 2 and a pencil mark of 10, cell with value 8.
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Third group is a cell with value 3 and a pencil mark of 10, cell with value 7.
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Fourth group is a cell with value 4 and a pencil mark of 10, cell with value 6.
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The last cell in the column is empty.][four-solutions-img]
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## Example 3: Cage with several combinations that is restricted
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In a 2-digit cage with a sum 10, where the column already contains a 1 and a 4, there are 2 possible combinations:
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- 28
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- 37
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19 and 46 are not possible due to the 1 and 4 in the column according to standard Sudoku rules.
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![Sudoku grid, all squares empty except for the middle column, column 5, which has 8 rows filled.
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The first row contains a 4, the second is empty, and the third contains a 1.
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The 1 is highlighted in red to indicate a mistake.
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The last 6 rows in the column form killer cages of two cells each.
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From top to bottom: first group is a cell with value 2 and a pencil mark indicating a cage sum of 10, cell with value 8.
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Second group is a cell with value 3 and a pencil mark of 10, cell with value 7.
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Third group is a cell with value 1, highlighted in red, and a pencil mark of 10, cell with value 9.][not-possible-img]
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## Trying it yourself
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If you want to give an approachable Killer Sudoku a go, you can try out [this puzzle][clover-puzzle] by Clover, featured by [Mark Goodliffe on Cracking The Cryptic on the 21st of June 2021][goodliffe-video].
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You can also find Killer Sudokus in varying difficulty in numerous newspapers, as well as Sudoku apps, books and websites.
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## Credit
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The screenshots above have been generated using [F-Puzzles.com](https://www.f-puzzles.com/), a Puzzle Setting Tool by Eric Fox.
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[sudoku-rules]: https://masteringsudoku.com/sudoku-rules-beginners/
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[killer-guide]: https://masteringsudoku.com/killer-sudoku/
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[one-solution-img]: https://assets.exercism.org/images/exercises/killer-sudoku-helper/example1.png
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[four-solutions-img]: https://assets.exercism.org/images/exercises/killer-sudoku-helper/example2.png
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[not-possible-img]: https://assets.exercism.org/images/exercises/killer-sudoku-helper/example3.png
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[clover-puzzle]: https://app.crackingthecryptic.com/sudoku/HqTBn3Pr6R
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[goodliffe-video]: https://youtu.be/c_NjEbFEeW0?t=1180

‎exercises/practice/killer-sudoku-helper/.meta/config.json

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{
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"authors": [
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"rabestro"
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],
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"files": {
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"solution": [
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"killer-sudoku-helper.awk"
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],
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"test": [
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"test-killer-sudoku-helper.bats"
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],
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"example": [
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".meta/example.awk"
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]
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},
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"blurb": "Write a tool that makes it easier to solve Killer Sudokus",
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"source": "Created by Sascha Mann, Jeremy Walker, and BethanyG for the Julia track on Exercism.",
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"source_url": "https://github.com/exercism/julia/pull/413"
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}

‎exercises/practice/killer-sudoku-helper/.meta/example.awk

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BEGIN {
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MaxDigit = 9
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}
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{
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cageSum = $1
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cageSize = $2
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for (i = 3; i <= NF; ++i) {
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ExcludedDigits[$i] = 1
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}
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NF = 0
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generate_recursive(1, cageSum, cageSize)
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}
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function generate_recursive(currentStartDigit, remainingSum, remainingSize, maxPossibleFirstDigit, digit) {
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NF++
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if (remainingSize == 1) {
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if (currentStartDigit <= remainingSum && remainingSum <= MaxDigit && !(remainingSum in ExcludedDigits)) {
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$NF = remainingSum
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print
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}
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} else {
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maxPossibleFirstDigit = MaxDigit - remainingSize + 1
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for (digit = currentStartDigit; digit <= maxPossibleFirstDigit; ++digit) {
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if (digit in ExcludedDigits)
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continue
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$NF = digit
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generate_recursive(digit + 1, remainingSum - digit, remainingSize - 1)
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}
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}
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NF--
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}

‎exercises/practice/killer-sudoku-helper/.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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[2aaa8f13-11b5-4054-b95c-a906e4d79fb6]
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description = "Trivial 1-digit cages -> 1"
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[4645da19-9fdd-4087-a910-a6ed66823563]
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description = "Trivial 1-digit cages -> 2"
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[07cfc704-f8aa-41b2-8f9a-cbefb674cb48]
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description = "Trivial 1-digit cages -> 3"
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[22b8b2ba-c4fd-40b3-b1bf-40aa5e7b5f24]
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description = "Trivial 1-digit cages -> 4"
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[b75d16e2-ff9b-464d-8578-71f73094cea7]
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description = "Trivial 1-digit cages -> 5"
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[bcbf5afc-4c89-4ff6-9357-07ab4d42788f]
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description = "Trivial 1-digit cages -> 6"
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[511b3bf8-186f-4e35-844f-c804d86f4a7a]
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description = "Trivial 1-digit cages -> 7"
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[bd09a60d-3aca-43bd-b6aa-6ccad01bedda]
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description = "Trivial 1-digit cages -> 8"
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[9b539f27-44ea-4ff8-bd3d-c7e136bee677]
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description = "Trivial 1-digit cages -> 9"
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[0a8b2078-b3a4-4dbd-be0d-b180f503d5c3]
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description = "Cage with sum 45 contains all digits 1:9"
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[2635d7c9-c716-4da1-84f1-c96e03900142]
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description = "Cage with only 1 possible combination"
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[a5bde743-e3a2-4a0c-8aac-e64fceea4228]
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description = "Cage with several combinations"
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[dfbf411c-737d-465a-a873-ca556360c274]
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description = "Cage with several combinations that is restricted"

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