binary-search-exercise: Added new exercise. (#133)

config.json

@@ -438,6 +438,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 6
+      },
+      {
+        "slug": "binary-search",
+        "name": "Binary Search",
+        "uuid": "fa1bd1bc-a6c4-426a-bbf6-2cd0cc711e31",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
       }
     ]
   },

exercises/practice/binary-search/.docs/instructions.md

@@ -0,0 +1,29 @@
+# Instructions
+
+Your task is to implement a binary search algorithm.
+
+A binary search algorithm finds an item in a list by repeatedly splitting it in half, only keeping the half which contains the item we're looking for.
+It allows us to quickly narrow down the possible locations of our item until we find it, or until we've eliminated all possible locations.
+
+~~~~exercism/caution
+Binary search only works when a list has been sorted.
+~~~~
+
+The algorithm looks like this:
+
+- Find the middle element of a _sorted_ list and compare it with the item we're looking for.
+- If the middle element is our item, then we're done!
+- If the middle element is greater than our item, we can eliminate that element and all the elements **after** it.
+- If the middle element is less than our item, we can eliminate that element and all the elements **before** it.
+- If every element of the list has been eliminated then the item is not in the list.
+- Otherwise, repeat the process on the part of the list that has not been eliminated.
+
+Here's an example:
+
+Let's say we're looking for the number 23 in the following sorted list: `[4, 8, 12, 16, 23, 28, 32]`.
+
+- We start by comparing 23 with the middle element, 16.
+- Since 23 is greater than 16, we can eliminate the left half of the list, leaving us with `[23, 28, 32]`.
+- We then compare 23 with the new middle element, 28.
+- Since 23 is less than 28, we can eliminate the right half of the list: `[23]`.
+- We've found our item.

exercises/practice/binary-search/.docs/introduction.md

@@ -0,0 +1,13 @@
+# Introduction
+
+You have stumbled upon a group of mathematicians who are also singer-songwriters.
+They have written a song for each of their favorite numbers, and, as you can imagine, they have a lot of favorite numbers (like [0][zero] or [73][seventy-three] or [6174][kaprekars-constant]).
+
+You are curious to hear the song for your favorite number, but with so many songs to wade through, finding the right song could take a while.
+Fortunately, they have organized their songs in a playlist sorted by the title — which is simply the number that the song is about.
+
+You realize that you can use a binary search algorithm to quickly find a song given the title.
+
+[zero]: https://en.wikipedia.org/wiki/0
+[seventy-three]: https://en.wikipedia.org/wiki/73_(number)
+[kaprekars-constant]: https://en.wikipedia.org/wiki/6174_(number)

exercises/practice/binary-search/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "SimaDovakin"
+  ],
+  "files": {
+    "solution": [
+      "binarySearch.u"
+    ],
+    "test": [
+      "binarySearch.test.u"
+    ],
+    "example": [
+      ".meta/examples/binarySearch.example.u"
+    ]
+  },
+  "blurb": "Implement a binary search algorithm.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Binary_search_algorithm"
+}

exercises/practice/binary-search/.meta/examples/binarySearch.example.u

@@ -0,0 +1,17 @@
+use data Array
+
+binarySearch.find : Array Nat -> Nat -> Optional Int
+binarySearch.find array target =
+  binSearch array target +0 (size array - 1 |> toInt)
+
+binarySearch.binSearch : Array Nat -> Nat -> Int -> Int -> Optional Int
+binarySearch.binSearch arr val = cases
+    startIndex, endIndex | endIndex < startIndex -> None
+    startIndex, endIndex ->
+      midIndex = (startIndex + endIndex) / +2
+      match at (toNat midIndex |> getOrElse 0) arr with
+        None -> None
+        Some v -> match ordering v val with
+                    Equal -> Some midIndex
+                    Less -> binSearch arr val (midIndex + +1) endIndex
+                    Greater -> binSearch arr val startIndex (midIndex - +1)

exercises/practice/binary-search/.meta/testAnnotation.json

@@ -0,0 +1,46 @@
+[
+  {
+    "name": "binarySearch.find.tests.ex1",
+    "test_code": "expect (Some +0 === binarySearch.find (Array.fromList [6]) 6)\n    |> Test.label \"finds a value in an array with one element\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex2",
+    "test_code": "expect (Some +3 === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 6)\n    |> Test.label \"finds a value in the middle of an array\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex3",
+    "test_code": "expect (Some +0 === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 1)\n    |> Test.label \"finds a value at the beginning of an array\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex4",
+    "test_code": "expect (Some +6 === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 11)\n    |> Test.label \"finds a value at the end of an array\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex5",
+    "test_code": "expect (Some +9 === binarySearch.find (Array.fromList [1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 634]) 144)\n    |> Test.label \"finds a value in an array of odd length\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex6",
+    "test_code": "expect (Some +5 === binarySearch.find (Array.fromList [1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]) 21)\n    |> Test.label \"finds a value in an array of even length\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex7",
+    "test_code": "expect (None === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 7)\n    |> Test.label \"identifies that a value is not included in the array\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex8",
+    "test_code": "expect (None === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 0)\n    |> Test.label \"a value smaller than the array's smallest value is not found\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex9",
+    "test_code": "expect (None === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 13)\n    |> Test.label \"a value larger than the array's largest value is not found\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex10",
+    "test_code": "expect (None === binarySearch.find (Array.fromList []) 1)\n    |> Test.label \"nothing is found in an empty array\""
+  },
+  {
+    "name": "binarySearch.find.tests.ex11",
+    "test_code": "expect (None === binarySearch.find (Array.fromList [1, 2]) 0)\n    |> Test.label \"nothing is found when the left and right bounds cross\""
+  }
+]

exercises/practice/binary-search/.meta/testLoader.md

@@ -0,0 +1,9 @@
+# Testing transcript for binary-search exercise
+
+```ucm
+.> load ./binarySearch.u
+.> add
+.> load ./binarySearch.test.u
+.> add
+.> move.term binarySearch.tests tests
+```

exercises/practice/binary-search/.meta/tests.toml

@@ -0,0 +1,43 @@
+# 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.
+
+[b55c24a9-a98d-4379-a08c-2adcf8ebeee8]
+description = "finds a value in an array with one element"
+
+[73469346-b0a0-4011-89bf-989e443d503d]
+description = "finds a value in the middle of an array"
+
+[327bc482-ab85-424e-a724-fb4658e66ddb]
+description = "finds a value at the beginning of an array"
+
+[f9f94b16-fe5e-472c-85ea-c513804c7d59]
+description = "finds a value at the end of an array"
+
+[f0068905-26e3-4342-856d-ad153cadb338]
+description = "finds a value in an array of odd length"
+
+[fc316b12-c8b3-4f5e-9e89-532b3389de8c]
+description = "finds a value in an array of even length"
+
+[da7db20a-354f-49f7-a6a1-650a54998aa6]
+description = "identifies that a value is not included in the array"
+
+[95d869ff-3daf-4c79-b622-6e805c675f97]
+description = "a value smaller than the array's smallest value is not found"
+
+[8b24ef45-6e51-4a94-9eac-c2bf38fdb0ba]
+description = "a value larger than the array's largest value is not found"
+
+[f439a0fa-cf42-4262-8ad1-64bf41ce566a]
+description = "nothing is found in an empty array"
+
+[2c353967-b56d-40b8-acff-ce43115eed64]
+description = "nothing is found when the left and right bounds cross"

exercises/practice/binary-search/binarySearch.test.u

@@ -0,0 +1,59 @@
+use data Array
+
+binarySearch.find.tests.ex1 =
+  expect (Some +0 === binarySearch.find (Array.fromList [6]) 6)
+    |> Test.label "finds a value in an array with one element"
+
+binarySearch.find.tests.ex2 =
+  expect (Some +3 === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 6)
+    |> Test.label "finds a value in the middle of an array"
+
+binarySearch.find.tests.ex3 =
+  expect (Some +0 === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 1)
+    |> Test.label "finds a value at the beginning of an array"
+
+binarySearch.find.tests.ex4 =
+  expect (Some +6 === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 11)
+    |> Test.label "finds a value at the end of an array"
+
+binarySearch.find.tests.ex5 =
+  expect (Some +9 === binarySearch.find (Array.fromList [1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 634]) 144)
+    |> Test.label "finds a value in an array of odd length"
+
+binarySearch.find.tests.ex6 =
+  expect (Some +5 === binarySearch.find (Array.fromList [1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]) 21)
+    |> Test.label "finds a value in an array of even length"
+
+binarySearch.find.tests.ex7 =
+  expect (None === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 7)
+    |> Test.label "identifies that a value is not included in the array"
+
+binarySearch.find.tests.ex8 =
+  expect (None === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 0)
+    |> Test.label "a value smaller than the array's smallest value is not found"
+
+binarySearch.find.tests.ex9 =
+  expect (None === binarySearch.find (Array.fromList [1, 3, 4, 6, 8, 9, 11]) 13)
+    |> Test.label "a value larger than the array's largest value is not found"
+
+binarySearch.find.tests.ex10 =
+  expect (None === binarySearch.find (Array.fromList []) 1)
+    |> Test.label "nothing is found in an empty array"
+
+binarySearch.find.tests.ex11 =
+  expect (None === binarySearch.find (Array.fromList [1, 2]) 0)
+    |> Test.label "nothing is found when the left and right bounds cross"
+
+test> binarySearch.tests = runAll [
+  binarySearch.find.tests.ex1,
+  binarySearch.find.tests.ex2,
+  binarySearch.find.tests.ex3,
+  binarySearch.find.tests.ex4,
+  binarySearch.find.tests.ex5,
+  binarySearch.find.tests.ex6,
+  binarySearch.find.tests.ex7,
+  binarySearch.find.tests.ex8,
+  binarySearch.find.tests.ex9,
+  binarySearch.find.tests.ex10,
+  binarySearch.find.tests.ex11
+]

exercises/practice/binary-search/binarySearch.u

@@ -0,0 +1,4 @@
+use data Array
+
+binarySearch.find : Array Nat -> Nat -> Optional Int
+binarySearch.find = todo "implement find"