Add knapsack exercise

config.json

@@ -554,6 +554,14 @@
         "prerequisites": [],
         "difficulty": 6
       },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "87922ec1-b30a-47ea-8c37-fdeb1b86b209",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
+      },
       {
         "slug": "parallel-letter-frequency",
         "name": "Parallel Letter Frequency",

exercises/practice/knapsack/.docs/instructions.md

@@ -0,0 +1,25 @@
+# Instructions
+
+Your task is to determine which items to take so that the total value of her selection is maximized, taking into account the knapsack's carrying capacity.
+
+Items will be represented as a list of items.
+Each item will have a weight and value.
+All values given will be strictly positive.
+Lhakpa can take only one of each item.
+
+For example:
+
+```text
+Items: [
+  { "weight": 5, "value": 10 },
+  { "weight": 4, "value": 40 },
+  { "weight": 6, "value": 30 },
+  { "weight": 4, "value": 50 }
+]
+
+Knapsack Maximum Weight: 10
+```
+
+For the above, the first item has weight 5 and value 10, the second item has weight 4 and value 40, and so on.
+In this example, Lhakpa should take the second and fourth item to maximize her value, which, in this case, is 90.
+She cannot get more than 90 as her knapsack has a weight limit of 10.

exercises/practice/knapsack/.docs/introduction.md

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+# Introduction
+
+Lhakpa is a [Sherpa][sherpa] mountain guide and porter.
+After months of careful planning, the expedition Lhakpa works for is about to leave.
+She will be paid the value she carried to the base camp.
+
+In front of her are many items, each with a value and weight.
+Lhakpa would gladly take all of the items, but her knapsack can only hold so much weight.
+
+[sherpa]: https://en.wikipedia.org/wiki/Sherpa_people#Mountaineering

exercises/practice/knapsack/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "erikschierboom"
+  ],
+  "files": {
+    "solution": [
+      "knapsack.ua"
+    ],
+    "test": [
+      "tests.ua"
+    ],
+    "example": [
+      ".meta/example.ua"
+    ]
+  },
+  "blurb": "Given a knapsack that can only carry a certain weight, determine which items to put in the knapsack in order to maximize their combined value.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Knapsack_problem"
+}

exercises/practice/knapsack/.meta/example.ua

@@ -0,0 +1,13 @@
+MaximumValue ← |2 memo(
+  ±⧻.
+  ⨬(0◌◌
+  | ⊃⊢↘₁
+    ↥⊃(
+      ⋅MaximumValue
+    | ◡(≥(⊃(⊢|⋅⋅∘)))
+      ⨬(0◌◌
+      | +⊃(⊣|MaximumValue ⊙-⊃(⋅∘|∘|⋅⋅∘)⊢)
+      )
+    )
+  )
+)

exercises/practice/knapsack/.meta/tests.toml

@@ -0,0 +1,36 @@
+# 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.
+
+[a4d7d2f0-ad8a-460c-86f3-88ba709d41a7]
+description = "no items"
+include = false
+
+[3993a824-c20e-493d-b3c9-ee8a7753ee59]
+description = "no items"
+reimplements = "a4d7d2f0-ad8a-460c-86f3-88ba709d41a7"
+
+[1d39e98c-6249-4a8b-912f-87cb12e506b0]
+description = "one item, too heavy"
+
+[833ea310-6323-44f2-9d27-a278740ffbd8]
+description = "five items (cannot be greedy by weight)"
+
+[277cdc52-f835-4c7d-872b-bff17bab2456]
+description = "five items (cannot be greedy by value)"
+
+[81d8e679-442b-4f7a-8a59-7278083916c9]
+description = "example knapsack"
+
+[f23a2449-d67c-4c26-bf3e-cde020f27ecc]
+description = "8 items"
+
+[7c682ae9-c385-4241-a197-d2fa02c81a11]
+description = "15 items"

exercises/practice/knapsack/knapsack.ua

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+# Calculate the maximum value of items that still fit in the knapsack
+# Value ? Items Capacity
+MaximumValue ← |2 ⊙⋅(⍤ "Please implement MaximumValue" 0)

exercises/practice/knapsack/tests.ua

@@ -0,0 +1,22 @@
+~ "knapsack.ua" ~ MaximumValue
+
+# no items
+⍤⤙≍ 0 MaximumValue [] 100
+
+# one item, too heavy
+⍤⤙≍ 0 MaximumValue [100_1] 10
+
+# five items (cannot be greedy by weight)
+⍤⤙≍ 21 MaximumValue [2_5 2_5 2_5 2_5 10_21] 10
+
+# five items (cannot be greedy by value)
+⍤⤙≍ 80 MaximumValue [2_20 2_20 2_20 2_20 10_50] 10
+
+# example knapsack
+⍤⤙≍ 90 MaximumValue [5_10 4_40 6_30 4_50] 10
+
+# 8 items
+⍤⤙≍ 900 MaximumValue [25_350 35_400 45_450 5_20 25_70 3_8 2_5 2_5] 104
+
+# 15 items
+⍤⤙≍ 1458 MaximumValue [70_135 73_139 77_149 80_150 82_156 87_163 90_173 94_184 98_192 106_201 110_210 113_214 115_221 118_229 120_240] 750