Add knapsack exercise

config.json

@@ -746,6 +746,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 5
+      },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "a385b861-22a5-4319-9fc0-c0228640ce26",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
       }
     ]
   },

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 his 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.
+Bob 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, Bob should take the second and fourth item to maximize his value, which, in this case, is 90.
+He cannot get more than 90 as his knapsack has a weight limit of 10.

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

@@ -0,0 +1,8 @@
+# Introduction
+
+Bob is a thief.
+After months of careful planning, he finally manages to crack the security systems of a fancy store.
+
+In front of him are many items, each with a value and weight.
+Bob would gladly take all of the items, but his knapsack can only hold so much weight.
+Bob has to carefully consider which items to take so that the total value of his selection is maximized.

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

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glennj"
+  ],
+  "files": {
+    "solution": [
+      "knapsack.coffee"
+    ],
+    "test": [
+      "knapsack.spec.coffee"
+    ],
+    "example": [
+      ".meta/example.coffee"
+    ]
+  },
+  "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.coffee

@@ -0,0 +1,19 @@
+# Algorithm taken from Wikipedia: https://en.wikipedia.org/wiki/Knapsack_problem
+
+maximumValue = ({maximumWeight, items}) ->
+  return 0 if items.length is 0
+
+  m = Array.from({length: items.length + 1}, -> new Array(maximumWeight + 1))
+  m[0].fill 0
+
+  for i in [1 .. items.length]
+    {weight, value} = items[i - 1]
+    for w in [0 .. maximumWeight]
+      if weight > w 
+        m[i][w] = m[i - 1][w]
+      else
+        m[i][w] = Math.max m[i - 1][w], m[i - 1][w - weight] + value
+
+  m[items.length][maximumWeight]
+
+module.exports = {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.coffee

@@ -0,0 +1,3 @@
+maximumValue = (args) ->
+
+module.exports = {maximumValue}

exercises/practice/knapsack/knapsack.spec.coffee

@@ -0,0 +1,93 @@
+Knapsack = require './knapsack'
+
+describe 'Knapsack', ->
+  it 'no items', ->
+    input = {
+      maximumWeight: 100,
+      items: []
+    }
+    expect(Knapsack.maximumValue input).toEqual 0
+
+  xit 'one item, too heavy', ->
+    input = {
+      maximumWeight: 10,
+      items: [{ weight: 100, value: 1 }]
+    }
+    expect(Knapsack.maximumValue input).toEqual 0
+
+  xit 'five items (cannot be greedy by weight)', ->
+    input = {
+      maximumWeight: 10,
+      items: [
+        { weight: 2, value: 5 },
+        { weight: 2, value: 5 },
+        { weight: 2, value: 5 },
+        { weight: 2, value: 5 },
+        { weight: 10, value: 21 }
+      ]
+    }
+    expect(Knapsack.maximumValue input).toEqual 21
+
+  xit 'five items (cannot be greedy by value)', ->
+    input = {
+      maximumWeight: 10,
+      items: [
+        { weight: 2, value: 20 },
+        { weight: 2, value: 20 },
+        { weight: 2, value: 20 },
+        { weight: 2, value: 20 },
+        { weight: 10, value: 50 }
+      ]
+    }
+    expect(Knapsack.maximumValue input).toEqual 80
+
+  xit 'example knapsack', ->
+    input = {
+      maximumWeight: 10,
+      items: [
+        { weight: 5, value: 10 },
+        { weight: 4, value: 40 },
+        { weight: 6, value: 30 },
+        { weight: 4, value: 50 }
+      ]
+    }
+    expect(Knapsack.maximumValue input).toEqual 90
+
+  xit '8 items', ->
+    input = {
+      maximumWeight: 104,
+      items: [
+        { weight: 25, value: 350 },
+        { weight: 35, value: 400 },
+        { weight: 45, value: 450 },
+        { weight: 5, value: 20 },
+        { weight: 25, value: 70 },
+        { weight: 3, value: 8 },
+        { weight: 2, value: 5 },
+        { weight: 2, value: 5 }
+      ]
+    }
+    expect(Knapsack.maximumValue input).toEqual 900
+
+  xit '15 items', ->
+    input = {
+      maximumWeight: 750,
+      items: [
+        { weight: 70, value: 135 },
+        { weight: 73, value: 139 },
+        { weight: 77, value: 149 },
+        { weight: 80, value: 150 },
+        { weight: 82, value: 156 },
+        { weight: 87, value: 163 },
+        { weight: 90, value: 173 },
+        { weight: 94, value: 184 },
+        { weight: 98, value: 192 },
+        { weight: 106, value: 201 },
+        { weight: 110, value: 210 },
+        { weight: 113, value: 214 },
+        { weight: 115, value: 221 },
+        { weight: 118, value: 229 },
+        { weight: 120, value: 240 }
+      ]
+    }
+    expect(Knapsack.maximumValue input).toEqual 1458