Add knapsack exercise (#57)

Author: keiravillekode

config.json

@@ -342,6 +342,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "e35d9981-453c-444d-b7a4-7c8646d0b2d0",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "nth-prime",
         "name": "Nth Prime",

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

@@ -0,0 +1,10 @@
+# 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": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "knapsack.fut"
+    ],
+    "test": [
+      "test.fut"
+    ],
+    "example": [
+      ".meta/example.fut"
+    ]
+  },
+  "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.fut

@@ -0,0 +1,15 @@
+def maximum_value [n] (weights: [n]i32) (values: [n]i32) (maximum_weight: i32): i32 =
+  let a = loop a = replicate (i64.i32 maximum_weight + 1) 0 for i in 0..<n do
+    let weight = weights[i]
+    let value = values[i]
+    in
+      if weight > maximum_weight then a else
+      let a2 = loop a2 = a for j in 0...(maximum_weight - weight) do
+        let update = a2[j + weight] + value
+        in
+          if update <= a2[j] then a2 else
+          a2 with [j] = update
+      in
+        a2
+  in
+    a[0]

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.fut

@@ -0,0 +1 @@
+def maximum_value [n] (weights: [n]i32) (values: [n]i32) (maximum_weight: i32): i32 = ???

exercises/practice/knapsack/test.fut

@@ -0,0 +1,39 @@
+import "knapsack"
+
+-- no items
+-- ==
+-- input { empty([0]i32) empty([0]i32) 100 }
+-- output { 0 }
+
+-- one item, too heavy
+-- ==
+-- input { [100] [1] 10 }
+-- output { 0 }
+
+-- five items (cannot be greedy by weight)
+-- ==
+-- input { [2, 2, 2, 2, 10] [5, 5, 5, 5, 21] 10 }
+-- output { 21 }
+
+-- five items (cannot be greedy by value)
+-- ==
+-- input { [2, 2, 2, 2, 10] [20, 20, 20, 20, 50] 10 }
+-- output { 80 }
+
+-- example knapsack
+-- ==
+-- input { [5, 4, 6, 4] [10, 40, 30, 50] 10 }
+-- output { 90 }
+
+-- 8 items
+-- ==
+-- input { [25, 35, 45, 5, 25, 3, 2, 2] [350, 400, 450, 20, 70, 8, 5, 5] 104 }
+-- output { 900 }
+
+-- 15 items
+-- ==
+-- input { [70, 73, 77, 80, 82, 87, 90, 94, 98, 106, 110, 113, 115, 118, 120] [135, 139, 149, 150, 156, 163, 173, 184, 192, 201, 210, 214, 221, 229, 240] 750 }
+-- output { 1458 }
+
+def main [n] (weights: [n]i32) (values: [n]i32) (maximum_weight: i32): i32 =
+  maximum_value weights values maximum_weight