Add knapsack exercise (#525)

Author: kahgoh

config.json

@@ -549,6 +549,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 2
+      },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "c3bd5203-459c-4ea8-9b20-f4f5099808d8",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
       }
     ]
   },

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": [
+    "kahgoh"
+  ],
+  "files": {
+    "solution": [
+      "knapsack.ml"
+    ],
+    "test": [
+      "test.ml"
+    ],
+    "example": [
+      ".meta/example.ml"
+    ]
+  },
+  "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.ml

@@ -0,0 +1,30 @@
+type item = {
+    weight : int;
+    value : int;
+}
+
+let max_value (i: item) (prev_values: int list) (capacity: int): int =
+  let value_without = List.nth prev_values capacity in
+  match (i.weight, capacity) with
+  | (w, c) when c < w -> value_without
+  | (w, c) -> let value_with = (List.nth prev_values (c - w)) + i.value in
+                Int.max value_with value_without
+
+let next_values (i: item) (prev_values: int list): int list =
+  List.mapi (fun capacity _v -> max_value i prev_values capacity) prev_values
+
+let rec calculate_values (items: item list) (values: int list): int list =
+  match items with
+  | [] -> values
+  | i :: next -> calculate_values next (next_values i values)
+
+let rec last_value (v: int) (l: int list): int =
+  match l with
+  | [] -> v
+  | n :: r -> last_value n r
+
+let maximum_value (items: item list) (capacity: int): int =
+  let size = capacity + 1 in
+  let initial = List.init size (fun (_) -> 0) in
+    calculate_values items initial
+    |> last_value 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/Makefile

@@ -0,0 +1,9 @@
+default: clean test
+
+test: 
+	dune runtest
+
+clean:
+	dune clean
+
+.PHONY: clean

exercises/practice/knapsack/dune

@@ -0,0 +1,16 @@
+(executable
+ (name test)
+ (libraries base ounit2))
+
+(alias
+  (name    runtest)
+  (deps    (:x test.exe))
+  (action  (run %{x})))
+
+(alias
+  (name    buildtest)
+  (deps    (:x test.exe)))
+
+(env
+  (dev
+    (flags (:standard -warn-error -A))))

exercises/practice/knapsack/dune-project

@@ -0,0 +1,2 @@
+(lang dune 1.1)
+(version 1.0)

exercises/practice/knapsack/knapsack.ml

@@ -0,0 +1,7 @@
+type item = {
+    weight : int;
+    value : int;
+}
+
+let maximum_value (items: item list) (capacity: int): int =
+  failwith "Please implement 'maximum_value'"