Add knapsack exercise (#264)

* Add knapsack exercise

* Tidy up knapsack exercise

* Move record to test

* Make line ending consistent

Co-authored-by: Victor Goff <[email protected]>

* Revert "Move record to test"

This reverts commit 84a0058.

This is to go back to putting the record in an include file.

* Add comment to include

* Add instructions.append.md

---------

Co-authored-by: Victor Goff <[email protected]>

Author: kahgoh

config.json

@@ -549,6 +549,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 8
+      },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "5b7094ea-9702-41ca-b13b-c2100cda0bdc",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
       }
     ]
   },

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

@@ -0,0 +1,13 @@
+The items are represented by [records](https://lfe.gitbooks.io/reference-guide/content/16.html), defined in `item.lfe`.
+Use `item-weight` to get the weight and `item-value` to get the value. 
+
+```
+;; Create an item with weight=5, value=50
+(set item (make-item weight 5 value 50))
+
+;; Get the weight. Returns 5.
+(item-weight item)
+
+;; Get the value. Returns 50.
+(item-value item)
+```

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 +1,22 @@
+{
+  "authors": [
+    "kahgoh"
+  ],
+  "files": {
+    "solution": [
+      "src/knapsack.lfe"
+    ],
+    "test": [
+      "test/knapsack-tests.lfe"
+    ],
+    "example": [
+      ".meta/example.lfe"
+    ],
+    "editor": [
+      "include/item.lfe"
+    ]
+  },
+  "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.lfe

@@ -0,0 +1,48 @@
+(defmodule knapsack
+  (export (maximum-value 2)))
+
+(include-lib "include/item.lfe")
+
+(defun find-max
+    (item last-values capacity)
+        (let*
+            ((value-without (lists:nth (+ capacity 1) last-values))
+             (weight-value (item-weight item))
+             (value-value (item-value item))
+             (left-over-capacity (- capacity weight-value)))
+            (if 
+                (< left-over-capacity 0)
+                value-without
+                (let 
+                    ((value-with
+                        (+
+                            (lists:nth (+ left-over-capacity 1) last-values)
+                            value-value)))
+                    (if (> value-with value-without) value-with value-without)))))
+
+(defun next-values
+    ([item last-values -1 acc] acc)
+    ([item last-values capacity acc] 
+        (next-values 
+            item 
+            last-values 
+            (- capacity 1) 
+            (cons (find-max item last-values capacity) acc))))
+
+(defun do-maximum-values
+    (['() last-values capacity] (lists:last last-values))
+    ([(cons item remaining) last-values capacity]
+        (do-maximum-values
+            remaining 
+            (next-values item last-values capacity '())
+            capacity)))
+
+(defun maximum-value
+    (('() _capacity) 0)
+    ((items capacity)
+        (do-maximum-values 
+            items
+            (lists:duplicate 
+                (+ capacity 1)
+                0)
+            capacity)))

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 +1,21 @@
+ERL    := $(shell which erl)
+REBAR3 := $(shell which rebar3)
+
+null  :=
+space := $(null) #
+comma := ,
+
+ifeq ($(ERL),)
+  $(error Can't find Erlang executable 'erl')
+else ifeq ($(REBAR3),)
+  $(error Can't find rebar3)
+endif
+
+compile: ; $(REBAR3) compile
+
+clean: ; $(REBAR3) clean
+
+.PHONY: test
+test:
+	$(REBAR3) eunit \
+	-m $(subst $(space),$(comma),$(basename $(notdir $(wildcard test/*.lfe))))

exercises/practice/knapsack/include/item.lfe

@@ -0,0 +1,4 @@
+; This include file defines the item record used in the exercise.
+; There shouldn't be any need to modify this file.
+
+(defrecord item weight value)

exercises/practice/knapsack/rebar.config

@@ -0,0 +1,11 @@
+{plugins, [{rebar3_lfe, "0.4.10"}]}.
+
+{provider_hooks, [{post, [{compile, {lfe, compile}}]}]}.
+
+{deps, [{lfe, "2.1.3"}]}.
+
+{profiles,
+ [{test,
+   [{eunit_compile_opts, [{src_dirs, ["src", "test"]}]},
+    {deps,
+     [{ltest, "0.13.8"}]}]}]}.

exercises/practice/knapsack/rebar.lock

@@ -0,0 +1,8 @@
+{"1.2.0",
+[{<<"lfe">>,{pkg,<<"lfe">>,<<"2.1.3">>},0}]}.
+[
+{pkg_hash,[
+ {<<"lfe">>, <<"6EFCB2BBC1FFC21DC5D1C092F00EFDB397EAC889474AC5C86EDF78A3557CC730">>}]},
+{pkg_hash_ext,[
+ {<<"lfe">>, <<"4E4BAD515A169AE418FEB7374EA1C8D741FAEA9D95E266CE343B45BCC377F55B">>}]}
+].

exercises/practice/knapsack/src/knapsack.app.src

@@ -0,0 +1,11 @@
+%% -*- erlang -*-
+{application, 'knapsack',
+ [{description, "exercism.org - knapsack"},
+  {vsn, "0.0.1"},
+  {modules,
+   ['knapsack']},
+  {registered, []},
+  {applications,
+   [kernel, stdlib]},
+  {included_applications, []},
+  {env, []}]}.

exercises/practice/knapsack/src/knapsack.lfe

@@ -0,0 +1,7 @@
+(defmodule knapsack
+  (export (maximum-value 2)))
+
+(include-lib "include/item.lfe")
+
+; Please implement the exported function(s).
+

exercises/practice/knapsack/test/knapsack-tests.lfe

@@ -0,0 +1,84 @@
+(defmodule knapsack-tests
+  (behaviour ltest-unit)
+  (export all))
+
+(include-lib "include/item.lfe")
+(include-lib "ltest/include/ltest-macros.lfe")
+
+(deftest no-items
+  (is-equal 0 (knapsack:maximum-value '() 100)))
+
+(deftest one-item-too-heavy
+  (is-equal 0
+            (knapsack:maximum-value
+              (list
+                (make-item weight 100 value 1))
+              10)))
+
+(deftest five-items-cannot-be-greedy-by-weight
+  (is-equal 21
+            (knapsack:maximum-value
+              (list
+                (make-item weight 2 value 5)
+                (make-item weight 2 value 5)
+                (make-item weight 2 value 5)
+                (make-item weight 2 value 5)
+                (make-item weight 10 value 21))
+              10)))
+
+(deftest five-items-cannot-be-greedy-by-value
+  (is-equal 80
+            (knapsack:maximum-value
+              (list
+                (make-item weight 2 value 20)
+                (make-item weight 2 value 20)
+                (make-item weight 2 value 20)
+                (make-item weight 2 value 20)
+                (make-item weight 10 value 50))
+              10)))
+
+(deftest example-knapsack
+  (is-equal 90
+            (knapsack:maximum-value
+              (list
+                (make-item weight 5 value 10)
+                (make-item weight 4 value 40)
+                (make-item weight 6 value 30)
+                (make-item weight 4 value 50))
+              10)))
+
+(deftest 8-items
+  (is-equal 900
+            (knapsack:maximum-value
+              (list
+                (make-item weight 25 value 350)
+                (make-item weight 35 value 400)
+                (make-item weight 45 value 450)
+                (make-item weight 5 value 20)
+                (make-item weight 25 value 70)
+                (make-item weight 3 value 8)
+                (make-item weight 2 value 5)
+                (make-item weight 2 value 5))
+              104)))
+
+(deftest 15-items
+  (is-equal 1458
+            (knapsack:maximum-value
+              (list
+                (make-item weight 70 value 135)
+                (make-item weight 73 value 139)
+                (make-item weight 77 value 149)
+                (make-item weight 80 value 150)
+                (make-item weight 82 value 156)
+                (make-item weight 87 value 163)
+                (make-item weight 90 value 173)
+                (make-item weight 94 value 184)
+                (make-item weight 98 value 192)
+                (make-item weight 106 value 201)
+                (make-item weight 110 value 210)
+                (make-item weight 113 value 214)
+                (make-item weight 115 value 221)
+                (make-item weight 118 value 229)
+                (make-item weight 120 value 240))
+              750)))
+