Add knapsack exercise (#343)

* Add knapsack exercise

* Reviewer feedback:

- remove #:transparent from struct definition
- ask dr. racket to reindent test code

config.json

@@ -598,6 +598,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1
+      },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "e08ec6c5-85bc-492a-b670-51ca95db4352",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 3
       }
     ]
   },

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

@@ -0,0 +1,35 @@
+# Instructions
+
+In this exercise, let's try to solve a classic problem.
+
+Bob is a thief.
+After months of careful planning, he finally manages to crack the security systems of a high-class apartment.
+
+In front of him are many items, each with a value (v) and weight (w).
+Bob, of course, wants to maximize the total value he can get; he would gladly take all of the items if he could.
+However, to his horror, he realizes that the knapsack he carries with him can only hold so much weight (W).
+
+Given a knapsack with a specific carrying capacity (W), help Bob determine the maximum value he can get from the items in the house.
+Note that Bob can take only one of each item.
+
+All values given will be strictly positive.
+Items will be represented as a list of items.
+Each item will have a weight and value.
+
+For example:
+
+```none
+Items: [
+  { "weight": 5, "value": 10 },
+  { "weight": 4, "value": 40 },
+  { "weight": 6, "value": 30 },
+  { "weight": 4, "value": 50 }
+]
+
+Knapsack Limit: 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/.meta/config.json

@@ -0,0 +1,17 @@
+{
+  "authors": ["blakelewis"],
+  "files": {
+    "solution": [
+      "knapsack.rkt"
+    ],
+    "test": [
+      "knapsack-test.rkt"
+    ],
+    "example": [
+      ".meta/example.rkt"
+    ]
+  },
+  "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.rkt

@@ -0,0 +1,17 @@
+#lang racket
+
+(provide item maximum-value)
+
+(struct item (weight value))
+
+(define (maximum-value maximum-weight items)
+  (for/fold
+    ([top-value (make-vector (add1 maximum-weight) 0)]
+     #:result (vector-ref top-value maximum-weight))
+    ([it items])
+    (for/vector ([w (in-inclusive-range 0 maximum-weight)])
+      (if (> (item-weight it) w)
+	(vector-ref top-value w)
+	(max (vector-ref top-value w)
+             (+ (vector-ref top-value (- w (item-weight it)))
+		(item-value it)))))))

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-test.rkt

@@ -0,0 +1,78 @@
+#lang racket/base
+
+(require "knapsack.rkt")
+
+(module+ test
+  (require rackunit rackunit/text-ui))
+
+(module+ test
+  (define suite
+    (test-suite
+     "knapsack tests"
+
+     (test-equal? "no items"
+                  (maximum-value 100 '())
+                  0)
+
+     (test-equal? "one item, too heavy"
+                  (maximum-value 10 (list (item 100 1)))
+                  0)
+
+     (test-equal? "five items (cannot be greedy by weight)"
+                  (maximum-value 10
+                                 (list (item 2 5)
+                                       (item 2 5)
+                                       (item 2 5)
+                                       (item 2 5)
+                                       (item 10 21)))
+                  21)
+
+     (test-equal? "five items (cannot be greedy by value)"
+                  (maximum-value 10
+                                 (list (item 2 20)
+                                       (item 2 20)
+                                       (item 2 20)
+                                       (item 2 20)
+                                       (item 10 50)))
+                  80)
+
+     (test-equal? "example knapsack"
+                  (maximum-value 10
+                                 (list (item 5 10)
+                                       (item 4 40)
+                                       (item 6 30)
+                                       (item 4 50)))
+                  90)
+
+     (test-equal? "8 items"
+                  (maximum-value 104
+                                 (list (item 25 350)
+                                       (item 35 400)
+                                       (item 45 450)
+                                       (item 5 20)
+                                       (item 25 70)
+                                       (item 3 8)
+                                       (item 2 5)
+                                       (item 2 5)))
+                  900)
+
+     (test-equal? "15 items"
+                  (maximum-value 750
+                                 (list (item 70 135)
+                                       (item 73 139)
+                                       (item 77 149)
+                                       (item 80 150)
+                                       (item 82 156)
+                                       (item 87 163)
+                                       (item 90 173)
+                                       (item 94 184)
+                                       (item 98 192)
+                                       (item 106 201)
+                                       (item 110 210)
+                                       (item 113 214)
+                                       (item 115 221)
+                                       (item 118 229)
+                                       (item 120 240)))
+                  1458)))
+
+  (run-tests suite))

exercises/practice/knapsack/knapsack.rkt

@@ -0,0 +1,8 @@
+#lang racket
+
+(provide item maximum-value)
+
+(struct item (weight value) #:transparent)
+
+(define (maximum-value maximum-weight items)
+  (error "Not implemented yet"))