Add exercise knapsack

config.json

@@ -979,6 +979,14 @@
           "events",
           "reactive_programming"
         ]
+      },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "6cd9b4d2-2274-4b56-98cf-1c820f1da836",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
       }
     ]
   },

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 +1,19 @@
+{
+  "authors": [
+    "siebenschlaefer"
+  ],
+  "files": {
+    "solution": [
+      "knapsack.nim"
+    ],
+    "test": [
+      "test_knapsack.nim"
+    ],
+    "example": [
+      ".meta/example.nim"
+    ]
+  },
+  "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.nim

@@ -0,0 +1,8 @@
+type Item = tuple[weight: int, value: int]
+
+proc maximumValue*(maximumWeight: int, items: openArray[Item]): int =
+  var dp = newSeq[int](maximumWeight + 1)
+  for item in items:
+    for weight in countdown(maximumWeight, item.weight):
+      dp[weight] = max(dp[weight], item.value + dp[weight - item.weight])
+  result = dp[maximumWeight]

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.nim

@@ -0,0 +1,4 @@
+type Item = tuple[weight: int, value: int]
+
+proc maximumValue*(maximumWeight: int, items: openArray[Item]): int =
+  discard

exercises/practice/knapsack/test_knapsack.nim

@@ -0,0 +1,64 @@
+import unittest
+import knapsack
+
+suite "knapsack":
+  test "no items":
+    const maximumWeight = 100
+    const items: array[0, tuple[weight: int, value: int]] = []
+    const expected = 0
+    check maximumValue(maximumWeight, items) == expected
+
+  test "one item, too heavy":
+    const maximumWeight = 10
+    const items = [(weight: 100, value: 1)]
+    const expected = 0
+    check maximumValue(maximumWeight, items) == expected
+
+  test "five items (cannot be greedy by weight)":
+    const maximumWeight = 10
+    const items = [
+      (weight: 2, value: 5), (weight: 2, value: 5), (weight: 2, value: 5),
+      (weight: 2, value: 5), (weight: 10, value: 21)
+    ]
+    const expected = 21
+    check maximumValue(maximumWeight, items) == expected
+
+  test "five items (cannot be greedy by value)":
+    const maximumWeight = 10
+    const items = [
+      (weight: 2, value: 20), (weight: 2, value: 20), (weight: 2, value: 20),
+      (weight: 2, value: 20), (weight: 10, value: 50)
+    ]
+    const expected = 80
+    check maximumValue(maximumWeight, items) == expected
+
+  test "example knapsack":
+    const maximumWeight = 10
+    const items = [
+      (weight: 5, value: 10), (weight: 4, value: 40), (weight: 6, value: 30),
+      (weight: 4, value: 50)
+    ]
+    const expected = 90
+    check maximumValue(maximumWeight, items) == expected
+
+  test "8 items":
+    const maximumWeight = 104
+    const 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)
+    ]
+    const expected = 900
+    check maximumValue(maximumWeight, items) == expected
+
+  test "15 items":
+    const maximumWeight = 750
+    const 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)
+    ]
+    const expected = 1458
+    check maximumValue(maximumWeight, items) == expected