Knapsack (#765)

* add practice exercise knapsack

* fixed typo in a comment

Author: colinleach

config.json

@@ -970,6 +970,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "7c4ecd30-dbd0-489e-a68c-513e9ecb12d9",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "game-of-life",
         "name": "Conway's Game of Life",

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": [
+    "colinleach"
+  ],
+  "files": {
+    "solution": [
+      "knapsack.jl"
+    ],
+    "test": [
+      "runtests.jl"
+    ],
+    "example": [
+      ".meta/example.jl"
+    ]
+  },
+  "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.jl

@@ -0,0 +1,27 @@
+function maximum_value(maximum_weight, items)
+    # See https://en.wikipedia.org/wiki/Knapsack_problem#Dynamic_programming_in-advance_algorithm
+
+    numitems = length(items)
+    numitems == 0 && return 0
+
+    # Remember, Julia uses 1-based array indexing
+    # so maxes[r,c] indexing needs to be r+1, c+1, compared to the Wiki reference
+
+    maxes = zeros(UInt16, numitems + 1, maximum_weight + 1)
+    for item_count in 1:numitems
+        for weight in 1:(maximum_weight)
+            curr_weight = items[item_count].weight
+            if curr_weight > weight
+                # copy the row above, the new item is no use to us
+                maxes[item_count + 1, weight + 1] = maxes[item_count, weight + 1]
+            else
+                # perhaps drop an old item, add the new one?
+                replace_last = maxes[item_count, weight - curr_weight + 1] + items[item_count].value
+                maxes[item_count + 1, weight + 1] = max(maxes[item_count, weight + 1], replace_last)
+            end
+        end
+    end
+
+    # converting to signed int is not essential, but it can help with debugging
+    Int(maxes[end, end])
+end

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.jl

@@ -0,0 +1,3 @@
+function maximum_value(maximum_weight, items)
+ 
+end

exercises/practice/knapsack/runtests.jl

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+using Test
+
+include("knapsack.jl")
+
+struct Item
+    weight
+    value
+end
+
+@testset verbose = true "tests" begin
+    @testset "no items" begin
+        @test maximum_value(100, []) == 0
+    end
+
+    @testset "one item, too heavy" begin
+        @test maximum_value(10, [Item(100, 1),]) == 0
+    end
+
+    @testset "five items (cannot be greedy by weight)" begin
+        items = [Item(2, 5), Item(2, 5), Item(2, 5), Item(2, 5), Item(10, 21)]
+        @test maximum_value(10, items) == 21
+    end
+
+    @testset "five items (cannot be greedy by value)" begin
+        items = [Item(2, 20), Item(2, 20), Item(2, 20), Item(2, 20), Item(10, 50)]
+        @test maximum_value(10, items) == 80
+    end
+
+    @testset "example knapsack" begin
+        items = [Item(5, 10), Item(4, 40), Item(6, 30), Item(4, 50)]
+        @test maximum_value(10, items) == 90
+    end
+
+    @testset "8 items" begin
+        items = [Item(25, 350), Item(35, 400), Item(45, 450), Item(5, 20), 
+        Item(25, 70), Item(3, 8), Item(2, 5), Item(2, 5)]
+        @test maximum_value(104, items) == 900
+    end
+
+    @testset "15 items" begin
+        items = [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)]
+        @test maximum_value(750, items) == 1458
+    end
+end