Add knapsack exercise (#415)

config.json

@@ -136,6 +136,14 @@
         ],
         "difficulty": 1
       },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "ffa03fc8-0503-4524-ae40-9f3202349003",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "armstrong-numbers",
         "name": "Armstrong Numbers",

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": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "knapsack.zig"
+    ],
+    "test": [
+      "test_knapsack.zig"
+    ],
+    "example": [
+      ".meta/example.zig"
+    ]
+  },
+  "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.zig

@@ -0,0 +1,32 @@
+const std = @import("std");
+const mem = std.mem;
+
+pub const Item = struct {
+    weight: usize,
+    value: usize,
+
+    pub fn init(weight: usize, value: usize) Item {
+        return Item{
+            .weight = weight,
+            .value = value,
+        };
+    }
+};
+
+pub fn maximumValue(allocator: mem.Allocator, maximumWeight: usize, items: []const Item) !usize {
+    const table = try allocator.alloc(usize, maximumWeight + 1);
+    defer allocator.free(table);
+    @memset(table, 0);
+    for (items, 0..) |item, itemIndex| {
+        _ = itemIndex;
+        var index = maximumWeight + 1;
+        while (index > item.weight) {
+            index -= 1;
+            const value = item.value + table[index - item.weight];
+            if (table[index] < value) {
+                table[index] = value;
+            }
+        }
+    }
+    return table[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.zig

@@ -0,0 +1,19 @@
+const std = @import("std");
+const mem = std.mem;
+
+pub const Item = struct {
+    // This struct, as well as its fields and init method, needs to be implemented.
+
+    pub fn init(weight: usize, value: usize) Item {
+        _ = weight;
+        _ = value;
+        @compileError("please implement the init method");
+    }
+};
+
+pub fn maximumValue(allocator: mem.Allocator, maximumWeight: usize, items: []const Item) !usize {
+    _ = allocator;
+    _ = maximumWeight;
+    _ = items;
+    @compileError("please implement the maximumValue function");
+}

exercises/practice/knapsack/test_knapsack.zig

@@ -0,0 +1,98 @@
+const std = @import("std");
+const testing = std.testing;
+
+const knapsack = @import("knapsack.zig");
+const Item = knapsack.Item;
+
+test "no items" {
+    const expected: usize = 0;
+    const items: [0]Item = .{};
+    const actual = try knapsack.maximumValue(testing.allocator, 100, &items);
+    try testing.expectEqual(expected, actual);
+}
+
+test "one item, too heavy" {
+    const expected: usize = 0;
+    const items: [1]Item = .{
+        Item.init(100, 1),
+    };
+    const actual = try knapsack.maximumValue(testing.allocator, 10, &items);
+    try testing.expectEqual(expected, actual);
+}
+
+test "five items (cannot be greedy by weight)" {
+    const expected: usize = 21;
+    const items: [5]Item = .{
+        Item.init(2, 5),
+        Item.init(2, 5),
+        Item.init(2, 5),
+        Item.init(2, 5),
+        Item.init(10, 21),
+    };
+    const actual = try knapsack.maximumValue(testing.allocator, 10, &items);
+    try testing.expectEqual(expected, actual);
+}
+
+test "five items (cannot be greedy by value)" {
+    const expected: usize = 80;
+    const items: [5]Item = .{
+        Item.init(2, 20),
+        Item.init(2, 20),
+        Item.init(2, 20),
+        Item.init(2, 20),
+        Item.init(10, 50),
+    };
+    const actual = try knapsack.maximumValue(testing.allocator, 10, &items);
+    try testing.expectEqual(expected, actual);
+}
+
+test "example knapsack" {
+    const expected: usize = 90;
+    const items: [4]Item = .{
+        Item.init(5, 10),
+        Item.init(4, 40),
+        Item.init(6, 30),
+        Item.init(4, 50),
+    };
+    const actual = try knapsack.maximumValue(testing.allocator, 10, &items);
+    try testing.expectEqual(expected, actual);
+}
+
+test "8 items" {
+    const expected: usize = 900;
+    const items: [8]Item = .{
+        Item.init(25, 350),
+        Item.init(35, 400),
+        Item.init(45, 450),
+        Item.init(5, 20),
+        Item.init(25, 70),
+        Item.init(3, 8),
+        Item.init(2, 5),
+        Item.init(2, 5),
+    };
+    const actual = try knapsack.maximumValue(testing.allocator, 104, &items);
+    try testing.expectEqual(expected, actual);
+}
+
+test "15 items" {
+    const expected: usize = 1458;
+    const items: [15]Item = .{
+        Item.init(70, 135),
+        Item.init(73, 139),
+        Item.init(77, 149),
+        Item.init(80, 150),
+        Item.init(82, 156),
+        Item.init(87, 163),
+        Item.init(90, 173),
+        Item.init(94, 184),
+        Item.init(98, 192),
+        Item.init(106, 201),
+        Item.init(110, 210),
+        Item.init(113, 214),
+        Item.init(115, 221),
+        Item.init(118, 229),
+        Item.init(120, 240),
+    };
+    const actual = try knapsack.maximumValue(testing.allocator, 750, &items);
+    try testing.expectEqual(expected, actual);
+}