[New Exercise]: Knapsack

config.json

@@ -984,6 +984,14 @@
         "prerequisites": [],
         "difficulty": 6
       },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "e59c633c-f5d1-45e6-bfb3-b32f0bb12f18",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
+      },
       {
         "slug": "book-store",
         "name": "Book Store",

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/Knapsack.example.ps1

@@ -0,0 +1,47 @@
+Function Get-MaximumValue() {
+    <#
+    .SYNOPSIS
+    Implement a function to solve the classic knapsack problem.
+
+    .DESCRIPTION
+    Given a knapsack with a specific carrying capacity (W), determine the maximum value we can get from the list of items.
+    Note that each item can only be taken once.
+
+    All values given will be strictly positive.
+
+    .PARAMETER MaxWeight
+    An integer represent the maximum weight to be carried.
+
+    .PARAMETER Items
+    An array of object represent the items, each object will have a Weight and a Value property.
+
+    .EXAMPLE
+    $items = @(
+        [PSCustomObject]@{Weight = 1; Value = 3}
+        [PSCustomObject]@{Weight = 2; Value = 5}
+        [PSCustomObject]@{Weight = 3; Value = 7}
+        [PSCustomObject]@{Weight = 4; Value = 8}
+    )
+
+    Get-MaximumValue -MaxWeight 5 -Items $items
+    Returns: 12
+    #>
+    [CmdletBinding()]
+    Param(
+        [int]$MaxWeight,
+        [object[]]$Items
+    )
+    if (-not $Items.Count) {return 0}
+    $table = 0..$Items.Count | ForEach-Object { ,(@(0) * ($MaxWeight + 1)) }
+
+    for ($i = 0; $i -le $Items.Count; $i++) {
+        for ($j = 0; $j -le $MaxWeight; $j++) {
+            if ($Items[$i].Weight -le $j) {
+                $table[$i][$j] = [math]::Max($table[$i-1][$j], $table[$i-1][$j-$Items[$i].Weight] + $Items[$i].Value)
+            }else{
+                $table[$i][$j] = $table[$i-1][$j]
+            }
+        }
+    }
+    $table[$Items.Count - 1][$MaxWeight]
+}

exercises/practice/knapsack/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glaxxie"
+  ],
+  "files": {
+    "solution": [
+      "Knapsack.ps1"
+    ],
+    "test": [
+      "Knapsack.tests.ps1"
+    ],
+    "example": [
+      ".meta/Knapsack.example.ps1"
+    ]
+  },
+  "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/tests.toml

@@ -0,0 +1,31 @@
+# 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"
+
+[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.ps1

@@ -0,0 +1,35 @@
+Function Get-MaximumValue() {
+    <#
+    .SYNOPSIS
+    Implement a function to solve the classic knapsack problem.
+
+    .DESCRIPTION
+    Given a knapsack with a specific carrying capacity (W), determine the maximum value we can get from the list of items.
+    Note that each item can only be taken once.
+
+    All values given will be strictly positive.
+
+    .PARAMETER MaxWeight
+    An integer represent the maximum weight to be carried.
+
+    .PARAMETER Items
+    An array of object represent the items, each object will have a Weight and a Value property.
+
+    .EXAMPLE
+    $items = @(
+        [PSCustomObject]@{Weight = 1; Value = 3}
+        [PSCustomObject]@{Weight = 2; Value = 5}
+        [PSCustomObject]@{Weight = 3; Value = 7}
+        [PSCustomObject]@{Weight = 4; Value = 8}
+    )
+
+    Get-MaximumValue -MaxWeight 5 -Items $items
+    Returns: 12
+    #>
+    [CmdletBinding()]
+    Param(
+        [int]$MaxWeight,
+        [object[]]$Items
+    )
+    Throw "Please implement this function"
+}

exercises/practice/knapsack/Knapsack.tests.ps1

@@ -0,0 +1,106 @@
+BeforeAll {
+    . "./Knapsack.ps1"
+}
+
+Describe "Knapsack test cases" {
+    It "no items" {
+        $items = @()
+        $got  = Get-MaximumValue -MaxWeight 100 -Items $items
+        $want = 0
+
+        $got | Should -BeExactly $want
+    }
+
+    It "one item, too heavy" {
+        $items = @(
+            [PSCustomObject]@{Weight = 100; Value = 1}
+        )
+        $got  = Get-MaximumValue -MaxWeight 10 -Items $items
+        $want = 0
+
+        $got | Should -BeExactly $want
+    }
+
+    It "five items (cannot be greedy by weight)" {
+        $items = @(
+            [PSCustomObject]@{Weight = 2; Value = 5}
+            [PSCustomObject]@{Weight = 2; Value = 5}
+            [PSCustomObject]@{Weight = 2; Value = 5}
+            [PSCustomObject]@{Weight = 2; Value = 5}
+            [PSCustomObject]@{Weight = 10; Value = 21}
+        )
+        $got  = Get-MaximumValue -MaxWeight 10 -Items $items
+        $want = 21
+
+        $got | Should -BeExactly $want
+    }
+
+    It "five items (cannot be greedy by value)" {
+        $items = @(
+            [PSCustomObject]@{Weight = 2; Value = 20}
+            [PSCustomObject]@{Weight = 2; Value = 20}
+            [PSCustomObject]@{Weight = 2; Value = 20}
+            [PSCustomObject]@{Weight = 2; Value = 20}
+            [PSCustomObject]@{Weight = 10; Value = 50}
+        )
+        $got  = Get-MaximumValue -MaxWeight 10 -Items $items
+        $want = 80
+
+        $got | Should -BeExactly $want
+    }
+
+    It "example knapsack" {
+        $items = @(
+            [PSCustomObject]@{Weight = 5; Value = 10}
+            [PSCustomObject]@{Weight = 4; Value = 40}
+            [PSCustomObject]@{Weight = 6; Value = 30}
+            [PSCustomObject]@{Weight = 4; Value = 50}
+        )
+        $got  = Get-MaximumValue -MaxWeight 10 -Items $items
+        $want = 90
+
+        $got | Should -BeExactly $want
+    }
+
+    It "8 items" {
+        $items = @(
+            [PSCustomObject]@{Weight = 25; Value = 350}
+            [PSCustomObject]@{Weight = 35; Value = 400}
+            [PSCustomObject]@{Weight = 45; Value = 450}
+            [PSCustomObject]@{Weight = 5; Value = 20}
+            [PSCustomObject]@{Weight = 25; Value = 70}
+            [PSCustomObject]@{Weight = 3; Value = 8}
+            [PSCustomObject]@{Weight = 2; Value = 5}
+            [PSCustomObject]@{Weight = 2; Value = 5}
+        )
+        $got  = Get-MaximumValue -MaxWeight 104 -Items $items
+        $want = 900
+
+        $got | Should -BeExactly $want
+    }
+
+    It "15 items" {
+        $items = @(
+            [PSCustomObject]@{Weight = 70; Value = 135}
+            [PSCustomObject]@{Weight = 73; Value = 139}
+            [PSCustomObject]@{Weight = 77; Value = 149}
+            [PSCustomObject]@{Weight = 80; Value = 150}
+            [PSCustomObject]@{Weight = 82; Value = 156}
+            [PSCustomObject]@{Weight = 87; Value = 163}
+            [PSCustomObject]@{Weight = 90; Value = 173}
+            [PSCustomObject]@{Weight = 94; Value = 184}
+            [PSCustomObject]@{Weight = 98; Value = 192}
+            [PSCustomObject]@{Weight = 106; Value = 201}
+            [PSCustomObject]@{Weight = 110; Value = 210}
+            [PSCustomObject]@{Weight = 113; Value = 214}
+            [PSCustomObject]@{Weight = 115; Value = 221}
+            [PSCustomObject]@{Weight = 118; Value = 229}
+            [PSCustomObject]@{Weight = 120; Value = 240}
+        )
+        $got  = Get-MaximumValue -MaxWeight 750 -Items $items
+        $want = 1458
+
+        $got | Should -BeExactly $want
+    }
+
+}