knapsack: add exercise

config.json

@@ -672,6 +672,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1
+      },
+      {
+        "slug": "knapsack",
+        "name": "Knapsack",
+        "uuid": "cfd8e973-fd62-4ffe-8e16-faa5e34a6340",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
       }
     ]
   },

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.R"
+    ],
+    "test": [
+      "test_knapsack.R"
+    ],
+    "example": [
+      ".meta/example.R"
+    ]
+  },
+  "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.R

@@ -0,0 +1,28 @@
+maximum_value <- function(max_wt, items) {
+  # This URL is > 80 chars, ignore whining from the linter:
+  # https://en.wikipedia.org/wiki/Knapsack_problem#Dynamic_programming_in-advance_algorithm
+
+  num_items <- length(items)
+  if (num_items == 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 <- matrix(0, nrow = num_items + 1, ncol = max_wt + 1)
+  for (item in 1:num_items) {
+    for (weight in 1:max_wt) {
+      curr_wt <- items[[item]]$weight
+      if (curr_wt > weight) {
+        # copy the row above, the new item is no use to us
+        maxes[item + 1, weight + 1] <- maxes[item, weight + 1]
+      } else {
+        # perhaps drop an old item, add the new one?
+        drop_last <- maxes[item, weight - curr_wt + 1] + items[[item]]$value
+        maxes[item + 1, weight + 1] <- max(maxes[item, weight + 1], drop_last)
+      }
+    }
+  }
+  # maxes[nrow(maxes), ncol(maxes)]
+  # shorter way to get the bottom-right element:
+  tail(c(maxes), 1)
+}

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.R

@@ -0,0 +1,3 @@
+maximum_value <- function(max_wt, items) {
+
+}

exercises/practice/knapsack/test_knapsack.R

@@ -0,0 +1,80 @@
+source("./knapsack.R")
+library(testthat)
+
+test_that("no items", {
+  expect_equal(maximum_value(100, list()), 0)
+})
+
+test_that("one item, too heavy", {
+  items <- list(
+    list(weight=100, value=1)
+  )
+  expect_equal(maximum_value(10, items), 0)
+})
+
+test_that("five items (cannot be greedy by weight)" , {
+  items <- list(
+    list(weight=2, value=5),
+    list(weight=2, value=5),
+    list(weight=2, value=5),
+    list(weight=2, value=5),
+    list(weight=10, value=21)
+  )
+  expect_equal(maximum_value(10, items), 21)
+})
+
+test_that("five items (cannot be greedy by value)", {
+  items <- list(
+    list(weight=2, value=20),
+    list(weight=2, value=20),
+    list(weight=2, value=20),
+    list(weight=2, value=20),
+    list(weight=10, value=50)
+  )
+  expect_equal(maximum_value(10, items), 80)
+})
+
+test_that("example knapsack", {
+  items <- list(
+    list(weight=5, value=10),
+    list(weight=4, value=40),
+    list(weight=6, value=30),
+    list(weight=4, value=50)
+  )
+  expect_equal(maximum_value(10, items), 90)
+})
+
+test_that("8 items", {
+  items <- list(
+    list(weight=25, value=350),
+    list(weight=35, value=400),
+    list(weight=45, value=450),
+    list(weight=5, value=20),
+    list(weight=25, value=70),
+    list(weight=3, value=8),
+    list(weight=2, value=5),
+    list(weight=2, value=5)
+  )
+  expect_equal(maximum_value(104, items), 900)
+})
+
+test_that("15 items", {
+  items <- list(
+    list(weight=70, value=135),
+    list(weight=73, value=139),
+    list(weight=77, value=149),
+    list(weight=80, value=150),
+    list(weight=82, value=156),
+    list(weight=87, value=163),
+    list(weight=90, value=173),
+    list(weight=94, value=184),
+    list(weight=98, value=192),
+    list(weight=106, value=201),
+    list(weight=110, value=210),
+    list(weight=113, value=214),
+    list(weight=115, value=221),
+    list(weight=118, value=229),
+    list(weight=120, value=240)
+  )
+  expect_equal(maximum_value(750, items), 1458)
+})