diff --git a/config.json b/config.json index ae90f33f..2e87bfa9 100644 --- a/config.json +++ b/config.json @@ -681,6 +681,14 @@ "prerequisites": [], "difficulty": 1 }, + { + "slug": "knapsack", + "name": "Knapsack", + "uuid": "cfd8e973-fd62-4ffe-8e16-faa5e34a6340", + "practices": [], + "prerequisites": [], + "difficulty": 5 + }, { "slug": "high-scores", "name": "High Scores", diff --git a/exercises/practice/knapsack/.docs/instructions.md b/exercises/practice/knapsack/.docs/instructions.md new file mode 100644 index 00000000..3411db98 --- /dev/null +++ b/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. diff --git a/exercises/practice/knapsack/.docs/introduction.md b/exercises/practice/knapsack/.docs/introduction.md new file mode 100644 index 00000000..9b2bed8b --- /dev/null +++ b/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. diff --git a/exercises/practice/knapsack/.meta/config.json b/exercises/practice/knapsack/.meta/config.json new file mode 100644 index 00000000..96624d5f --- /dev/null +++ b/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" +} diff --git a/exercises/practice/knapsack/.meta/example.R b/exercises/practice/knapsack/.meta/example.R new file mode 100644 index 00000000..3a1832f8 --- /dev/null +++ b/exercises/practice/knapsack/.meta/example.R @@ -0,0 +1,29 @@ +maximum_value <- function(max_wt, items) { + # nolint start + # https://en.wikipedia.org/wiki/Knapsack_problem#Dynamic_programming_in-advance_algorithm + # nolint end + + 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) +} diff --git a/exercises/practice/knapsack/.meta/tests.toml b/exercises/practice/knapsack/.meta/tests.toml new file mode 100644 index 00000000..8e013ef1 --- /dev/null +++ b/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" diff --git a/exercises/practice/knapsack/knapsack.R b/exercises/practice/knapsack/knapsack.R new file mode 100644 index 00000000..592df693 --- /dev/null +++ b/exercises/practice/knapsack/knapsack.R @@ -0,0 +1,3 @@ +maximum_value <- function(max_weight, items) { + +} diff --git a/exercises/practice/knapsack/test_knapsack.R b/exercises/practice/knapsack/test_knapsack.R new file mode 100644 index 00000000..4e8bab16 --- /dev/null +++ b/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) +})