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Add Knapsack #700
Add Knapsack #700
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"custom-types" | ||
], | ||
"difficulty": 6 | ||
}, | ||
{ | ||
"slug": "knapsack", | ||
"name": "Knapsack", | ||
"uuid": "9bf186d3-e904-42f2-a705-dffbe98adb08", | ||
"practices": [], | ||
"prerequisites": [ | ||
"comparison", | ||
"lists", | ||
"records" | ||
], | ||
"difficulty": 6 | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Feel like a 7 or an 8, because the algorithm isn't trivial. What do you think? There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. I think a 7 is also reasonable. My hesitance with going to an 8 is seeing Zebra puzzle at 8 (and me thinking its not quite as hard Zebra Puzzle). The other thought I have is this example solution uses memoization. A simpler solution could be to use recursion without the memoization (although it won't be as efficient). There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Yes you're right, it's not quite a Zebra puzzle. |
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} | ||
] | ||
}, | ||
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# Instructions | ||
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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. | ||
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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. | ||
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For example: | ||
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```text | ||
Items: [ | ||
{ "weight": 5, "value": 10 }, | ||
{ "weight": 4, "value": 40 }, | ||
{ "weight": 6, "value": 30 }, | ||
{ "weight": 4, "value": 50 } | ||
] | ||
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Knapsack Maximum Weight: 10 | ||
``` | ||
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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. |
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# Introduction | ||
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Bob is a thief. | ||
After months of careful planning, he finally manages to crack the security systems of a fancy store. | ||
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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. |
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{ | ||
"authors": [ | ||
"kahgoh" | ||
], | ||
"files": { | ||
"solution": [ | ||
"src/Knapsack.elm" | ||
], | ||
"test": [ | ||
"tests/Tests.elm" | ||
], | ||
"example": [ | ||
".meta/src/Knapsack.example.elm" | ||
] | ||
}, | ||
"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" | ||
} |
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module Knapsack exposing (Item, maximumValue) | ||
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type alias Item = | ||
{ value : Int | ||
, weight : Int | ||
} | ||
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maximumValue : Int -> List Item -> Int | ||
maximumValue capacity items = | ||
doMaximumValue items (List.repeat (capacity + 1) 0) | ||
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last : List Int -> Int | ||
last list = | ||
List.foldl (\x _ -> x) 0 list | ||
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valueAt : List a -> Int -> Result String a | ||
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valueAt list index = | ||
case list of | ||
[] -> | ||
Err "Index out of bounds" | ||
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n :: rem -> | ||
if index == 0 then | ||
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Ok n | ||
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else | ||
valueAt rem (index - 1) | ||
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nextRow : Item -> List Int -> List Int | ||
nextRow item lastRow = | ||
List.indexedMap | ||
(\cap val -> | ||
let | ||
req = | ||
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cap - item.weight | ||
in | ||
if req < 0 then | ||
val | ||
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else | ||
case valueAt lastRow req of | ||
Ok v -> | ||
let | ||
withItem = | ||
v + item.value | ||
in | ||
if withItem > val then | ||
withItem | ||
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else | ||
val | ||
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Err _ -> | ||
val | ||
) | ||
lastRow | ||
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doMaximumValue : List Item -> List Int -> Int | ||
doMaximumValue items lastRow = | ||
case items of | ||
[] -> | ||
last lastRow | ||
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n :: rest -> | ||
doMaximumValue rest (nextRow n lastRow) |
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# 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. | ||
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[a4d7d2f0-ad8a-460c-86f3-88ba709d41a7] | ||
description = "no items" | ||
include = false | ||
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[3993a824-c20e-493d-b3c9-ee8a7753ee59] | ||
description = "no items" | ||
reimplements = "a4d7d2f0-ad8a-460c-86f3-88ba709d41a7" | ||
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[1d39e98c-6249-4a8b-912f-87cb12e506b0] | ||
description = "one item, too heavy" | ||
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[833ea310-6323-44f2-9d27-a278740ffbd8] | ||
description = "five items (cannot be greedy by weight)" | ||
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[277cdc52-f835-4c7d-872b-bff17bab2456] | ||
description = "five items (cannot be greedy by value)" | ||
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[81d8e679-442b-4f7a-8a59-7278083916c9] | ||
description = "example knapsack" | ||
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[f23a2449-d67c-4c26-bf3e-cde020f27ecc] | ||
description = "8 items" | ||
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[7c682ae9-c385-4241-a197-d2fa02c81a11] | ||
description = "15 items" |
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{ | ||
"type": "application", | ||
"source-directories": [ | ||
"src" | ||
], | ||
"elm-version": "0.19.1", | ||
"dependencies": { | ||
"direct": { | ||
"elm/core": "1.0.5", | ||
"elm/json": "1.1.3", | ||
"elm/parser": "1.1.0", | ||
"elm/random": "1.0.0", | ||
"elm/regex": "1.0.0", | ||
"elm/time": "1.0.0" | ||
}, | ||
"indirect": {} | ||
}, | ||
"test-dependencies": { | ||
"direct": { | ||
"elm-explorations/test": "2.1.0", | ||
"rtfeldman/elm-iso8601-date-strings": "1.1.4" | ||
}, | ||
"indirect": { | ||
"elm/bytes": "1.0.8", | ||
"elm/html": "1.0.0", | ||
"elm/virtual-dom": "1.0.3" | ||
} | ||
} | ||
} |
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module Knapsack exposing (Item, maximumValue) | ||
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type alias Item = | ||
{ value : Int | ||
, weight : Int | ||
} | ||
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maximumValue : Int -> List Item -> Int | ||
maximumValue capacity items = | ||
Debug.todo "Please implement this function" | ||
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module Tests exposing (tests) | ||
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import Expect | ||
import Knapsack exposing (..) | ||
import Test exposing (..) | ||
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tests : Test | ||
tests = | ||
describe "Knapsack" | ||
[ test "no items" <| | ||
\() -> | ||
Expect.equal 0 <| maximumValue 100 [] | ||
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, skip <| | ||
test "one item, too heavy" <| | ||
\() -> | ||
Expect.equal 0 <| maximumValue 10 [ { weight = 100, value = 1 } ] | ||
, skip <| | ||
test "five items (cannot be greedy by weight)" <| | ||
\() -> | ||
Expect.equal 21 <| | ||
maximumValue 10 | ||
[ { weight = 2, value = 5 } | ||
, { weight = 2, value = 5 } | ||
, { weight = 2, value = 5 } | ||
, { weight = 2, value = 5 } | ||
, { weight = 10, value = 21 } | ||
] | ||
, skip <| | ||
test "five items (cannot be greedy by value)" <| | ||
\() -> | ||
Expect.equal 80 <| | ||
maximumValue 10 | ||
[ { weight = 2, value = 20 } | ||
, { weight = 2, value = 20 } | ||
, { weight = 2, value = 20 } | ||
, { weight = 2, value = 20 } | ||
, { weight = 10, value = 50 } | ||
] | ||
, skip <| | ||
test "example knapsack" <| | ||
\() -> | ||
Expect.equal 90 <| | ||
maximumValue 10 | ||
[ { weight = 5, value = 10 } | ||
, { weight = 4, value = 40 } | ||
, { weight = 6, value = 30 } | ||
, { weight = 4, value = 50 } | ||
] | ||
, skip <| | ||
test "8 items" <| | ||
\() -> | ||
Expect.equal 900 <| | ||
maximumValue 104 | ||
[ { weight = 25, value = 350 } | ||
, { weight = 35, value = 400 } | ||
, { weight = 45, value = 450 } | ||
, { weight = 5, value = 20 } | ||
, { weight = 25, value = 70 } | ||
, { weight = 3, value = 8 } | ||
, { weight = 2, value = 5 } | ||
, { weight = 2, value = 5 } | ||
] | ||
, skip <| | ||
test "15 items" <| | ||
\() -> | ||
Expect.equal 1458 <| | ||
maximumValue 750 | ||
[ { weight = 70, value = 135 } | ||
, { weight = 73, value = 139 } | ||
, { weight = 77, value = 149 } | ||
, { weight = 80, value = 150 } | ||
, { weight = 82, value = 156 } | ||
, { weight = 87, value = 163 } | ||
, { weight = 90, value = 173 } | ||
, { weight = 94, value = 184 } | ||
, { weight = 98, value = 192 } | ||
, { weight = 106, value = 201 } | ||
, { weight = 110, value = 210 } | ||
, { weight = 113, value = 214 } | ||
, { weight = 115, value = 221 } | ||
, { weight = 118, value = 229 } | ||
, { weight = 120, value = 240 } | ||
] | ||
] |
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[You don't need to do anything here] This is also a good candidate for #692