Lhakpa is a Sherpa mountain guide and porter. After months of careful planning, the expedition Lhakpa works for is about to leave. She will be paid the value she carried to the base camp.
In front of her are many items, each with a value and weight. Lhakpa would gladly take all of the items, but her knapsack can only hold so much weight.
Your task is to determine which items to take so that the total value of her 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. Lhakpa can take only one of each item.
For example:
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, Lhakpa should take the second and fourth item to maximize her value, which, in this case, is 90. She cannot get more than 90 as her knapsack has a weight limit of 10.
In the scheme version the aruguments are the capacity
of the knapsack and a list of the weights
and a list of the values
.
It won't be necessary to validate the input -- the
test inputs have valid values and same length lists.
Simply type make chez
if you're using ChezScheme or make guile
if you're using GNU Guile.
Sometimes the name for the scheme binary on your system will differ from the defaults.
When this is the case, you'll need to tell make by running make chez chez=your-chez-binary
or make guile guile=your-guile-binary
.
(load "test.scm")
at the repl prompt.knapsack.scm
reloading as you go.(test)
to check your solution.If some of the test cases fail, you should see the failing input and the expected output.
The failing input is presented as a list because the tests call your solution by (apply knapsack input-list)
.
To learn more about apply
see The Scheme Programming Language -- Chapter 5
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