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# Instructions | ||
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Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for positive integers. | ||
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The Greek mathematician [Nicomachus][nicomachus] devised a classification scheme for positive integers, identifying each as belonging uniquely to the categories of [perfect](#perfect), [abundant](#abundant), or [deficient](#deficient) based on their [aliquot sum][aliquot-sum]. | ||
The _aliquot sum_ is defined as the sum of the factors of a number not including the number itself. | ||
For example, the aliquot sum of `15` is `1 + 3 + 5 = 9`. | ||
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## Perfect | ||
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A number is perfect when it equals its aliquot sum. | ||
For example: | ||
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- `6` is a perfect number because `1 + 2 + 3 = 6` | ||
- `28` is a perfect number because `1 + 2 + 4 + 7 + 14 = 28` | ||
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## Abundant | ||
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A number is abundant when it is less than its aliquot sum. | ||
For example: | ||
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- `12` is an abundant number because `1 + 2 + 3 + 4 + 6 = 16` | ||
- `24` is an abundant number because `1 + 2 + 3 + 4 + 6 + 8 + 12 = 36` | ||
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## Deficient | ||
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A number is deficient when it is greater than its aliquot sum. | ||
For example: | ||
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- `8` is a deficient number because `1 + 2 + 4 = 7` | ||
- Prime numbers are deficient | ||
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## Task | ||
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Implement a way to determine whether a given number is [perfect](#perfect). | ||
Depending on your language track, you may also need to implement a way to determine whether a given number is [abundant](#abundant) or [deficient](#deficient). | ||
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[nicomachus]: https://en.wikipedia.org/wiki/Nicomachus | ||
[aliquot-sum]: https://en.wikipedia.org/wiki/Aliquot_sum |
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{ | ||
"authors": [ | ||
"gvrooyen" | ||
], | ||
"files": { | ||
"solution": [ | ||
"perfect_numbers.odin" | ||
], | ||
"test": [ | ||
"perfect_numbers_test.odin" | ||
], | ||
"example": [ | ||
".meta/perfect_numbers_example.odin" | ||
] | ||
}, | ||
"blurb": "Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for positive integers.", | ||
"source": "Taken from Chapter 2 of Functional Thinking by Neal Ford.", | ||
"source_url": "https://www.oreilly.com/library/view/functional-thinking/9781449365509/" | ||
} |
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exercises/practice/perfect-numbers/.meta/perfect_numbers_example.odin
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package perfect_numbers | ||
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import "core:math" | ||
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Classification :: enum { | ||
Perfect, | ||
Abundant, | ||
Deficient, | ||
Undefined, | ||
} | ||
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// Returns the sum of the divisors of `number` (excluding `number` itself). | ||
// For example, the aliquot sum of 15 is (1 + 3 + 5) = 9 | ||
aliquot_sum :: proc(number: uint) -> uint { | ||
if number <= 1 do return 0 | ||
result: uint = 1 | ||
for i in 2 ..= (number / 2) { | ||
if number % i == 0 do result += i | ||
} | ||
return result | ||
} | ||
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// Returns whether `number` is less than, equal to, or greater than its aliquot sum. | ||
// `ok` will be false if invalid input (i.e. 0) is provided. | ||
classify :: proc(number: uint) -> Classification { | ||
using Classification | ||
if number == 0 do return Undefined | ||
sum := aliquot_sum(number) | ||
switch { | ||
case number < sum: | ||
return Abundant | ||
case number > sum: | ||
return Deficient | ||
case: | ||
return Perfect | ||
} | ||
} |
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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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[163e8e86-7bfd-4ee2-bd68-d083dc3381a3] | ||
description = "Perfect numbers -> Smallest perfect number is classified correctly" | ||
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[169a7854-0431-4ae0-9815-c3b6d967436d] | ||
description = "Perfect numbers -> Medium perfect number is classified correctly" | ||
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[ee3627c4-7b36-4245-ba7c-8727d585f402] | ||
description = "Perfect numbers -> Large perfect number is classified correctly" | ||
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[80ef7cf8-9ea8-49b9-8b2d-d9cb3db3ed7e] | ||
description = "Abundant numbers -> Smallest abundant number is classified correctly" | ||
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[3e300e0d-1a12-4f11-8c48-d1027165ab60] | ||
description = "Abundant numbers -> Medium abundant number is classified correctly" | ||
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[ec7792e6-8786-449c-b005-ce6dd89a772b] | ||
description = "Abundant numbers -> Large abundant number is classified correctly" | ||
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[e610fdc7-2b6e-43c3-a51c-b70fb37413ba] | ||
description = "Deficient numbers -> Smallest prime deficient number is classified correctly" | ||
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[0beb7f66-753a-443f-8075-ad7fbd9018f3] | ||
description = "Deficient numbers -> Smallest non-prime deficient number is classified correctly" | ||
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[1c802e45-b4c6-4962-93d7-1cad245821ef] | ||
description = "Deficient numbers -> Medium deficient number is classified correctly" | ||
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[47dd569f-9e5a-4a11-9a47-a4e91c8c28aa] | ||
description = "Deficient numbers -> Large deficient number is classified correctly" | ||
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[a696dec8-6147-4d68-afad-d38de5476a56] | ||
description = "Deficient numbers -> Edge case (no factors other than itself) is classified correctly" | ||
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[72445cee-660c-4d75-8506-6c40089dc302] | ||
description = "Invalid inputs -> Zero is rejected (as it is not a positive integer)" | ||
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[2d72ce2c-6802-49ac-8ece-c790ba3dae13] | ||
description = "Invalid inputs -> Negative integer is rejected (as it is not a positive integer)" |
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package perfect_numbers | ||
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Classification :: enum { | ||
Perfect, | ||
Abundant, | ||
Deficient, | ||
Undefined, | ||
} | ||
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classify :: proc(number: uint) -> Classification { | ||
#panic("Please implement the `classify` procedure.") | ||
} |
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exercises/practice/perfect-numbers/perfect_numbers_test.odin
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/* These are the unit tests for the exercise. Only the first one is enabled to start with. You can | ||
* enable the other tests by uncommenting the `@(test)` attribute of the test procedure. Your | ||
* solution should pass all tests before it is ready for submission. | ||
*/ | ||
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package perfect_numbers | ||
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import "core:testing" | ||
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@(test) | ||
test_smallest_perfect_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(6), Classification.Perfect) | ||
} | ||
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// @(test) | ||
test_medium_perfect_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(28), Classification.Perfect) | ||
} | ||
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// @(test) | ||
test_large_perfect_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(33550336), Classification.Perfect) | ||
} | ||
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// @(test) | ||
test_smallest_abundant_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(12), Classification.Abundant) | ||
} | ||
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// @(test) | ||
test_medium_abundant_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(30), Classification.Abundant) | ||
} | ||
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// @(test) | ||
test_large_abundant_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(33550335), Classification.Abundant) | ||
} | ||
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// @(test) | ||
test_smallest_prime_deficient_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(2), Classification.Deficient) | ||
} | ||
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// @(test) | ||
test_smallest_non_prime_deficient_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(4), Classification.Deficient) | ||
} | ||
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// @(test) | ||
test_medium_deficient_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(32), Classification.Deficient) | ||
} | ||
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// @(test) | ||
test_large_deficient_number :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(33550337), Classification.Deficient) | ||
} | ||
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// @(test) | ||
test_1_is_edge_case :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(1), Classification.Deficient) | ||
} | ||
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// @(test) | ||
test_zero_is_undefined :: proc(t: ^testing.T) { | ||
testing.expect_value(t, classify(0), Classification.Undefined) | ||
} |