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add practice exercise palindrome-products (#758)
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exercises/practice/palindrome-products/.docs/instructions.md
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# Instructions | ||
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Detect palindrome products in a given range. | ||
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A palindromic number is a number that remains the same when its digits are reversed. | ||
For example, `121` is a palindromic number but `112` is not. | ||
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Given a range of numbers, find the largest and smallest palindromes which | ||
are products of two numbers within that range. | ||
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Your solution should return the largest and smallest palindromes, along with the factors of each within the range. | ||
If the largest or smallest palindrome has more than one pair of factors within the range, then return all the pairs. | ||
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## Example 1 | ||
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Given the range `[1, 9]` (both inclusive)... | ||
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And given the list of all possible products within this range: | ||
`[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 15, 21, 24, 27, 20, 28, 32, 36, 25, 30, 35, 40, 45, 42, 48, 54, 49, 56, 63, 64, 72, 81]` | ||
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The palindrome products are all single digit numbers (in this case): | ||
`[1, 2, 3, 4, 5, 6, 7, 8, 9]` | ||
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The smallest palindrome product is `1`. | ||
Its factors are `(1, 1)`. | ||
The largest palindrome product is `9`. | ||
Its factors are `(1, 9)` and `(3, 3)`. | ||
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## Example 2 | ||
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Given the range `[10, 99]` (both inclusive)... | ||
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The smallest palindrome product is `121`. | ||
Its factors are `(11, 11)`. | ||
The largest palindrome product is `9009`. | ||
Its factors are `(91, 99)`. |
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{ | ||
"authors": [], | ||
"files": { | ||
"solution": [ | ||
"palindrome-products.jl" | ||
], | ||
"test": [ | ||
"runtests.jl" | ||
], | ||
"example": [ | ||
".meta/example.jl" | ||
] | ||
}, | ||
"blurb": "Detect palindrome products in a given range.", | ||
"source": "Problem 4 at Project Euler", | ||
"source_url": "https://projecteuler.net/problem=4" | ||
} |
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getfactors(n, low, high) = [[i, n÷i] for i in low:isqrt(n) if iszero(n%i) && low ≤ n÷i ≤ high] | ||
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function nextpal(n, smallest) | ||
smallest && occursin(r"^9+$", "$n") && return n + 2 | ||
!smallest && occursin(r"^10*1$", "$n") && return n - 2 | ||
half = "$(parse(Int, "$n"[1:(ndigits(n)+1)÷2]) + (-1)^!smallest)" | ||
parse(Int, half * reverse(half)[1+isodd(ndigits(n)):end]) | ||
end | ||
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function nearestvalidpal(bound, smallest) | ||
half = "$bound"[1:(ndigits(bound)+1)÷2] | ||
pal = parse(Int, half * reverse(half)[1+isodd(ndigits(bound)):end]) | ||
inrange = smallest ? bound ≤ pal : pal ≤ bound | ||
inrange ? pal : nextpal(pal, smallest) | ||
end | ||
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function pal_n_facts(pal, low, high, smallest) | ||
((smallest && pal > high^2) || (!smallest && pal < low^2)) && return nothing, [] | ||
facts = getfactors(pal, low, high) | ||
isempty(facts) ? pal_n_facts(nextpal(pal, smallest), low, high, smallest) : (pal, facts) | ||
end | ||
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function palindromeproducts(low, high, smallest) | ||
high < low && throw(ArgumentError("low is greater than high: $low > $high")) | ||
bound = smallest ? low^2 : high^2 | ||
pal_n_facts(nearestvalidpal(bound, smallest), low, high, smallest) | ||
end |
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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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[5cff78fe-cf02-459d-85c2-ce584679f887] | ||
description = "find the smallest palindrome from single digit factors" | ||
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[0853f82c-5fc4-44ae-be38-fadb2cced92d] | ||
description = "find the largest palindrome from single digit factors" | ||
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[66c3b496-bdec-4103-9129-3fcb5a9063e1] | ||
description = "find the smallest palindrome from double digit factors" | ||
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[a10682ae-530a-4e56-b89d-69664feafe53] | ||
description = "find the largest palindrome from double digit factors" | ||
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[cecb5a35-46d1-4666-9719-fa2c3af7499d] | ||
description = "find the smallest palindrome from triple digit factors" | ||
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[edab43e1-c35f-4ea3-8c55-2f31dddd92e5] | ||
description = "find the largest palindrome from triple digit factors" | ||
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[4f802b5a-9d74-4026-a70f-b53ff9234e4e] | ||
description = "find the smallest palindrome from four digit factors" | ||
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[787525e0-a5f9-40f3-8cb2-23b52cf5d0be] | ||
description = "find the largest palindrome from four digit factors" | ||
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[58fb1d63-fddb-4409-ab84-a7a8e58d9ea0] | ||
description = "empty result for smallest if no palindrome in the range" | ||
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[9de9e9da-f1d9-49a5-8bfc-3d322efbdd02] | ||
description = "empty result for largest if no palindrome in the range" | ||
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[12e73aac-d7ee-4877-b8aa-2aa3dcdb9f8a] | ||
description = "error result for smallest if min is more than max" | ||
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[eeeb5bff-3f47-4b1e-892f-05829277bd74] | ||
description = "error result for largest if min is more than max" | ||
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[16481711-26c4-42e0-9180-e2e4e8b29c23] | ||
description = "smallest product does not use the smallest factor" |
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exercises/practice/palindrome-products/palindrome-products.jl
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function palindromeproducts(low::Int, high::Int, smallest::Bool) | ||
# Your code here | ||
palindrome, factors | ||
end |
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using Test | ||
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include("palindrome-products.jl") | ||
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@testset verbose = true "tests" begin | ||
@testset "find the smallest palindrome from single digit factors" begin | ||
palindrome, factors = palindromeproducts(1, 9, true) | ||
@test palindrome == 1 | ||
@test factors == [[1, 1]] | ||
end | ||
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@testset "find the largest palindrome from single digit factors" begin | ||
palindrome, factors = palindromeproducts(1, 9, false) | ||
@test palindrome == 9 | ||
@test sort(factors) == [[1, 9], [3, 3]] | ||
end | ||
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@testset "find the smallest palindrome from double digit factors" begin | ||
palindrome, factors = palindromeproducts(10, 99, true) | ||
@test palindrome == 121 | ||
@test factors == [[11, 11]] | ||
end | ||
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@testset "find the largest palindrome from double digit factors" begin | ||
palindrome, factors = palindromeproducts(10, 99, false) | ||
@test palindrome == 9009 | ||
@test factors == [[91, 99]] | ||
end | ||
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@testset "find the smallest palindrome from triple digit factors" begin | ||
palindrome, factors = palindromeproducts(100, 999, true) | ||
@test palindrome == 10201 | ||
@test factors == [[101, 101]] | ||
end | ||
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@testset "find the largest palindrome from triple digit factors" begin | ||
palindrome, factors = palindromeproducts(100, 999, false) | ||
@test palindrome == 906609 | ||
@test factors == [[913, 993]] | ||
end | ||
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@testset "find the smallest palindrome from four digit factors" begin | ||
palindrome, factors = palindromeproducts(1000, 9999, true) | ||
@test palindrome == 1002001 | ||
@test factors == [[1001, 1001]] | ||
end | ||
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@testset "find the largest palindrome from four digit factors" begin | ||
palindrome, factors = palindromeproducts(1000, 9999, false) | ||
@test palindrome == 99000099 | ||
@test factors == [[9901, 9999]] | ||
end | ||
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@testset "empty result for smallest if no palindrome in the range" begin | ||
palindrome, factors = palindromeproducts(1002, 1003, true) | ||
@test isnothing(palindrome) | ||
@test isempty(factors) | ||
end | ||
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@testset "empty result for largest if no palindrome in the range" begin | ||
palindrome, factors = palindromeproducts(15, 15, false) | ||
@test isnothing(palindrome) | ||
@test isempty(factors) | ||
end | ||
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@testset "error result for smallest if min is more than max" begin | ||
@test_throws ArgumentError palindromeproducts(10000, 1, true) | ||
end | ||
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@testset "error result for largest if min is more than max" begin | ||
@test_throws ArgumentError palindromeproducts(10000, 1, false) | ||
end | ||
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@testset "smallest product does not use the smallest factor" begin | ||
palindrome, factors = palindromeproducts(3215, 4000, true) | ||
@test palindrome == 10988901 | ||
@test factors == [[3297, 3333]] | ||
end | ||
end |