First perfect square in base n with n unique digits: Difference between revisions
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=={{header|Julia}}== |
=={{header|Julia}}== |
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Runs in about 4 seconds with using occursin(). |
Runs in about 4 seconds with using occursin(). |
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<lang julia> |
<lang julia>const num = "0123456789abcdef" |
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const num = "0123456789abcdef" |
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hasallin(n, numerals, b) = (s = string(n, base=b); all(x -> occursin(x, s), numerals)) |
hasallin(n, numerals, b) = (s = string(n, base=b); all(x -> occursin(x, s), numerals)) |
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Revision as of 08:52, 21 May 2019
Find the first perfect square in a given base N that has at least N digits and exactly N significant unique digits when expressed in base N.
E.G. In base 10, the first perfect square with at least 10 unique digits is 1026753849 (32043²).
You may use analytical methods to reduce the search space, but the code must do a search. Do not use magic numbers or just feed the code the answer to verify it is correct.
- Task
- Find and display here, on this page, the first perfect square in base N, with N significant unique digits when expressed in base N, for each of base 2 through 12. Display each number in the base N for which it was calculated.
- (optional) Do the same for bases 13 through 16.
Julia
Runs in about 4 seconds with using occursin(). <lang julia>const num = "0123456789abcdef" hasallin(n, numerals, b) = (s = string(n, base=b); all(x -> occursin(x, s), numerals))
function squaresearch(bas)
basenumerals = [c for c in num[1:bas]] highest = parse(Int, "10" * num[3:bas], base=bas) lowest = Int(trunc(sqrt(highest))) for n in lowest:highest nsquared = n * n if hasallin(nsquared, basenumerals, bas) return nsquared end end throw("failed to find num for base $bas")
end
println("Base Root N") for b in 2:16
n = squaresearch(b) println(lpad(b, 3), lpad(string(Int(trunc(sqrt(n))), base=b), 10), " ", string(n, base=b))
end
</lang>
- Output:
Base Root N 2 10 100 3 22 2101 4 33 3201 5 243 132304 6 523 452013 7 1431 2450361 8 3344 13675420 9 11642 136802574 10 32043 1026753849 11 111453 1240a536789 12 3966b9 124a7b538609
Perl 6
<lang perl6># Only search perfect squares that have at least N digits;
- smaller could not possibly match.
sub first-square (Int $n) {
my $start = (($n - 1)/2).exp($n).floor || 1; my $sq = ($start .. *).map( *² ).hyper.first: *.base($n).comb.Bag.elems >= $n; sprintf "Base %2d: %10s² == %s", $n, $sq.sqrt.base($n), $sq.base($n);
}
say "First perfect square with N unique digits in base N: "; say .&first-square for flat
2 .. 12, # required 13 .. 16 # optional
- </lang>
- Output:
First perfect square with N unique digits in base N: Base 2: 10² == 100 Base 3: 22² == 2101 Base 4: 33² == 3201 Base 5: 243² == 132304 Base 6: 523² == 452013 Base 7: 1431² == 2450361 Base 8: 3344² == 13675420 Base 9: 11642² == 136802574 Base 10: 32043² == 1026753849 Base 11: 111453² == 1240A536789 Base 12: 3966B9² == 124A7B538609 Base 13: 3828943² == 10254773CA86B9 Base 14: 3A9DB7C² == 10269B8C57D3A4 Base 15: 1012B857² == 102597BACE836D4 Base 16: 404A9D9B² == 1025648CFEA37BD9