37 lines
1.1 KiB
Erlang
37 lines
1.1 KiB
Erlang
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-module(joe_euler87).
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-export([go/0]).
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go() ->
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Max = 50000000,
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Primes = sieve(Max),
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Sums = find_pow234(Max, Primes),
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length(Sums).
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%%% find all solutions for X^2+Y^3+Z^4 smaller Max
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find_pow234(Max, Primes) ->
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XPrimes = lists:takewhile(fun(P) -> pow2(P) < Max end, Primes),
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YPrimes = lists:takewhile(fun(P) -> pow3(P) < Max end, Primes),
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ZPrimes = lists:takewhile(fun(P) -> pow4(P) < Max end, Primes),
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lists:usort(lists:filter(
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fun(Num) -> Num < Max end,
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[powsum234(A, B, C) || A<-XPrimes, B<-YPrimes, C<-ZPrimes])).
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%%% generate a list of all primes smaller Max
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sieve(Max) ->
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Until = trunc(math:sqrt(Max)),
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sieve([], 2, 3, Until).
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sieve(Primes, LastPrime, N, Until) when (N > Until) ->
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lists:append(Primes, [LastPrime]);
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sieve(Primes, LastPrime, N, Until) ->
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case lists:all(fun(P) -> (N rem P)=/=0 end, Primes) of
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true -> sieve(lists:append(Primes, [LastPrime]), N, N+2, Until);
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false -> sieve(Primes, LastPrime, N+2, Until)
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end.
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%%% helper functions
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powsum234(X, Y, Z) -> pow2(X) + pow3(Y) + pow4(Z).
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pow2(X) -> X*X.
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pow3(X) -> X*X*X.
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pow4(X) -> X*X*X*X.
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