Project Euler in Erlang

project_euler.erl

-module(project_euler).
-export([prob1/0, prob2/0, prob3/0, prob4/0, prob5/0, prob6/0, prob7/0, prob8/0, prob9/0]).

prob1() -> lists:sum([X || X <- lists:seq(3, 999), (X rem 3 == 0) or (X rem 5 == 0)]). 

prob2_help(A, B, Sum) when (A+B) > 4000000 -> Sum;
prob2_help(A, B, Sum) when (A+B) rem 2 == 0 -> prob2_help(B, A+B, Sum+A+B);
prob2_help(A, B, Sum) -> prob2_help(B, A+B, Sum).

prob2() -> prob2_help(1, 2, 2). 

prime_factors(N) -> prime_factors(N, [], 2).

prime_factors(N, R, I) when I*I > N -> [N|R];
prime_factors(N, R, I) when N rem I == 0 -> prime_factors(N div I, [I|R], I);
prime_factors(N, R, 2) -> prime_factors(N, R, 3);
prime_factors(N, R, I) -> prime_factors(N, R, I+2).

prob3() -> lists:max(prime_factors(600851475143)).

is_palindrome_number(N) -> integer_to_list(N) == lists:reverse(integer_to_list(N)).

prob4() -> lists:max([X*Y|| X <- lists:seq(100, 999), Y <- lists:seq(100, 999), is_palindrome_number(X*Y)]).

list_product(List) -> lists:foldl(fun(X, Prod) -> X * Prod end, 1, List).

prob5() -> list_product(lists:foldl(fun(E, List) -> (E -- List) ++ List end, [], lists:map(fun(X) -> prime_factors(X) end, lists:seq(2, 20)))). 

sum_of_squares(N) -> N*(N+1)*(2*N+1)/6.

square_of_sum(N) -> N*N*(N+1)*(N+1)/4.

prob6() -> square_of_sum(100) - sum_of_squares(100).

nth_prime(N) -> nth_prime(3, [2], N).

nth_prime(_, Primes, 0) -> Primes;
nth_prime(X, Primes, N) -> case lists:any(fun(A) -> X rem A == 0 end, Primes) of
                                true -> nth_prime(X+2, Primes, N);
                                false -> nth_prime(X+2, Primes ++ [X], N-1)
                            end.

prob7() -> lists:nth(10001, nth_prime(10001)).



string_to_integer_list(S) -> lists:map(fun(A) -> A - 48 end, S).

max_prod(S) -> max_prod(string_to_integer_list(S), 1, 0).

max_prod(List, Index, Max) -> case Index + 13 > length(List) + 1 of
                                true -> Max;
                                false -> max_prod(List, Index + 1, lists:max([Max, list_product(lists:sublist(List, Index, 13))]))
                              end.

prob8_digits() -> "731671765313306249192251196744265747423553491949349698352031277450632623957831801698480186947885184385861560789112949495459501737958331952853208805511125406987471585238630507156932909632952274430435576689664895044524452316173185640309871112172238311362229893423380308135336276614282806444486645238793035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450".

prob8() -> 
    lists:max(
        lists:map(fun(B) -> max_prod(B) end, 
                  lists:filter(fun(A) -> string:len(A) >= 13 end, 
                               string:tokens(prob8_digits(), "0")))).

prob9() -> trunc(list_product(
    tuple_to_list(
        lists:nth(
            1,
            lists:filter(
                fun({X1, X2, X3}) -> 
                    (trunc(X3) == X3) and 
                    (X1 + X2 + X3 == 1000) and 
                    (X1 < X2) 
                end, 
                [{A, B, math:sqrt(A*A+B*B)}|| A <- lists:seq(3, 332), B <- lists:seq(4, 499)]))))).