% min_scalar_product.pi (in Picat)
% by M. Bionchik, July, 2015
% https://code.google.com/codejam/contest/32016/dashboard#s=p0
% Round 1A 2008
% Problem A. Minimum Scalar Product
%
% to use: picat min_scalar_product < input_file > output_file
%

% The intuition is as follows:  if we're to get the minimum scalar product, we
% must multiply the largest numbers by the smallest numbers so that the sum of
% products is minimized.

main =>
    T = read_int(),
    foreach (I in 1..T)
        do_case(I)
    end.

do_case(Case) =>
    N = read_int(),
    V1 = [read_int() : _ in 1..N].sort(),
    V2 = [read_int() : _ in 1..N].sort_down(),
    Prod = sum([E1*E2 : {E1,E2} in zip(V1,V2)]),
    printf("Case #%w: %w%n", Case, Prod).

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