% Round 2 2016
% https://code.google.com/codejam/contest/10224486/dashboard
% in Picat, by N.F. Zhou, 11/03/2016

% to use: picat showdown < input_file > output_file

import sat, util.

main =>
    T = read_line().to_int(),
    foreach (TC in 1..T)
        [N,R,P,S] = [to_int(Token) : Token in read_line().split()],
        not not do_case(TC,N,R,P,S)                        
    end.

do_case(TC,N,R,P,S) ?=>
    M = 2**N,
    Row = new_list(M),
    Row :: 0..2,   
    global_cardinality(Row,$[0-P, 1-R, 2-S]),
    has_winner(Row,M),
    solve(Row),
    lineup(Row,1,Lineup),
    printf("Case #%w: ", TC),
    foreach (E in Lineup)
        print(cond(E==0, 'P', cond(E==1, 'R', 'S')))
    end,
    nl.
do_case(TC,_N,_R,_P,_S) =>
    printf("Case #%w: IMPOSSIBLE\n", TC).

has_winner([_],_) => true.
has_winner([C1,C2],_) => C1 #< C2.
has_winner(Row,M) =>
    M2 = M div 2,
    Row1 = new_list(M2),
    Row1 :: 0..2,
    compete(Row,Row1),
    has_winner(Row1,M2).

compete([],_) => true.
compete([C1,C2,C3,C4|Row],[W1,W2|Row1]) =>
    Table = [{0,1,0},
             {0,2,2},
             {1,0,0},
             {1,2,1},
             {2,0,2},
             {2,1,1}],
    table_in({C1,C2,W1}, Table),
    table_in({C3,C4,W2}, Table),
    W1 #< W2,
    compete(Row,Row1).

lineup(Row,ChunkSize,Lineup) =>
    chunks_of(Row,ChunkSize) = Chunks,
    (Chunks = [_] ->
        Lineup = Row
    ;
        rearrange(Chunks,Chunks1),
        lineup(flatten(Chunks1),ChunkSize*2,Lineup)
    ).

rearrange([],NewChunks) => NewChunks = [].
rearrange([Chunk1,Chunk2|Chunks],NewChunks), Chunk1 @< Chunk2 =>
    NewChunks = [Chunk1,Chunk2|NewChunksR],
    rearrange(Chunks,NewChunksR).
rearrange([Chunk1,Chunk2|Chunks],NewChunks) =>
    NewChunks = [Chunk2,Chunk1|NewChunksR],
    rearrange(Chunks,NewChunksR).

picat-lang.org