% 2017 Qualification Round, Problem D, in Picat, by Afa Zhou
% https://code.google.com/codejam/contest/3264486/dashboard#s=p3
% Fashion Show

import mip, util.

main =>
    T = read_line().to_int(),
    OS = open("out",write),
    foreach (TC in 1..T)
        [N,M] = [to_int(Token) : Token in read_line().split()],
        once dc(TC,N,M,OS)                        
    end,
    close(OS).

dc(TC,N,M,OS) =>
    Mx0 = new_array(N,N),
    Mp0 = new_array(N,N),
    Mx = new_array(N,N), Mx :: 0..1,
    Mp = new_array(N,N), Mp :: 0..1,
    foreach (_I in 1..M)
        [MToken,RToken,CToken] = read_line().split(),
        MToken = [Model],
        R = RToken.to_int(),
        C = CToken.to_int(),
        fill(Model,R,C,Mx0,Mp0,Mx,Mp)
    end,
    bind_vars(Mx0,0), bind_vars(Mp0,0),  % a cell is 0 if it is not occupied in the given configuration
    foreach (I in 1..N)
        sum([Mx[I,C] : C in 1..N]) #= 1,
        sum([Mx[R,I] : R in 1..N]) #= 1
    end,
    foreach(K in 1-N..N-1) 
       sum([Mp[R,C] : R in 1..N, C = R-K, C >= 1, C =< N]) #=< 1
    end,
    foreach(K in 2..2*N)   
       sum([Mp[R,C] : R in 1..N, C = K-R, C >= 1, C =< N]) #=< 1
    end,
    sum([Mp[R,C] : R in 1..N, C in 1..N]) #= NumP,    
    solve($[max(NumP)],(Mp,Mx)),
    output(TC,NumP,N,Mx0,Mp0,Mx,Mp,OS).

fill('o',R,C,Mx0,Mp0,Mx,Mp) =>
    Mx0[R,C] = 1, Mp0[R,C] = 1, Mx[R,C] = 1, Mp[R,C] = 1.
fill('+',R,C,_Mx0,Mp0,_Mx,Mp) =>
    Mp0[R,C] = 1, Mp[R,C] = 1.
fill('x',R,C,Mx0,_Mp0,Mx,_Mp) =>
    Mx0[R,C] = 1, Mx[R,C] = 1.

output(TC,Nump,N,Mx0,Mp0,Mx,Mp,OS) =>
    Count = 0,
    foreach (R in 1..N, C in 1..N)
        if (Mx[R,C] != Mx0[R,C] || Mp[R,C] != Mp0[R,C]) then
            Count := Count+1
        end
    end,
    printf(OS,"Case #%w: %w %w\n", TC,Nump+N,Count),
    foreach (R in 1..N, C in 1..N)
        if (Mx[R,C] != Mx0[R,C] || Mp[R,C] != Mp0[R,C]) then
            if (Mx[R,C] == 1 && Mp[R,C] == 1) then
                Model = 'o'
            elseif (Mx[R,C] == 1) then 
                Model = 'x'
            else
                Model = '+'
            end,
            printf(OS,"%w %w %w\n",Model,R,C)
        end
    end.

picat-lang.org