/* 

  Assignment problem in Picat.

  Marriott & Stuckey "Programming with Constraints", page 266.

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
  profit(Profit),
  NumWorkers = Profit.len,
  NumProducts = Profit[1].len,

  X = new_array(NumWorkers,NumProducts),
  X :: 0..1,

  SumProfit #= sum([X[W,P]*Profit[W,P] : W in 1..NumWorkers, P in 1..NumProducts]),

  foreach(W in 1..NumWorkers)
    sum([X[W,P] : P in 1..NumProducts]) #= 1
  end,

  foreach(P in 1..NumProducts)
    sum([X[W,P] : W in 1..NumWorkers]) #= 1
  end,
  
  solve($[max(SumProfit)],X),

  println(sum_profit=SumProfit),

  foreach(Row in X)
    println(Row.to_list)
  end,

  nl.


profit(Profit) =>
 Profit = [[7,1,3,4],
           [8,2,5,1],
           [4,3,7,2],
           [3,1,6,3]].