/* 

  Nonlinear problem in Picat.

  From Taha: "Operations Research", page 2.
   The optimal solution is
    w = h = L/4.


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

*/

import util.
import sat.

main => go.


% 0.0s / 0 backtracks
go =>

  L :: 0..100,
  WH #= W*H,

  W #>= 0,  
  H #>= 0, 
  WH #>= 625, 
  H #>= 2,

  2*(W+H) #= L, 

  println([wh=WH,l=L,w=W,h=H]),

  solve($[max(WH)],[L,W,H]),

  println([l=L,w=W,h=H,wh=WH]), 
  println('L/4'=L/4), 

  
  nl.

% sat solver can handle this
go2 =>

  L :: 0..100,
  W :: 0..100,  
  H :: 2..100, 
  WH #>= 625, 
  WH #= W*H,
  H #>= 2,

  2*(W+H) #= L, 

  println([wh=WH,l=L,w=W,h=H]),

  solve($[max(WH)],[L,W,H]),

  println([l=L,w=W,h=H,wh=WH]), 
  println('L/4'=L/4), 

  
  nl.


%
% pure logic programming: 
%
go3 =>

  % Ordering of the variables matter:

  % fastest: 0.82s
  between(0,100,H),
  between(0,100,W),
  between(0,100,L),

  % 0.84s
  % between(0,100,H),
  % between(0,100,L),
  % between(0,100,W),

  % 0.92s
  % between(0,100,W),
  % between(0,100,L),
  % between(0,100,H),

  % 0.86s
  % between(0,100,W),
  % between(0,100,H),
  % between(0,100,L),

  % 5.6s
  % between(0,100,L),
  % between(0,100,W),
  % between(0,100,H),

  % slowest: 5.7s
  % between(0,100,L),
  % between(0,100,H),
  % between(0,100,W),

  maxof(problem(L,H,W,WH), WH),

  println([l=L,w=W,h=H,wh=WH]), 
  println('L/4'=L/4), 

  nl.


problem(L,H,W,WH) =>
  % println($problem(L,H,W,WH)),
  WH = W*H,
  WH >= 625, 
  % println($problem(L,H,W,WH)),
  H >= 2,
  2*(W+H) = L.