/* 

  Entropy in Picat.

  http://rosettacode.org/wiki/Entropy

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

*/


% import util.
import cp.


main => go.


go =>
  ["1223334444",
   "Rosetta Code is the best site in the world!",
   "1234567890abcdefghijklmnopqrstuvwxyz",
   "Picat is fun"].map(entropy).println(),
  nl.

% generate a string that matches an entropy...
go2 ?=>
  Alpha = "abcdefghijklmnopqrstuvwxyz1234567890",
  Wanted = math.e,
  A = 1..4,
  member(N,1..10),
  println(n=N),
  Cs = new_list(N),
  foreach(I in 1..N)
    member(Cs[I],A)
  end,
  increasing(Cs),
  L = [ [Alpha[I] : _ in 1..Len] : {Len,I} in zip(Cs,1..Cs.len)].flatten,
  entropy(L) = Entropy,
  % println(L=Entropy),
  abs(Entropy-Wanted) < 0.01,
  println(cs=Cs=sum(Cs)),
  println(l=L=Entropy),
  nl,
  fail,
  nl.
go2 => true.


% probabilities of each element/character in L
entropy(L) = Entropy => 
  Len = L.length,
  Occ = new_map(), % # of occurrences
  foreach(E in L)
    Occ.put(E, Occ.get(E,0) + 1)
  end,
  Entropy = -sum([P2*log2(P2) : _C=P in Occ, P2 = P/Len]).