/**
 * Warranty & Liability
 * To the extent permitted by applicable law and unless explicitly
 * otherwise agreed upon, XLOG Technologies AG makes no warranties
 * regarding the provided information. XLOG Technologies AG assumes
 * no liability that any problems might be solved with the information
 * provided by XLOG Technologies AG.
 *
 * Rights & License
 * All industrial property rights regarding the information - copyright
 * and patent rights in particular - are the sole property of XLOG
 * Technologies AG. If the company was not the originator of some
 * excerpts, XLOG Technologies AG has at least obtained the right to
 * reproduce, change and translate the information.
 *
 * Reproduction is restricted to the whole unaltered document. Reproduction
 * of the information is only allowed for non-commercial uses. Selling,
 * giving away or letting of the execution of the library is prohibited.
 * The library can be distributed as part of your applications and libraries
 * for execution provided this comment remains unchanged.
 *
 * Restrictions
 * Only to be distributed with programs that add significant and primary
 * functionality to the library. Not to be distributed with additional
 * software intended to replace any components of the library.
 *
 * Trademarks
 * Jekejeke is a registered trademark of XLOG Technologies AG.
 */

:- ensure_loaded(library(util/aggregate)).
:- ensure_loaded(library(edge/silkworm)).

/**
 * https://changyaochen.github.io/egg-drop-problem/
 */

% drop(+Integer, +Integer, -Integer)
:- table(drop/3).
drop(0, _, R) :- !, R = 0.
drop(_, 0, R) :- !, R = 0.
drop(F, 1, R) :- !, R = F.
drop(F, E, M) :- E > 1, F > 0,
   aggregate_all(min(N), (between(1,F,K),
       E2 is E-1,
       F1 is K-1,
       drop(F1, E2, N1),
       F2 is F-K,
       drop(F2, E, N2),
       N is 1+max(N1,N2)), M).

% egg
egg :-
   abolish_all_tables,
   drop(100, 10, _).