% FILE: crypto_2345_short.pro of crypto_xps
% TYPE: Prolog source
% LINE: Essential Crypto problem solver -- the short way
% Date: 2019

%--------------------------------------------------------------------------------------------
% LOAD FILES

:- consult('../combinatorial_sets/combinatorial_sets.pro').
:- consult('crypto_tester.pro').

%---------------------------------------------------------------------------------------------
% ORDER 2 CRYPTO PROBLEM SOLVER

crypto(N1,N2,Goal,ex(N1,+,N2)) :- Goal is (N1+N2).
crypto(N1,N2,Goal,ex(N1,*,N2)) :- Goal is (N1*N2).
crypto(N1,N2,Goal,ex(N1,-,N2)) :- Goal is (N1-N2).
crypto(N1,N2,Goal,ex(N1,-,N2)) :- Goal is (N2-N1).
crypto(N1,N2,Goal,ex(N1,/,N2)) :- nonzero(N2), Goal is (N1/N2).
crypto(N1,N2,Goal,ex(N1,/,N2)) :- nonzero(N1), Goal is (N2/N1).

nonzero(N) :- N>0.
nonzero(N) :- N<0.

%----------------------------------------------------------
% ORDER 3 CRYPTO PROBLEM SOLVER

crypto(N1,N2,N3,G,Expr) :- 
comb(set(N1,N2,N3),comb(A,B),extras(C)),
crypto(A,B,SG,SGE),
crypto(C,SG,G,UGE),
substitute(SGE,SG,UGE,Expr).


%-----------------------------------------------------------------------------------------
% ORDER 4 CRYPTO PROBLEM SOLVER

crypto(N1,N2,N3,N4,G,Expr) :- 
comb(set(N1,N2,N3,N4),comb(A,B),extras(C,D)),
crypto(A, B, SG,SGE),
crypto(C,D,SG,G,UGE),
substitute(SGE,SG,UGE,Expr).

%------------------------------------------------------------------------------------------
% ORDER 5 CRYPTO PROBLEM SOLVER

crypto(N1,N2,N3,N4,N5,G,Expr) :- 
comb(set(N1,N2,N3,N4,N5),comb(A,B),extras(C,D,E)),
crypto(A,B,SG,SGE),
crypto(C,D,E,SG,G,UGE),
substitute(SGE,SG,UGE,Expr).

%------------------------------------------------------------------------------------------
% SUBSTITUTION CODE

substitute(New,Old,ex(Old,O,Z),ex(New,O,Z)).
substitute(New,Old,ex(X,O,Old),ex(X,O,New)).
substitute(New,Old,ex(X,O,Z),ex(Y,O,Z)) :-
substitute(New,Old,X,Y).
substitute(New,Old,ex(X,O,Z),ex(X,O,Y)) :-
substitute(New,Old,Z,Y).