% Langford's number problem in MiniZinc. % % This model is based on the EssencePrime model in the Minion Translator examples: % % http://www.cs.st-andrews.ac.uk/~andrea/examples/langford/langford.eprime % """ % Langford's number problem (CSP lib problem 24) % % Arrange 2 sets of positive integers 1..k to a sequence, % such that, following the first occurence of an integer i, % each subsequent occurrence of i, appears i+1 indices later % than the last. % For example, for k=4, a solution would be 41312432 % """ % % Also see: http://www.csplib.org/Problems/prob024/ % % However, I added a better representation were we see the numbers in their % proper positions: the solution array. % % Model created by Hakan Kjellerstrand, hakank@gmail.com % See also my MiniZinc page: http://www.hakank.org/minizinc % % Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/ % % Solution for k = 4: % [4, 1, 3, 1, 2, 4, 3, 2] % include "globals.mzn"; int: k; set of int: positionDomain = 1..2*k; array[positionDomain] of var positionDomain: position; % better presentation: array[positionDomain] of var 1..k: solution; solve :: int_search(position, first_fail, indomain_min, complete) satisfy; constraint forall(i in 1..k) ( position[i+k] = position[i] + i+1 /\ % hakank: added this solution[position[i]] = i /\ solution[position[k+i]] = i ) /\ all_different(position) /\ % symmetry breaking solution[1] < solution[2*k] ; output [ show(solution), "\n" ]; % % data % k = 4; % k = 7; % k = 8; % k = 10; % k = 20;