Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
88 lines
3.0 KiB
MiniZinc
88 lines
3.0 KiB
MiniZinc
% RUNS ON mzn20_fd
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% RUNS ON mzn-fzn_fd
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% RUNS ON minizinc_cpx
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% RUNS ON mzn20_mip
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%-----------------------------------------------------------------------------%
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% Langford's Problem (CSPlib problem 24)
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%
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% June 2006; Sebastian Brand
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%
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% Instance L(k,n):
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% Arrange k sets of numbers 1 to n so that each appearance of the number m is m
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% numbers on from the last. For example, the L(3,9) problem is to arrange 3
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% sets of the numbers 1 to 9 so that the first two 1's and the second two 1's
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% appear one number apart, the first two 2's and the second two 2's appear two
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% numbers apart, etc.
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%-----------------------------------------------------------------------------%
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% MiniZinc version
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% Peter Stuckey September 30
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include "globals.mzn";
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%-----------------------------------------------------------------------------%
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% Instance
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%-----------------------------------------------------------------------------%
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% int: n = 10; % numbers 1..n
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% int: k = 2; % sets 1..k
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int: n = 9;
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int: k = 3;
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%-----------------------------------------------------------------------------%
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% Input
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%-----------------------------------------------------------------------------%
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set of int: numbers = 1..n; % numbers
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set of int: sets = 1..k; % sets of numbers
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set of int: num_set = 1..n*k;
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set of int: positions = 1..n*k; % positions of (number, set) pairs
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%-----------------------------------------------------------------------------%
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% Primal model
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%-----------------------------------------------------------------------------%
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array[num_set] of var positions: Pos;
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% Pos[ns]: position of (number, set)
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% pair in the sought sequence
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constraint
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forall(i in 1..n, j in 1..k-1) (
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Pos[k*(i-1) + j+1] - Pos[k*(i-1) + j] = i+1
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);
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constraint
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alldifferent(Pos);
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%-----------------------------------------------------------------------------%
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% Dual model (partial)
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%-----------------------------------------------------------------------------%
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array[positions] of var num_set: Num; % Num[p]: (number, set) pair at
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% position p in the sought sequence
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constraint
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alldifferent(Num);
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%-----------------------------------------------------------------------------%
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% Channelling between primal model and dual model
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%-----------------------------------------------------------------------------%
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constraint
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forall(i in numbers, j in sets, p in positions) (
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(Pos[k*(i-1) + j] = p) <-> (Num[p] = k*(i-1) + j)
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);
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%-----------------------------------------------------------------------------%
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% Without specifying a sensible search order this problem takes
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% forever to solve.
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%
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solve :: int_search(Pos, first_fail, indomain_split, complete)
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satisfy;
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output
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[ if j = 1 then "\n" ++ show(i) ++ "s at " else ", " endif ++
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show(Pos[k*(i-1) + j])
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| i in 1..n, j in 1..k
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] ++
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[ "\n" ];
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