% Filename: knight.mzn
%
% Usage:
% $ minizinc knight.mzn -a --soln-sep "" --search-complete-msg "" -D"s=2;r=3" -D "n=10" | awk 'NF' | sort
%
% See also: http://www.minizinc.org
%

int: n;
int: s;
int: r;
array[int,int] of int: move = [|0,0|s,-r|s,r|r,-s|r, s|];
int: zidx = 1;

constraint assert(0 < s /\ s <= r, "invalid parameters");

array[1..n] of var index_set_1of2(move): x;
array[1..n+1] of var int: h;

constraint h[1] == 0 /\ h[n+1] == 0;
constraint forall([h[i] >= 0 | i in 1..n+1]);
constraint forall([h[i+1] - h[i] == move[x[i],2] | i in 1..n]);
constraint forall([x[i] == zidx -> x[i+1] == zidx | i in 1..n-1]);
constraint sum([move[x[i],1] | i in 1..n]) == n;

solve satisfy;

output [if fix(x[i]) != zidx then show(x[i]) ++ " " else "" endif | i in 1..n]