include "alldifferent_except_0.mzn";

int: n;                        % size
array[1..n,0..n] of int: p;    % prize for edge (i,j), p[i,0] = 0

array[1..n] of var 0..n: next; % next posn in tour
array[1..n] of var 0..n: pos;  % posn on node i in path, 0=not in
array[1..n] of var int: prize = [p[i,next[i]] | i in 1..n];
                               % prize for outgoing edge

constraint forall(i in 1..n)(
	(pos[i] = 0 <-> next[i] = 0) /\
	(next[i] > 1 -> pos[next[i]] = pos[i] + 1)
);

constraint alldifferent_except_0(next) /\ pos[1] = 1;

solve minimize sum(i in 1..n)(prize[i]);