5.170. ith_pos_different_from_0

Origin

Used for defining the automaton of min_n.

Constraint

ith_pos_different_from_0​(ITH,​POS,​VARIABLES)​

Argument(s)

ITH	int
POS	dvar
VARIABLES	collection​(var−dvar)​

Restriction(s)

ITH≥1

ITH≤|VARIABLES|

POS≥ITH

POS≤|VARIABLES|

required​(VARIABLES,​var)​

Purpose

POS is the position of the ITH^th non-zero item of the sequence of variables VARIABLES.

Example

​(2,​4,​〈3,​0,​0,​8,​6〉)​

The ith_pos_different_from_0 constraint holds since 4 corresponds to the position of the 2^th non-zero item of the sequence 3 0 0 8 6.

See also

min_n.

Key words

characteristic of a constraint: joker value, automaton, automaton with counters.

constraint network structure: alpha-acyclic constraint network(3).

constraint type: data constraint.

modelling: table.

Automaton

Figure 5.170.1 depicts the automaton associated with the ith_pos_different_from_0 constraint. To each variable VAR_i of the collection VARIABLES corresponds a 0-1 signature variable S_i. The following signature constraint links VAR_i and S_i: VAR_i=0⇔S_i.

Figure 5.170.1. Automaton of the ith_pos_different_from_0 constraint

Figure 5.170.2. Hypergraph of the reformulation corresponding to the automaton of the ith_pos_different_from_0 constraint