Complex Constraints

• Some complex constraints allow expressing simpler constraints
• E.g.: cardinality operator
  
  $$\char93 (L, [c_1, \ldots, c_n], U)$$
  
  
  the number of true constraints in $c_1, \ldots, c_n$ lies between $L$ and $U$
  • If $L = U = n$, all constraints must hold
  • If $L = U = 1$, only one constraint must be true
  • $U = 0$: the conjunction of the negations must be true
• Disjunctive constructive constraint: $c_1 \vee c_2$
  • If properly handled, avoids search and backtracking
  • E.g.: