include "fzn_bin_packing.mzn";
include "fzn_bin_packing_reif.mzn";

/**  @group globals.packing
  Requires that each item \p i with weight \a w[\p i], be put into \a bin[\p i] such 
  that the sum of the weights of the items in each bin does not exceed the 
  capacity \a c.

  Assumptions:
  - forall \p i, \a w[\p i] >=0
  - \a c >=0
*/
predicate bin_packing(int: c,
                      array[int] of var int: bin,
                      array[int] of int: w) =
    assert(index_set(bin) == index_set(w),
        "bin_packing: the bin and weight arrays must have identical index sets",
    assert(lb_array(w) >= 0,
        "bin_packing: the weights must be non-negative",
    assert(c >= 0, "bin_packing: capacity must be non-negative",
        fzn_bin_packing(c, bin, w)
    )));

predicate bin_packing_reif(int: c,
                      array[int] of var int: bin,
                      array[int] of int: w,
                      var bool: b) =
    assert(index_set(bin) == index_set(w),
        "bin_packing: the bin and weight arrays must have identical index sets",
    assert(lb_array(w) >= 0,
        "bin_packing: the weights must be non-negative",
    assert(c >= 0, "bin_packing: capacity must be non-negative",
        fzn_bin_packing_reif(c, bin, w, b)
    )));

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