all_different

Purpose

The all_different constraint states that all variables in this constraint must be pairwise different:

Synopsis

function all_different(vars:set of cpvar, propagation: integer) : cpctr

function all_different(vars:set of cpvar) : cpctr

function all_different(vars:array(range) of cpvar, propagation:integer) : cpctr

function all_different(vars:array(range) of cpvar) : cpctr

function all_different(vars:cpvarlist, propagation:integer) : cpctr

function all_different(vars:cpvarlist) : cpctr

Arguments

vars	the list of variables
propagation	Propagation type selected using a constant KALIS_FORWARD_CHECKING, KALIS_GEN_ARC_CONSISTENCY

Return value

An all different constraint over vars

Example

Consider the following simple problem where one must determine the arrival positions of a set of six runners:Dominique, Ignace, Naren, Olivier, Philippe and Pascal.
The constraints are the following:

All runners have different positions
Olivier is not last
Dominique, Pascal, and Ignace are before Naren and Olivier
Dominique is better than third
Philippe is among the first four
Ignace is neither second nor third
Pascal is three places higher than Naren
Neither Ignace nor Dominique are in fourth position

This problem can be modeled as follows. We create one variable per runner, whose value will be his arrival position. The initial domains of the variables will be the available arrival positions (1-6). Since we admit there are no ties, the positions are all pairwise different.

model "all_different example"
 uses "kalis"

 declarations
  PEOPLE = {"Sebastian", "Frederic", "Jan-Georg",
            "Krzysztof","Maarten","Luca"}  ! Set of speakers
  x: array(PEOPLE) of cpvar                ! Time slot per person
 end-declarations

 3 <= x("Sebastian") ; x("Sebastian") <= 6
 3 <= x("Frederic")  ;  x("Frederic") <= 4
 2 <= x("Jan-Georg") ; x("Jan-Georg") <= 5
 2 <= x("Krzysztof") ; x("Krzysztof") <= 4
 3 <= x("Maarten")   ;   x("Maarten") <= 4
 1 <= x("Luca")      ;      x("Luca") <= 6

! A different time slot for every person
 all_different(x)

! Solve the problem
 if not(cp_find_next_sol) then
  writeln("Problem is infeasible")
  exit(1)
 end-if

! Solution printout
 writeln(x)

end-model

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