"""
K4P2 Graceful Graph in cpmpy.

http://www.csplib.org/Problems/prob053/
'''
Proposed by Karen Petrie
A labelling f of the nodes of a graph with q edges is graceful if f assigns each node a unique label
from 0,1,...,q and when each edge xy is labelled with |f(x)-f(y)|, the edge labels are all different.
Gallian surveys graceful graphs, i.e. graphs with a graceful labelling, and lists the graphs whose status
is known.

[ picture ]

All-Interval Series is a special case of a graceful graph where the graph is a line.
'''

This cpmpy model was written by Hakan Kjellerstrand (hakank@gmail.com)
See also my cpmpy page: http://hakank.org/cpmpy/
  
"""
from cpmpy import *
import cpmpy.solvers
import numpy as np
from cpmpy_hakank import *


def k4p2gracefulgraph2():

  graph = [[0, 1],
           [0, 2],
           [0, 3],
           [1, 2],
           [1, 3],
           [2, 3],
           [4, 5],
           [4, 6],
           [4, 7],
           [5, 6],
           [5, 7],
           [6, 7],
           [0, 4],
           [1, 5],
           [2, 6],
           [3, 7]]


  # data
  q = len(graph)
  n = len(np.unique(graph))

  # variables
  nodes = intvar(0,q,shape=n,name="nodes")
  edges = intvar(1,q,shape=q,name="edges")

  # constraints
  model = Model(AllDifferent(edges),
                AllDifferent(nodes),
                [abs(nodes[s] - nodes[t]) for (s,t) in graph] == edges
           )

  print(model)
  # from cpmpy.transformations.flatten_model import flatten_constraint, flatten_model
  # from cpmpy.transformations.get_variables import print_variables
  # mf = flatten_model(model)
  # print_variables(mf)
  # print(mf)

  ss = CPM_ortools(model)
  ss.ort_solver.parameters.linearization_level = 0
  ss.ort_solver.parameters.cp_model_probing_level = 0
  num_solutions = ss.solveAll(display=nodes)
  print("num_solutions:",num_solutions)

k4p2gracefulgraph2()