#!/usr/bin/python -u # -*- coding: latin-1 -*- # # Global constraint clique in Z3 # # From Globals constraint catalogue: # http://www.emn.fr/x-info/sdemasse/gccat/Cclique.html # """ # Consider a digraph G described by the NODES collection: to the ith # item of the NODES collection corresponds the ith vertex of G; To # each value j of the ith succ variable corresponds an arc from the # ith vertex to the jth vertex. Select a subset S of the vertices of G # that forms a clique of size SIZE_CLIQUE (i.e., there is an arc # between each pair of distinct vertices of S). # # Example # [The graph is # 1 -> 2,4 # 2 -> 1,3,5 # 3 -> 2,5 # 4 -> 1,5 # 5 -> 2,3,4 # ] # # (3,< # index-1 succ-{}, # index-2 succ-{3,5}, # index-3 succ-{2,5}, # index-4 succ-{}, # index-5 succ-{2,3} # > # ) # # The clique constraint holds since the NODES collection depicts a # clique involving 3 vertices (namely vertices 2, 3 and 5) and since # its first argument SIZE_CLIQUE is set to the number of vertices of # this clique. # """ # # This Z3 model was written by Hakan Kjellerstrand (hakank@gmail.com) # See also my Z3 page: http://hakank.org/z3/ # from z3_utils_hakank import * import random def check_clique(graph,type="all",card1=None): sol = SimpleSolver() n = len(graph) # variables x = makeIntVector(sol, "x", n, 0,1) card = makeIntVar(sol,"card",0,n) # constraints if card1 != None: sol.add(card == card1) clique(sol,graph,x, card) num_solutions = 0 max_card = 0 while sol.check() == sat: num_solutions += 1 mod = sol.model() print("card:", mod.eval(card), "x :", [i for i in range(n) if mod.eval(x[i]).as_long() == 1]) max_card = mod.eval(card) if type == "max": getGreaterSolution(sol,mod,card) # maximum clique else: getDifferentSolution(sol,mod,[x[i] for i in range(n)]) # all cliques (including sub cliques) print("num_solutions:", num_solutions) return max_card # # make a symmetric random graph (0/1) of size # def random_graph(n): g = {} for i in range(n): for j in range(n): if i == j: g[(i,j)] = 1 else: g[(i,j)] = random.randint(0,1) g[(j,i)] = g[i,j] # Translate return [ [g[(i,j)] for j in range(n) ] for i in range(n)] # Two cliques: (0,1,3) and (2,4) graph1 = [[1, 1, 0, 1, 0], # 0,1,3 [1, 1, 0, 1, 0], # 0,1,3 [0, 0, 1, 0, 1], # 2,4 [1, 1, 0, 1, 0], # 0,1,3 [0, 0, 1, 0, 1]] # 2,4 # # A larger graph # The cliques are # 0,1,2 # 3,4,5 # 5,6,7,8,9 # (and their sub cliques) # graph2 =[[1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 1, 1, 1, 1, 1]] # The graph from the Global Constraint catalogue (the example above) # # 1 -> 1,3 # 2 -> 0,2,4 # 3 -> 1,4 # 4 -> 0,4 # 5 -> 1,2,3 # # The found (maximal) clique (N=3) is {1,2,4}. # graph3 = [[1,1,0,1,0], [1,1,1,0,1], [0,1,1,0,1], [1,0,0,1,1], [0,1,1,1,1]] # # A random graph of size 100 (generated by another program). # There are 3515 clique of size >= 3 (including sub cliques], # and four of size 6. # graph4 = [[0,0,1,0,1,0,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,1,1], [1,0,0,1,1,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,0,1], [1,0,0,0,0,0,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0,0,1,1,0,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,1,1], [0,0,0,1,1,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0,1,1,1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,1,0,1,0,1,1], [1,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,1,1,1,1,1,1,0], [1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,1,0,1,1,0,0,1,1], [1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,1,1,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0], [1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0,0,1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,1], [1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,1], [0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,1,1,0,1,1,1,1,1,1,0,1,0,1,1,1,0,1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,1,0,1,1,1,1,0,0], [1,0,0,0,0,1,0,1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0,0], [0,0,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,1,0,1,1,0,0], [1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,1,1,1,0,1,1,1,1,0,0,1], 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[0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1,1,1,1,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0,0,1,1,1,0,1,0,1,1,1,1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0], [1,0,0,1,0,0,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0], [1,0,1,0,0,0,0,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]] graph = graph4 # graph = random_graph(100) # print("all cliques and sub cliques") # check_clique(graph,"all") print("\nsearch for max card clique") max_card = check_clique(graph,"max") print("all cliques of size", max_card) check_clique(graph,"all",max_card)