qubo_lab/util/SAT2QUBO.py

#!/usr/bin/env python3

import numpy as np
from . import kSAT
from tqdm import tqdm
import math
import random

#__VERTEX_WEIGHT__ = -2
#__EDGE_WEIGHT__ = 2

__VERTEX_WEIGHT__ = 1
__EDGE_WEIGHT__ = -2

def WMISdictQUBO(kSATInstance):
    quboInstance = {}
    
    for clauseIndex in range(kSATInstance.getNumberOfClauses()):
        clause = kSATInstance.getClause(clauseIndex)
        
        # build triangles
        for varIndexInClause in range(len(clause)):
            label = kSATInstance.getLableOfBinding(clauseIndex,
                                                   clause[varIndexInClause])
            quboInstance[(label, label)] = __VERTEX_WEIGHT__
            
            for i in range(varIndexInClause + 1, len(clause)):
                targetLabel = kSATInstance.getLableOfBinding(clauseIndex,
                                                             clause[i])
                
                quboInstance[(label, targetLabel)] = __EDGE_WEIGHT__
        
    # connect conflicts
    for conflict in kSATInstance.getConflicts():
        quboInstance[(conflict[0], conflict[1])] = __EDGE_WEIGHT__
    
    return quboInstance

def WMISdictQUBO_2(kSATInstance):
    quboInstance = {}
    
    for clauseIndex in range(kSATInstance.getNumberOfClauses()):
        clause = kSATInstance.getClause(clauseIndex)
        
        # build triangles
        for varIndexInClause in range(len(clause)):
            lit = clause[varIndexInClause]
            var = abs(lit)
            
            aux = "z{}_{}".format(clauseIndex, var)
            var_node = "x{}".format(var)
            
            if lit < 0:
                quboInstance[(aux, aux)] = __VERTEX_WEIGHT__
                quboInstance[(var_node, aux)] = __EDGE_WEIGHT__
            else:
                quboInstance[(var_node, aux)] = __VERTEX_WEIGHT__
            
            
            
            for i in range(varIndexInClause + 1, len(clause)):
                var2 = abs(clause[i])
                
                aux2 = "z{}_{}".format(clauseIndex, var2)
                
                quboInstance[(aux, aux2)] = __EDGE_WEIGHT__
    
    return quboInstance

def WMISdictQUBO_3(kSATInstance):
    quboInstance = {}
    
    for clauseIndex in range(kSATInstance.getNumberOfClauses()):
        clause = kSATInstance.getClause(clauseIndex)
        
        # build triangles
        for varIndexInClause in range(len(clause)):
            lit = clause[varIndexInClause]
            var = abs(lit)
            
            aux = "z{}_{}".format(clauseIndex, var)
            var_node = "x{}".format(var)
            
            if lit < 0:
                quboInstance[(aux, aux)] = __VERTEX_WEIGHT__
                quboInstance[(var_node, aux)] = __EDGE_WEIGHT__
            else:
                quboInstance[(var_node, aux)] = __VERTEX_WEIGHT__
            
            
            
            for i in range(varIndexInClause + 1, len(clause)):
                var2 = abs(clause[i])
                
                aux2 = "z{}_{}".format(clauseIndex, var2)
                
                quboInstance[(aux, aux2)] = __EDGE_WEIGHT__ * 2
    
    return quboInstance

def WMISdictQUBO_4(kSATInstance):
    quboInstance = {}
    
    for clauseIndex in range(kSATInstance.getNumberOfClauses()):
        clause = kSATInstance.getClause(clauseIndex)
        
        # build triangles
        for varIndexInClause in range(len(clause)):
            lit = clause[varIndexInClause]
            var = abs(lit)
            
            aux = "z{}_{}".format(clauseIndex, var)
            var_node = "x{}".format(var)
            
            if lit < 0:
                quboInstance[(aux, aux)] = __VERTEX_WEIGHT__
                quboInstance[(var_node, aux)] = __EDGE_WEIGHT__ * 2
            else:
                quboInstance[(var_node, aux)] = __VERTEX_WEIGHT__
            
            
            
            for i in range(varIndexInClause + 1, len(clause)):
                var2 = abs(clause[i])
                
                aux2 = "z{}_{}".format(clauseIndex, var2)
                
                quboInstance[(aux, aux2)] = __EDGE_WEIGHT__
    
    return quboInstance

# only 3sat
def primitiveQUBO(sat):
    quboInstance = {}
    
    chains = {}
    
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sat.getClause(clauseIndex);
        
        #build clause primitives
        
        lit1 = "c{}_l{}".format(clauseIndex, clause[0])
        lit2 = "c{}_l{}".format(clauseIndex, clause[1])
        lit3 = "c{}_l{}".format(clauseIndex, clause[2])
        aux1 = "z{}_{}".format(clauseIndex, 1)
        aux2 = "z{}_{}".format(clauseIndex, 2)
        aux3 = "z{}_{}".format(clauseIndex, 3)
        aux4 = "z{}_{}".format(clauseIndex, 4)
        
        quboInstance[(lit1, lit1)] = 1;
        quboInstance[(lit2, lit2)] = 1;
        quboInstance[(lit3, lit3)] = 1;
        quboInstance[(aux1, aux1)] = -2;
        quboInstance[(aux2, aux2)] = 1;
        quboInstance[(aux3, aux3)] = -2;
        quboInstance[(aux4, aux4)] = -2;
        
        quboInstance[(lit1, lit2)] = 1;
        quboInstance[(lit1, aux1)] = -2;
        quboInstance[(lit2, aux1)] = -2;
        quboInstance[(aux1, aux2)] = -2;
        quboInstance[(aux2, aux3)] = -2;
        quboInstance[(aux2, lit3)] = 1;
        quboInstance[(lit3, aux3)] = -2;
        quboInstance[(aux3, aux4)] = -2;
        
        if clause[0] in chains:
            chains[clause[0]].append(lit1)
        else:
            chains[clause[0]] = [lit1]
            
        if clause[1] in chains:
            chains[clause[1]].append(lit2)
        else:
            chains[clause[1]] = [lit2]
            
        if clause[2] in chains:
            chains[clause[2]].append(lit3)
        else:
            chains[clause[2]] = [lit3]
    
    #build chains
    longestChain = 0;
    for lit, nodes in chains.items():
        if len(nodes) > longestChain:
            longestChain = len(nodes)
            
        if lit > 0 and -1 * lit in chains:
            len_smaller_chain = min(len(chains[lit]), len(chains[-lit]))
            
            indices = random.sample(list(range(len_smaller_chain)),
                                    round(len_smaller_chain / 2))
            
            for index in indices:
                quboInstance[(chains[lit][index], chains[-1*lit][index])] = 10
            
            #quboInstance[(chains[lit][0], chains[-1*lit][0])] = 2
            
    print("longest chain = {}".format(longestChain))
    
    for nodes in chains.values():
        while len(nodes) > 1:
            quboInstance[(nodes[0], nodes[1])] = -2;
            nodes.pop(0)
    
    return quboInstance

# only 3sat
def primitiveQUBO_2(sat):
    quboInstance = {}
    
    chains = {}
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sat.getClause(clauseIndex)
        
        lit1 = clause[0]
        lit2 = clause[1]
        lit3 = clause[2]
        
        var1 = abs(lit1)
        var2 = abs(lit2)
        var3 = abs(lit3)
        
        sign1 = 1 if lit1 > 0 else -1
        sign2 = 1 if lit2 > 0 else -1
        sign3 = 1 if lit3 > 0 else -1
        
        node_var1 = "x{}".format(var1)
        node_var2 = "x{}".format(var2)
        node_var3 = "x{}".format(var3)
        
        node_aux1 = "a{}_{}".format(clauseIndex, 1)
        node_aux2 = "a{}_{}".format(clauseIndex, 2)
        node_aux3 = "a{}_{}".format(clauseIndex, 3)
        node_aux4 = "a{}_{}".format(clauseIndex, 4)
        
        
        quboInstance[(node_var1, node_var1)] = 1 * sign1
        quboInstance[(node_var2, node_var2)] = 1 * sign2
        quboInstance[(node_var3, node_var3)] = 1 * sign3
        quboInstance[(node_aux1, node_aux1)] = -2
        quboInstance[(node_aux2, node_aux2)] = 1
        quboInstance[(node_aux3, node_aux3)] = -2
        quboInstance[(node_aux4, node_aux4)] = -2
        
        quboInstance[(node_var1, node_var2)] = 1 * sign1 * sign2
        quboInstance[(node_var1, node_aux1)] = -2 * sign1
        quboInstance[(node_var2, node_aux1)] = -2 * sign2
        quboInstance[(node_aux1, node_aux2)] = -2
        quboInstance[(node_aux2, node_var3)] = 1 * sign3
        
        quboInstance[(node_var3, node_aux3)] = -2 * sign3
        quboInstance[(node_aux2, node_aux3)] = -2
        quboInstance[(node_var3, node_aux4)] = -2
    
    return quboInstance

# only 3sat
def primitiveQUBO_3(sat):
    quboInstance = {}
    
    chains = {}
    
    lits = {}
    vars = {}
    
    n_clauses = sat.getNumberOfClauses()
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sat.getClause(clauseIndex)
        
        lit1 = clause[0]
        lit2 = clause[1]
        lit3 = clause[2]
        
        lits[lit1] = True
        lits[lit2] = True
        lits[lit3] = True
        
        var1 = abs(lit1)
        var2 = abs(lit2)
        var3 = abs(lit3)
        
        vars[var1] = True
        vars[var2] = True
        vars[var3] = True
        
        node_lit1 = "x{}".format(lit1)
        node_lit2 = "x{}".format(lit2)
        node_lit3 = "x{}".format(lit3)
        
        node_aux1 = "z{}_{}".format(clauseIndex, 1)
        node_aux2 = "z{}_{}".format(clauseIndex, 2)
        node_aux3 = "z{}_{}".format(clauseIndex, 3)
        node_aux4 = "z{}_{}".format(clauseIndex, 4)
        
        
        quboInstance[(node_lit1, node_lit1)] = 1
        quboInstance[(node_lit2, node_lit2)] = 1
        quboInstance[(node_lit3, node_lit3)] = 1
        quboInstance[(node_aux1, node_aux1)] = -2
        quboInstance[(node_aux2, node_aux2)] = 1
        quboInstance[(node_aux3, node_aux3)] = -2
        quboInstance[(node_aux4, node_aux4)] = -2
        
        quboInstance[(node_lit1, node_lit2)] = 1
        quboInstance[(node_lit1, node_aux1)] = -2
        quboInstance[(node_lit2, node_aux1)] = -2
        
        quboInstance[(node_aux1, node_aux2)] = -2
        
        quboInstance[(node_aux2, node_lit3)] = 1
        quboInstance[(node_lit3, node_aux3)] = -2
        quboInstance[(node_aux2, node_aux3)] = -2
        
        quboInstance[(node_aux3, node_aux4)] = -2
    
    for var in vars.keys():
        if var in lits and -var in lits:
            node_var = "x{}".format(var)
            node_nvar = "x{}".format(-var)
            
            print((node_var, node_nvar))
            quboInstance[(node_var, node_nvar)] = 2
            
    return quboInstance

def primitiveQUBO_4(sat):
    quboInstance = {}
    
    
    clauses_per_lit = {}
    
    lits = {}
    vars = {}
    
    n_clauses = sat.getNumberOfClauses()
    
    master_z = "zm"
    
    #quboInstance[(master_z, master_z)] = -2
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sat.getClause(clauseIndex)
        
        lit1 = clause[0]
        lit2 = clause[1]
        lit3 = clause[2]
        
        lits[lit1] = True
        lits[lit2] = True
        lits[lit3] = True
        
        sign1 = 1 if lit1 > 0 else -1
        sign2 = 1 if lit2 > 0 else -1
        sign3 = 1 if lit3 > 0 else -1
        
        for lit in clause:
            if lit in clauses_per_lit:
                clauses_per_lit[lit] += 1
            else:
                clauses_per_lit[lit] = 1
        
        var1 = abs(lit1)
        var2 = abs(lit2)
        var3 = abs(lit3)
        
        vars[var1] = True
        vars[var2] = True
        vars[var3] = True
        
        node_lit1 = "x{}".format(lit1)
        node_lit2 = "x{}".format(lit2)
        node_lit3 = "x{}".format(lit3)
        
        node_aux = "z{}".format(clauseIndex)
        
        #quboInstance[(node_aux, node_aux)] = -2
        #quboInstance[(node_aux, master_z)] = -2
        
        #quboInstance[(node_lit1, node_lit1)] = +1 #* sign3
        #quboInstance[(node_lit2, node_lit2)] = +1 #* sign3
        #quboInstance[(node_lit3, node_lit3)] = +1 #* sign3
        
        quboInstance[(node_lit1, node_aux)] = -2 #* sign1
        quboInstance[(node_lit2, node_aux)] = -2 #* sign2
        quboInstance[(node_lit3, node_aux)] = -2 #* sign3
    
    for lit in lits.keys():
        node_lit = "x{}".format(lit)
        
        #quboInstance[(node_lit, node_lit)] = 2 * clauses_per_lit[lit]
        
    for var in vars.keys():
        if var in lits and -var in lits:
            node_var = "x{}".format(var)
            node_nvar = "x{}".format(-var)
            
            max_clauses = max(clauses_per_lit[var], clauses_per_lit[-var])
            num_clauses = clauses_per_lit[var] + clauses_per_lit[-var]
             
            print((node_var, node_nvar))
            quboInstance[(node_var, node_nvar)] = 2 * num_clauses
            #quboInstance[(node_var, node_nvar)] = 2# * num_clauses
            
    return quboInstance

def primitiveQUBO_5(sat):
    quboInstance = {}
    
    
    clauses_per_lit = {}
    
    lits = {}
    vars = {}
    
    n_clauses = sat.getNumberOfClauses()
    
    master_z = "zm"
    
    #quboInstance[(master_z, master_z)] = -2
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sat.getClause(clauseIndex)
        
        lit1 = clause[0]
        lit2 = clause[1]
        lit3 = clause[2]
        
        lits[lit1] = True
        lits[lit2] = True
        lits[lit3] = True
        
        for lit in clause:
            if lit in clauses_per_lit:
                clauses_per_lit[lit] += 1
            else:
                clauses_per_lit[lit] = 1
        
        var1 = abs(lit1)
        var2 = abs(lit2)
        var3 = abs(lit3)
        
        vars[var1] = True
        vars[var2] = True
        vars[var3] = True
        
        node_lit1 = "x{}".format(lit1)
        node_lit2 = "x{}".format(lit2)
        node_lit3 = "x{}".format(lit3)
        
        node_aux1 = "z{}_1".format(clauseIndex)
        node_aux2 = "z{}_2".format(clauseIndex)
        
        quboInstance[(node_lit1, node_aux1)] = -2
        quboInstance[(node_lit2, node_aux1)] = -2
        quboInstance[(node_lit1, node_lit2)] = +2
        
        quboInstance[(node_aux1, node_lit3)] = +2
        quboInstance[(node_lit3, node_aux2)] = -2
        

        
    for var in vars.keys():
        if var in lits and -var in lits:
            node_var = "x{}".format(var)
            node_nvar = "x{}".format(-var)
            
            max_clauses = max(clauses_per_lit[var], clauses_per_lit[-var])
            num_clauses = clauses_per_lit[var] + clauses_per_lit[-var]
             
            #print((node_var, node_nvar))
            quboInstance[(node_var, node_nvar)] = 2 * max_clauses
            
    return quboInstance

def primitiveQUBO_6(sat):
    quboInstance = {}
    
    
    clauses_per_lit = {}
    
    lits = {}
    vars = {}
    
    n_clauses = sat.getNumberOfClauses()
    
    master_z = "zm"
    
    #quboInstance[(master_z, master_z)] = -2
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sat.getClause(clauseIndex)
        
        lit1 = clause[0]
        lit2 = clause[1]
        lit3 = clause[2]
        
        lits[lit1] = True
        lits[lit2] = True
        lits[lit3] = True
        
        for lit in clause:
            if lit in clauses_per_lit:
                clauses_per_lit[lit] += 1
            else:
                clauses_per_lit[lit] = 1
        
        var1 = abs(lit1)
        var2 = abs(lit2)
        var3 = abs(lit3)
        
        vars[var1] = True
        vars[var2] = True
        vars[var3] = True
        
        node_lit1 = "x{}".format(lit1)
        node_lit2 = "x{}".format(lit2)
        node_lit3 = "x{}".format(lit3)
        
        node_aux1 = "z{}_1".format(clauseIndex)
        node_aux2 = "z{}_2".format(clauseIndex)
        node_aux3 = "z{}_3".format(clauseIndex)
        node_aux4 = "z{}_4".format(clauseIndex)
        
        quboInstance[(node_lit1, node_aux1)] = -2
        quboInstance[(node_lit2, node_aux2)] = -2
        quboInstance[(node_aux1, node_aux2)] = +2
        
        quboInstance[(node_aux1, node_aux3)] = -2
        quboInstance[(node_aux2, node_aux3)] = -2
        
        quboInstance[(node_aux1, node_aux1)] = +2
        quboInstance[(node_aux2, node_aux2)] = +2
        
        quboInstance[(node_aux3, node_lit3)] = +2
        quboInstance[(node_lit3, node_aux4)] = -2
        

        
    for var in vars.keys():
        if var in lits and -var in lits:
            node_var = "x{}".format(var)
            node_nvar = "x{}".format(-var)
            
            max_clauses = max(clauses_per_lit[var], clauses_per_lit[-var])
            num_clauses = clauses_per_lit[var] + clauses_per_lit[-var]
             
            #print((node_var, node_nvar))
            quboInstance[(node_var, node_nvar)] = 2 * max_clauses
            
    return quboInstance

def primitiveQUBO_7(sat):
    quboInstance = {}
    
    
    clauses_per_lit = {}
    
    lits = {}
    vars = {}
    
    n_clauses = sat.getNumberOfClauses()
    
    master_z = "zm"
    
    #quboInstance[(master_z, master_z)] = -2
    direct_cupplers = {}
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sat.getClause(clauseIndex)
        
        lit1 = clause[0]
        lit2 = clause[1]
        lit3 = clause[2]
        
        lits[lit1] = True
        lits[lit2] = True
        lits[lit3] = True
        
        for lit in clause:
            if lit in clauses_per_lit:
                clauses_per_lit[lit] += 1
            else:
                clauses_per_lit[lit] = 1
        
        var1 = abs(lit1)
        var2 = abs(lit2)
        var3 = abs(lit3)
        
        vars[var1] = True
        vars[var2] = True
        vars[var3] = True
        
        node_lit1 = "x{}".format(lit1)
        node_lit2 = "x{}".format(lit2)
        node_lit3 = "x{}".format(lit3)
        
        node_aux1 = "z{}_1".format(clauseIndex)
        node_aux2 = "z{}_2".format(clauseIndex)
        
        quboInstance[(node_lit1, node_aux1)] = -2
        quboInstance[(node_lit2, node_aux1)] = -2
        quboInstance[(node_lit1, node_lit2)] = +2
        
        quboInstance[(node_aux1, node_lit3)] = +2
        quboInstance[(node_lit3, node_aux2)] = -2
        
        
        
        if (node_lit1, node_lit2) in direct_cupplers:
            direct_cupplers[(node_lit1, node_lit2)] += 1
        else:
            direct_cupplers[(node_lit1, node_lit2)] = 1
        

        
    for var in vars.keys():
        if var in lits and -var in lits:
            node_var = "x{}".format(var)
            node_nvar = "x{}".format(-var)
            
            max_clauses = max(clauses_per_lit[var], clauses_per_lit[-var])
            num_clauses = clauses_per_lit[var] + clauses_per_lit[-var]
             
            print((node_var, node_nvar))
            quboInstance[(node_var, node_nvar)] = 2 * max_clauses

            
    for coupler, count in direct_cupplers.items():        
        quboInstance[coupler] = count * 2
        
            
    return quboInstance

def primitiveQUBO_8(sat):
    quboInstance = {}
    
    
    clauses_per_lit = {}
    
    lits = {}
    vars = {}
    
    n_clauses = sat.getNumberOfClauses()

    direct_cupplers = {}
    
    for clauseIndex in range(sat.getNumberOfClauses()):
        clause = sorted(sat.getClause(clauseIndex))
        
        if clause[2] < 0:
            __add_3not_or_clause(quboInstance, clause, clauseIndex)
        elif clause[1] < 0:
            __add_2not_or_clause(quboInstance, clause, clauseIndex)
        elif clause[0] < 0:
            __add_1not_or_clause(quboInstance, clause, clauseIndex, direct_cupplers)
        else:
            __add_3_or_clause(quboInstance, clause, clauseIndex, direct_cupplers)

            
    for coupler, count in direct_cupplers.items():        
        quboInstance[coupler] = count * 2
        
            
    return quboInstance

def __add_3not_or_clause(quboInstance, clause, clause_index):
    var1 = abs(clause[0])
    var2 = abs(clause[1])
    var3 = abs(clause[2])
    
    
    node_var1 = "x{}".format(var1)
    node_var2 = "x{}".format(var2)
    node_var3 = "x{}".format(var3)
    
    node_aux1 = "z{}_1".format(clause_index)
    node_aux2 = "z{}_2".format(clause_index)
    node_aux3 = "z{}_3".format(clause_index)
    
    quboInstance[(node_var1, node_aux1)] = +2
    quboInstance[(node_var2, node_aux2)] = +2
    quboInstance[(node_aux1, node_aux2)] = +2
    
    quboInstance[(node_aux1, node_aux1)] = -2
    quboInstance[(node_aux2, node_aux2)] = -2
    
    quboInstance[(node_var1, node_aux3)] = -2
    quboInstance[(node_var2, node_aux3)] = -2
    quboInstance[(node_var3, node_aux3)] = +2
    quboInstance[(node_aux3, node_aux3)] = +2
    
def __add_2not_or_clause(quboInstance, clause, clause_index):
    var1 = abs(clause[0])
    var2 = abs(clause[1])
    var3 = abs(clause[2])
    
    
    node_var1 = "x{}".format(var1)
    node_var2 = "x{}".format(var2)
    node_var3 = "x{}".format(var3)
    
    node_aux1 = "z{}_1".format(clause_index)
    node_aux2 = "z{}_2".format(clause_index)
    node_aux3 = "z{}_3".format(clause_index)
    node_aux4 = "z{}_4".format(clause_index)
    node_aux5 = "z{}_5".format(clause_index)
    
    quboInstance[(node_var1, node_aux1)] = +2
    quboInstance[(node_var2, node_aux2)] = +2
    quboInstance[(node_aux1, node_aux2)] = +2
    
    quboInstance[(node_aux1, node_aux3)] = -2
    quboInstance[(node_aux2, node_aux3)] = -2
    quboInstance[(node_aux3, node_aux3)] = +2
    
    quboInstance[(node_aux3, node_aux4)] = -2
    quboInstance[(node_var3, node_aux5)] = -2
    quboInstance[(node_aux4, node_aux5)] = +2

def __add_1not_or_clause(quboInstance, clause, clause_index, direct_cupplers):
    var1 = abs(clause[1])
    var2 = abs(clause[2])
    var3 = abs(clause[0])
    
    
    node_var1 = "x{}".format(var1)
    node_var2 = "x{}".format(var2)
    node_var3 = "x{}".format(var3)
    
    node_aux1 = "z{}_1".format(clause_index)
    node_aux2 = "z{}_2".format(clause_index)
    
    quboInstance[(node_var1, node_var2)] = +2
    quboInstance[(node_var1, node_aux1)] = -2
    quboInstance[(node_var2, node_aux1)] = -2
    
    quboInstance[(node_aux1, node_aux2)] = +2
    quboInstance[(node_var3, node_aux2)] = +2
    
    quboInstance[(node_aux2, node_aux2)] = -2
    
    if (node_var1, node_var2) in direct_cupplers:
        direct_cupplers[(node_var1, node_var2)] += 1
    else:
        direct_cupplers[(node_var1, node_var2)] = 1
        
def __add_3_or_clause(quboInstance, clause, clause_index, direct_cupplers):
    var1 = abs(clause[0])
    var2 = abs(clause[1])
    var3 = abs(clause[2])
    
    
    node_var1 = "x{}".format(var1)
    node_var2 = "x{}".format(var2)
    node_var3 = "x{}".format(var3)
    
    node_aux1 = "z{}_1".format(clause_index)
    node_aux2 = "z{}_2".format(clause_index)
    
    quboInstance[(node_var1, node_var2)] = +2
    quboInstance[(node_var1, node_aux1)] = -2
    quboInstance[(node_var2, node_aux1)] = -2
    
    quboInstance[(node_aux1, node_var3)] = +2
    quboInstance[(node_var3, node_aux2)] = -2
    
    if (node_var1, node_var2) in direct_cupplers:
        direct_cupplers[(node_var1, node_var2)] += 1
    else:
        direct_cupplers[(node_var1, node_var2)] = 1

    
class QuboWriter:
    def __init__(self, qubo):
        self.__labelIndexDict = {}
        self.__qubo = qubo
        
        self.__initLabelIndexDict(self.__qubo)
        
        print(self.__labelIndexDict)
    
    def __initLabelIndexDict(self, qubo):
        indexCount = 0
        
        for coupler in qubo:
            
            label1 = coupler[0]
            label2 = coupler[1]
            
            if label1 not in self.__labelIndexDict:
                self.__labelIndexDict[label1] = indexCount
                indexCount += 1
            
            if label2 not in self.__labelIndexDict:
                self.__labelIndexDict[label2] = indexCount
                indexCount += 1
    
    def write(self, filePath):
        quboFile = open(filePath, "w")
    
        self.__writeQuboFileHeader(quboFile)
        self.__writeQuboFileNodes(quboFile)
        self.__writeQuboFileCouplers(quboFile)
    
        quboFile.close()
    
    def __writeQuboFileHeader(self, quboFile):
        numberOfNodes = len(self.__labelIndexDict)
        numberOfCouplers = len(self.__qubo) - numberOfNodes
    
        quboFile.write("c\n")
        quboFile.write("c this is a generated qubo file\n")
        quboFile.write("c\n")
    
        quboFile.write("p qubo 0 %d %d %d\n" %(numberOfNodes,
                                               numberOfNodes,
                                               numberOfCouplers))
                                               
    def __writeQuboFileNodes(self, quboFile):
        for label in self.__labelIndexDict:
            self.__writeCoupler(quboFile, (label, label))
            
    def __writeCoupler(self, quboFile, coupler):
            indices = self.__getNodeIndicesFromCoupler(coupler)
    
            quboFile.write("%d %d  %d\n" % (indices[0],
                                            indices[1],
                                            self.__qubo[coupler]))

    def __getNodeIndicesFromCoupler(self, coupler):
        index1 = self.__labelIndexDict[coupler[0]]
        index2 = self.__labelIndexDict[coupler[1]]
        
        if index1 <= index2:
            return [index1, index2]
        else:
            return [index2, index1]
            
    def __writeQuboFileCouplers(self, quboFile):
        for coupler in self.__qubo:
            if coupler[0] != coupler[1]:
                self.__writeCoupler(quboFile, coupler)