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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _elimination_trees(theta, decision_variables):
 """From Theta and the decision variables, determine the elimination order and the induced trees. """

    # auxiliary variables are any variables that are not decision
    auxiliary_variables = set(n for n in theta.linear if n not in decision_variables)

    # get the adjacency of the auxiliary subgraph
    adj = {v: {u for u in theta.adj[v] if u in auxiliary_variables}
           for v in theta.adj if v in auxiliary_variables}

    # get the elimination order that minimizes treewidth
    tw, order = dnx.treewidth_branch_and_bound(adj)

    ancestors = {}
    for n in order:
        ancestors[n] = set(adj[n])

        # now make v simplicial by making its neighborhood a clique, then
        # continue
        neighbors = adj[n]
        for u, v in itertools.combinations(neighbors, 2):
            adj[u].add(v)
            adj[v].add(u)
        for v in neighbors:
            adj[v].discard(n)
        del adj[n]

    roots = {}
    nodes = {v: {} for v in ancestors}
    for vidx in range(len(order) - 1, -1, -1):
        v = order[vidx]

        if ancestors[v]:
            for u in order[vidx + 1:]:
                if u in ancestors[v]:
                    # v is a child of u
                    nodes[u][v] = nodes[v]  # nodes[u][v] = children of v
                    break
        else:
            roots[v] = nodes[v]  # roots[v] = children of v

    return roots, ancestors