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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 min_width_heuristic(G):
 """Computes an upper bound on the treewidth of graph G based on the min-width heuristic for the elimination ordering. Parameters G : NetworkX graph The graph on which to compute an upper bound for the treewidth. Returns ------- treewidth_upper_bound : int An upper bound on the treewidth of the graph G. order : list An elimination order that induces the treewidth. Examples -------- This example computes an upper bound for the treewidth of the :math:`K_4` complete graph. References Based on the algorithm presented in [GD]_ """

    # we need only deal with the adjacency structure of G. We will also
    # be manipulating it directly so let's go ahead and make a new one
    adj = {v: set(G[v]) for v in G}

    num_nodes = len(adj)

    # preallocate the return values
    order = [0] * num_nodes
    upper_bound = 0

    for i in range(num_nodes):
        # get the node with the smallest degree. We add random() which picks a value
        # in the range [0., 1.). This is ok because the lens are all integers. By
        # adding a small random value, we randomize which node is chosen without affecting
        # correctness.
        v = min(adj, key=lambda u: len(adj[u]) + random())

        # if the number of neighbours of v is higher than upper_bound, update
        dv = len(adj[v])
        if dv > upper_bound:
            upper_bound = dv

        # make v simplicial by making its neighborhood a clique then remove the
        # node
        _elim_adj(adj, v)
        order[i] = v

    return upper_bound, order