from graphviz import Digraph


def make_pow2_sum_tree(n=8):
    dot = Digraph("FullTree")
    dot.attr(rankdir="TB")  # направление сверху вниз
    dot.attr("node", shape="circle", style="filled", fillcolor="lightgray")

    node_count = 0

    def new_node(label):
        nonlocal node_count
        node_id = f"n{node_count}"
        node_count += 1
        dot.node(node_id, label)
        return node_id

    def pow2_node(xi):
        n1 = new_node("pow2")
        n2 = new_node(xi)
        dot.edge(n1, n2)
        return n1

    def plus(a, b):
        n = new_node("+")
        dot.edge(n, a)
        dot.edge(n, b)
        return n

    all_terms = []
    for i in range(1, n + 1):
        terms = [pow2_node(f"x{j}") for j in range(1, i + 1)]
        s = terms[0]
        for t in terms[1:]:
            s = plus(s, t)
        all_terms.append(s)

    root = all_terms[0]
    for t in all_terms[1:]:
        root = plus(root, t)

    dot.node("root", "f(x)")
    dot.edge("root", root)

    return dot


if __name__ == "__main__":
    g = make_pow2_sum_tree(8)
    g.render("original_tree", format="png", cleanup=True)