#Rooted Tree Arrangement

import itertools


class Node:
    def __init__(self, key):
        self.key = key
        self.children = []


def rooted_tree_arrangement(root):
    # Initialize the best solution to a large value
    best_cuts = float('inf')
    best_solution = None

    # Define a function to calculate the number of cuts of a solution
    def calculate_cuts(solution):
        cuts = 0
        for i in range(len(solution)):
            for j in range(i + 1, len(solution)):
                if solution[j] in solution[i].children:
                    cuts += 1
        return cuts

    # Define a function to perform the branch-and-bound search
    def search(node, solution=[]):
        nonlocal best_cuts, best_solution
        if not node.children:
            cuts = calculate_cuts(solution)
            if cuts < best_cuts:
                best_cuts = cuts
                best_solution = solution
        else:
            # Use a heuristic function to order the children nodes
            # in the next level of the search tree
            heuristic = lambda c: len(c.children)
            for c in sorted(node.children, key=heuristic):
                search(c, solution + [c])

    search(root)
    return best_solution


# Example usage
root = Node(1)
root.children = [Node(2), Node(3), Node(4)]
root.children[0].children = [Node(5), Node(6)]
root.children[1].children = [Node(7), Node(8), Node(9)]

print([n.key for n in rooted_tree_arrangement(root)])
