#Rooted Tree Arrangement





    # Initialize the best solution to a large value

    # Define a function to calculate the number of cuts of a solution

    # Define a function to perform the branch-and-bound search
            # Use a heuristic function to order the children nodes
            # in the next level of the search tree



# Example usage


if __name__ == '__main__':
    import itertools
    class Node:
        def __init__(self, key):
            self.key = key
            self.children = []
    def rooted_tree_arrangement(root):
        best_cuts = float('inf')
        best_solution = None
        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
        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:
                heuristic = lambda c: len(c.children)
                for c in sorted(node.children, key=heuristic):
                    search(c, solution + [c])
        search(root)
        return best_solution
    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)])
