import random

# function to generate a ring-preserving network
def generate_network(C, L):
    # assign IDs to nodes
    node_ids = list(range(1, C+1))
    random.shuffle(node_ids)

    # create links between nodes
    links = []
    for i in range(1, C+1):
        # link to the next node in a clockwise direction
        j = (i % C) + 1
        links.append((node_ids[i-1], node_ids[j-1]))
        # link to the previous node in a counter-clockwise direction
        k = i - 1 if i > 1 else C
        links.append((node_ids[i-1], node_ids[k-1]))
    # link the first and last nodes to complete the ring
    links.append((node_ids[0], node_ids[C-1]))

    # randomly permute node IDs
    random.shuffle(node_ids)

    # sort links by new IDs and endpoints
    links = sorted([(min(node_ids.index(u)+1, node_ids.index(v)+1), max(node_ids.index(u)+1, node_ids.index(v)+1)) for (u,v) in links])

    # find a ring in the permuted network
    ring = []
    visited = set()
    start_node = node_ids[0]
    current_node = start_node
    while current_node not in visited:
        ring.append(current_node)
        visited.add(current_node)
        # follow the clockwise direction to the next node
        next_node = None
        for (u, v) in links:
            if u == current_node and v not in visited:
                next_node = v
                break
        # follow the counter-clockwise direction to the next node
        if next_node is None:
            for (u, v) in links:
                if v == current_node and u not in visited:
                    next_node = u
                    break
        current_node = next_node

    # output the IDs of nodes in the ring
    return ring