import random

def generate_network(C, L):
    # Generate a random ring of C computers
    ring = list(range(1, C+1))
    random.shuffle(ring)
    links = []
    # Add bidirectional links between consecutive computers
    for i in range(C):
        j = (i+1) % C
        links.append((ring[i], ring[j]))
        links.append((ring[j], ring[i]))
    # Add extra links randomly until L links are achieved
    while len(links) < L:
        i = random.randint(0, C-1)
        j = random.randint(0, C-1)
        if i != j and (ring[i], ring[j]) not in links:
            links.append((ring[i], ring[j]))
            links.append((ring[j], ring[i]))
    # Sort links by the smallest endpoint first, then lexicographically
    links.sort(key=lambda x: (min(x), max(x)))
    # Return the network design as a tuple (ring, links)
    return (ring, links)

def find_ring(network):
    ring, links = network
    # Create a dictionary of neighbors for each computer
    neighbors = {i: [] for i in ring}
    for i, j in links:
        neighbors[i].append(j)
    # Use depth-first search to find a ring
    visited = set()
    stack = [ring[0]]
    while stack:
        current = stack.pop()
        visited.add(current)
        for neighbor in neighbors[current]:
            if neighbor == ring[0] and len(visited) == len(ring):
                # Found a ring
                return True
            if neighbor not in visited:
                stack.append(neighbor)
    # No ring found
    return False

# Example usage
network = generate_network(6, 10)
print(network)
print(find_ring(network))