Suppose a client host tries to detect the number of servers in a cloud computing data center. The client observes that the IP protocol stamps a certain sequence ID number (SIN) on each IP packet. The SIN of the first packet generated by a server is a random number starting from 6000, and SINs of the next packets are sequentially assigned. Assume all IP packets constructed by servers behind NAT are sent to the outside world beyond the data center. Recall that NAT in a data center is incorporated in the load balancer

(a) Assuming you can sniff all packets transmitted by NAT to the outside, present an algorithm that detects the number of unique servers behind the NAT/load balancer.
(b) Reconsider the conditions presented in part (a), this time considering that the SINs are not sequentially assigned.
(c) If the number of servers is substantially large, which is the case in practice, comment on how efficient your algorithm executes the objectives of the algorithm.