(Solution) - Consider a generalized version of the scheme described in the -(2025 Original AI-Free Solution)

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Consider a generalized version of the scheme described in the previous problem. Instead of using binary numbers, we now treat key and peer identifiers as base-b numbers where b > 2, and then use the metric in the previous problem to design a DHT (with 2 replace with b). Compare this DHT based on base-b numbers with the DHT based on binary numbers. In the worst case, which DHT generates more messages per query? Why?