The asymptotic lower bound for sorting n elements is established as n*log(n). However, when sorting n elements with k distinct values, the complexity can be reduced to n*log(k). By mapping each of the k distinct values to integers from 1 to k, the sorting process becomes more efficient. This method involves inspecting each value once, mapping it to an index, and incrementing the corresponding array element, followed by outputting the sorted list based on the counts in the array.
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