Decide whether all input elements are distinct. In the comparison model, this needs comparisons in the worst case. An accepting decision-tree leaf for distinct keys must force a total order: incomparable keys could otherwise be made equal consistently with its strict comparison outcomes. Thus the possible orders require different accepting leaves, giving a decision-tree depth of at least even for three-way comparisons.
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The Element Distinctness problem is a fundamental problem in computer science and algorithms, particularly in the area of data structures and complexity theory. The problem can be succinctly described as follows: **Problem Statement:** Given a set of \( n \) elements, determine if all the elements are distinct or if there are any duplicates in the set.