Derive max distinct frequencies for n items
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The question evaluates combinatorial reasoning, discrete mathematics, and constructive extremal analysis by asking for the maximum number of distinct frequency counts in an array and a matching construction.
For an array of length n (n ≥
- with arbitrary integer values, what is the maximum possible number of distinct frequency counts among its distinct values? Derive a tight expression in terms of n and prove optimality. Discuss constructive examples that achieve the bound.
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