Suppose that an array of length n contains k distinct elements x1, x2, . . . , x

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Suppose that an array of length n contains k distinct elements x1, x2, . . . , xk, where xi occurs ci times for i = 1, 2, . . . , k. (Therefore n = Pk i=1 ci .) Prove that every comparison-based sorting algorithm must use

?(lg (n! / c1!c2! ck!))

Suppose that an array of length n contains k distinct elements x1, x2, . . . , xk, where xi occurs ci times for i = 1, 2, . . . , k. (Therefore n = Pk i=1 ci .) Prove that every comparison-based sorting algorithm must use comparisons in the worst case to sort the array. (The algorithm does not know ahead of time the number and distribution of the duplicates.)

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