Consider a set X = {x1,...,xn } where every xi is a positive integer and xi ? nf for some constant f . We represent xi as strings over an alphabet 0, 1, . . . , 2t ? 1 (i.e., representing each xi in base 2t) and store all xi from X in a compressed trie T. For every node u of T we keep an array A(u) of size 2t + 1. A(u)[i] contains a pointer to the

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Consider a set X = {x1,...,xn } where every xi is a positive integer and xi ? nf for some constant f . We represent xi as strings over an alphabet 0, 1, . . . , 2t ? 1 (i.e., representing each xi in base 2t) and store all xi from X in a compressed trie T. For every node u of T we keep an array A(u) of size 2t + 1. A(u)[i] contains a pointer to the child ui of u such that the edge from u to ui is marked with i; A(u)[i] = NULL if there is no such ui in T.

Specify all of the following in big-O in terms of f, n, and t (as necessary). What is the maximum height of T? What is the total space usage of T and all A(u)? What time is

needed to search for a key k in T ?

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