Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

Describe what additional information Linda's algorithm could output so that
her algorithm's correctness could be established on any given S and T in
O(n) time.
C-11.2
Given two sets A and B represented as sorted sequences, describe an efficient
algorithm for computing A > B, which is the set of elements that are in A or B,
but not in both.
C-11.3
Suppose that we represent sets with balanced search trees. Describe and analyze
algorithms for each of the methods in the set ADT, assuming that one of the two
sets is much smaller than the other.
C-11.4
Describe and analyze an efficient method for removing all duplicates from a
collection A of n elements.
C-11.5
Consider sets whose elements are integers in the range [0,N − 1]. A popular
scheme for representing a set A of this type is by means of a Boolean array, B,
where we say that x is in A if and only if B[x] = true. Since each cell of B can be
represented with a single bit, B is sometimes referred to as a bit vector. Describe
and analyze efficient algorithms for performing the methods of the set ADT
assuming this representation.
C-11.6
Consider a version of deterministic quick-sort where we pick as our pivot the
median of the d last elements in the input sequence of n elements, for a fixed,
constant odd number d ≥ 3. Argue informally why this should be a good choice
for pivot. What is the asymptotic worst-case running time of quick-sort in this
case, in terms of n and d?
C-11.7
Another way to analyze randomized quick-sort is to use a recurrence equation.
In this case, we let T(n) denote the expected running time of randomized quicksort,
and we observe that, because of the worst-case partitions for good and bad
splits, we can write
T(n) ≤ 1/2 (T(3n/4) + T(n/4)) + (T(n − 1)) + bn,
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