Data Structure and Algorithm Analysis
Questions 291 to 300
291.

The mathematical definition for Omega can be defined as,
provided f,g:NàR^{+}
and c is a positive constant and n > n_{0},
(a) f(n) ≥ c. g(n) n
(b) f(n) £ c. g(n) n
(c) f(n) ≥ c + g(n) n
(d) f(n) £ c + g(n) n
(e) f(n) £ g(n) n.


The q notation is __________
I. Symmetric.
II. Reflexive.
III.
Transitive.
(a) Only (I) above
(b) Only (II) above
(c) Only (III) above
(d) Both (I) and
(II) above
(e) All (I), (II)
and (III) above.


From the following pick the one which does not belongs to
the same paradigm to which others belongs to.
(a) Minimum &
Maximum problem
(b) Knapsack problem
(c) Selection
problem
(d) Merge sort
(e) Quick sort.


The OBST algorithm in worst case takes _______ time if all
c(i, j )’s and r(i, j)’s are calculated.
(a) O(log n) (b) O(n^{4}) (c) O(n^{3}) (d) O(n log n) (e) O(n^{2}).


Read the following statements carefully, and choose the correct answer
I. For the
Backtracking algorithms stack data structure is used.
II. For
the Branchandbound algorithms queue data structure is used.
(a) (I) is FALSE but
(II) is TRUE
(b) (I) and (II)
both are FALSE
(c) (I) is TRUE but
(II) is FALSE
(d) (I) and (II)
both are TRUE
(e) (II) is TRUE and
(I) can’t be defined.


The weighted array used in TVS problems for the following
binary tree is __________
(a) [1,2,3,0,0,4,0,5,6]
(b) [1,2,3,0,0,4,0,5,0,0,0,0,6]
(c) [1,2,3,4,5,6]
(d) [1,2,3,0,0,4,5,6]
(e) [1,3,5,2,4,6].


Let f,_{ }t: N→ R^{+}, then t (n) Î Ω (f (n)), iff
f(n) Î O (t (n)) is known as __________
(a) Limit
rule (b) Rule of inference (c)
Duality rule
(d) Rule of consequences (e)
Rule of symmetricity.


Let f, t: N→R ^{≥ 0}, and t (n) ÎO (f (n)) iff t(n)
≤ c.f (n) where c is positive real
constant and n ≥ n_{o}, then n_{o} is ___________
(a) Upper
bound (b) Lower bound (c) Duality value
(d) Threshold value (e) Maximum value.


For the 15puzzle problem if the initial arrangement is as
follows, then the value of ‘x’ used to find the reachability is ________
(a) 0 (b) 1 (c) 8 (d) 14 (e) 13.


The time taken by nondeterministic sorting algorithm is
______
(a) O(1) (b) O(log n) (c) O(n^{2}) (d) O(n log
n) (e) O(n).

Answers
291.

Answer : (a)
Reason: According to
the definition of the Omega notation.


Answer : (e)
Reason: According to
the asymptotic notational rules, q notation is equivalence one


Answer : (b)
Reason: The
remaining all belongs to divide and conquer paradigm.


Answer : (c)
Reason: Because of
the memory functions in OBST we calculate c(i, j )’s, r(i, j)’s and w(i ,
j)’s.


Answer : (d)
Reason: According to
the need of the traverse, Backtracking algorithm uses stack and
Branchandbound algorithms uses queue.


Answer : (b)
Reason: For any null
node in the full binary tree it stores zeros.


Answer : (c)
Reason: According to
the asymptotic notational rules.


Answer : (d)
Reason: According to
the definition of Big Oh ( O )


Answer : (a)
Reason:
Accordingly the EMPTY cell is there in non shaded position
and hence value of ‘x’ is 0, otherwise value of ‘x’ is 1.


Answer : (e)
Reason: As there it
sorts the entries in one loop. Because in nondeterministic sorting algorithms
the abstractions are used which can’t be programmed.

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