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Recurence GATE CS PYQ Quiz
Question 1
Consider the following recurrence relation.
Which one of the following options is correct?
T(n) = Θ(n5/2)
T(n) = Θ(nlogn)
T(n) = Θ(n)
T(n) = Θ((logn)5/2)
Question 2
The given diagram shows the flowchart for a recursive function A(n). Assume that all statements, except for the recursive calls, have O(1) time complexity. If the worst case time complexity of this function is O(nα), then the least possible value (accurate up to two decimal positions) of α is __________
2.2 to 2.4
3.2 to 3.4
0 to 1.8
1
Question 3
Which one of the following correctly determines the solution of the recurrence relation with T(1) = 1?
T(n) = 2T(n/2) + Logn Θ(n)
Θ(nLogn)
Θ(n*n)
Θ(log n)
Question 4
The running time of an algorithm is represented by the following recurrence relation:
if n <= 3 then T(n) = n else T(n) = T(n/3) + cn
Which one of the following represents the time complexity of the algorithm?
(A) Θ(n)
(B) Θ(n log n)
(C) Θ(n2)
(D) Θ(n2log n)
A
B
C
D
Question 5
Consider the following recurrence:
Which one of the following is true?
(A) T(n) =
[Tex]\\theta[/Tex](loglogn)
(B) T(n) =
[Tex]\\theta[/Tex](logn)
(C) T(n) =
[Tex]\\theta[/Tex](sqrt(n)) (D) T(n) =
[Tex]\\theta[/Tex](n)
A
B
C
D
Question 6
Find the complexity
θ(log log n)
θ(log n)
θ(sqrt(n))
θ(n)
Question 7
Consider the following recurrence relation:
T(n)={√n T(√n)+n} for n>=1
T(n)=1 for n=1
Which one of the following options is CORRECT ?
T(n) =θ(n log log n)
T(n) =θ(n2 log n)
T(n) =θ(n log n)
T(n) =θ(n2 log log n)
Question 8
Let T(n) be the recurrence relation defined as follows:
T(0) = 1,
T(1) = 2, and
T(n) = 5T(n − 1) − 6T(n − 2) for n ≥ 2
Which one of the following statements is TRUE?
T(n) = θ(n.2n)
T(n) = θ(2n)
T(n) = θ(3n)
T(n) = θ(n.3n)
There are 8 questions to complete.