Top MCQs on Complexity Analysis using Recurrence Relations with Answers

What is the time complexity for the following C module? Assume that n>0 . int module(int n) { if (n == 1) return 1; else return (n + module(n-1)); }

Consider the recurrence relation a₁ = 8, a_n = 6n² + 2n + a_n-1. Let a₉₉ = k x 10⁴. The value of K is _____

 
Note : This question was asked as Numerical Answer Type.

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(n^α), then the least possible value (accurate up to two decimal positions) of α is __________

When n = 2^2k for some k ≥ 0, the recurrence relation
T(n) = √(2) T(n/2) + √n, T(1) = 1
evaluates to :

Let T(n) be the function defined by T(1)= 1, T(n)= 2T (⌊n/2⌋) + √n  for n≥2. Which of the following statement(s) is true? a.  T(n) = O(√n) b.  T(n) = O(n) c.  T(n) = O(log n) d. None of the above

Function F (n, m: integer): integer;
begin
    If (n<=0) or (m<=0) then F:=1
    else
      F:= F(n-1,m) + F(n, m-1);
    end;

The recurrence relation

 T(1) = 2
 T(n) = 3T(n/4)+n

has the solution, T(n) equals to

Match the following and choose the correct answer in the order A, B, C

(Bounds given may or may not be asymptotically tight)

Consider the following recurrence: T(n) = 2T(n^1/2) + 1 T(1) = 1 Which of the following is true?

Consider a list of recursive algorithms and a list of recurrence relations as shown below. Each recurrence relation corresponds to exactly one algorithm and is used to derive the time complexity of the algorithm.