Data Structure MCQ - Complexity
This section focuses on the "Complexity" of the Data Structure. These Multiple Choice Questions (mcq) should be practiced to improve the Data Structure skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.
1. Which of the following case does not exist in complexity theory?
Explanation:Null case does not exist in complexity Theory.
2. What is the time, space complexity of following code:
int a = 0, b = 0;
for (i = 0; i < N; i++)
a = a + rand();
for (j = 0; j < M; j++)
b = b + rand();
Explanation:The first loop is O(N) and the second loop is O(M). Since we don’t know which is bigger, we say this is O(N + M). This can also be written as O(max(N, M)).
Since there is no additional space being utilized, the space complexity is constant / O(1).
3. The complexity of linear search algorithm is
Explanation: The worst case complexity of linear search is O(n).
4.What is the time complexity of following code:
int a = 0;
for (i = 0; i < N; i++)
for (j = N; j > i; j--)
a = a + i + j;
Explanation:= N + (N – 1) + (N – 2) + … 1 + 0
= N * (N + 1) / 2
= 1/2 * N^2 + 1/2 * N
5. The Worst case occur in linear search algorithm when
Explanation:The Worst case occur in linear search algorithm when Item is the last element in the array or is not there at all.
6. What is the time complexity of following code:
int i, j, k = 0;
for (i = n / 2; i <= n; i++)
for (j = 2; j <= n; j = j * 2)
k = k + n / 2;
Explanation:Let’s take the examples here.
for n = 16, j = 2, 4, 8, 16
for n = 32, j = 2, 4, 8, 16, 32
So, j would run for O(log n) steps.
i runs for n/2 steps.
So, total steps = O(n/ 2 * log (n)) = O(n*logn)
7. The worst case occur in quick sort when
Explanation:This happens when the pivot is the smallest (or the largest) element. Then one of the partitions is empty, and we repeat recursively the procedure for N-1 elements.
8. What does it mean when we say that an algorithm X is asymptotically more efficient than Y?
Explanation: An algorithm X is said to be asymptotically better than Y if X takes smaller time than y for all input sizes n larger than a value n0 where n0 > 0.
9. The complexity of Fibonacci series is
Explanation:= Fibonacci is f(n) = f(n-1) + f(n-2), f(0) = 0, f(1) = 1. Let g(n) = 2n. Now prove inductively that f(n) > = g(n).
10. What is the time complexity of following code:
int a = 0, i = N;
while (i > 0)
a += i;
i /= 2;
Explanation:We have to find the smallest x such that N / 2^x N
x = log(N).
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