Question

The complexity of three algorithms is given as: O(n), O(n2) and O(n3). Which should execute slowest for large value of n? A. O(n) B. O(n2) C. O(n3) D. All will execute in same time.

Answer 1

Answer:

O($n^{3}$) will have slowest Runtime among the given three algorithms.

Explanation:

Big-O Analysis of Algorithms

• Algorithmic complexity is expressed using the big-O notation.

• For a problem of size n:

       A constant-time function is  - O(1)

       A linear-time function is  - O(n)

       A quadratic-time function is- O($n^{2}$)

Runtime Analysis of Algorithms

• The fastest running time for an algorithm is O(1) which is commonly referred to as Constant Running Time. In Constant Running Time, the algorithm  takes the same amount of time to execute regardless of its input size. Though it is the ideal runtime for an algorithm, it’s rarely achievable.

• The Runtime of an algorithm depends on  the size of the input n or the number of operations that is required for each input item.

The algorithms can be classified from the best-to-worst performance as follows :

• A logarithmic algorithm – O(log n)

• A linear algorithm – O(n)

• A super linear algorithm – O(n log n)

• A polynomial algorithm – O($n^{c}$)

• A exponential algorithm – O($c^{n}$)

• A factorial algorithm – O(n!)

Runtime grows the fastest and becomes quickly unusable for even

small values of n.

• O($n^{3}$) will have slowest Runtime among the given three algorithms.

To know more about Bog O notation and Complexity of an Algorithm,

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