Question

Give the time complexities (Big-O notation) of the following running times expressed as a function of the input size N.

a) N¹²+ 25N¹⁰+ 8

b) N + 3logN + 12n√n

c) 12NlogN + 15N² logN

Answer 1

Big - O notation is used to give the time complexity of a function. It describes the worst case scenario on the running time of a program.

(a)

n¹² + 25n¹⁰ + 8

Here the n¹² term grows faster than  25n¹⁰ for large inputs.

So time complexity is O(n¹²) .

(b)

n + 3logn + 12n√n

Here the 12n√n term grows faster than both  3logn and n  for large inputs.

So time complexity is O(n√n) .

(c)

12nlogn + 15n² logn

Here the 15n² logn term grows faster than 12nlogn for large inputs.

So time complexity is O(n² logn) .

Note that the time complexity notation subsumes any multiplied constant terms