Given an integer N, the task is to check if it is a Centered Octagonal number or not. If the number N is an Centered Octagonal Number then print “Yes” else print “No”.
Centered Octagonal number represents an octagon with a dot in the centre and others dots surrounding the centre dot in the successive octagonal layer.The first few Centered Octagonal numbers are 1, 9, 25, 49, 81, 121, 169, 225, 289, 361 …
Input: N = 9
Second Centered Octagonal number is 9.
1. The Kth term of the Centered Octagonal number is given as
2. As we have to check that the given number can be expressed as a Centered Octagonal Number or not. This can be checked as follows –
3. If the value of K calculated using the above formula is an integer, then N is a Centered Octagonal Number.
4. Else N is not a Centered Octagonal Number.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.