Given an integer N, the task is to check if N is a Centered Dodecagonal Number or not. If the number N is a Centered Dodecagonal Number then print “Yes” else print “No”.
Centered Dodecagonal Number represents a dot in the center and other dots surrounding it in successive Dodecagonal Number(12 sided polygon) layers. The first few Centered Dodecagonal Numbers are 1, 13, 37, 73 …
Input: N = 13
Second Centered dodecagonal number is 13.
Input: N = 30
1 The Kth term of the Centered Dodecagonal Number is given as:
2. As we have to check that the given number can be expressed as a Centered Dodecagonal Number or not. This can be checked as:
3. If the value of K calculated using the above formula is an integer, then N is a Centered Dodecagonal Number.
4. Else the number N is not a Centered Dodecagonal Number.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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