Given a number N, the task is to check if N is a Nonagonal Number or not. If the number N is an Nonagonal Number then print “Yes” else print “No”.
Nonagonal Number is a figurate number that extends the concept of triangular and square numbers to the Nonagon. Specifically, the nth Nonagonal Numbers count the number of dots in a pattern of n nested nonagons(9 sided polygon), all sharing a common corner, where the ith nonagon in the pattern has sides made of i dots spaced one unit apart from each other. The first few Nonagonal Numbers are 1, 9, 24, 46, 75, 111, 154, …
Input: N = 9
Second Nonagonal Number is 9.
Input: N = 20
1. The Kth term of the nonagonal number is given as
2. As we have to check that the given number can be expressed as a Nonagonal 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 Nonagonal Number.
4. Else N is not a Nonagonal Number.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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