Program to check if N is a Decagonal Number
Given a number N, the task is to check if N is a Decagonal Number or not. If the number N is an Decagonal Number then print “Yes” else print “No”.
Decagonal Number is a figurate number that extends the concept of triangular and square numbers to the decagon (10-sided polygon). The nth decagonal numbers count the number of dots in a pattern of n nested decagons, all sharing a common corner, where the ith decagon in the pattern has sides made of i dots spaced one unit apart from each other. The first few decagonal numbers are 1, 10, 27, 52, 85, 126, 175, …
Input: N = 10
Second decagonal number is 10.
Input: N = 30
- The Kth term of the decagonal number is given as
- As we have to check that the given number can be expressed as a Decagonal Number or not. This can be checked as:
- If the value of K calculated using the above formula is an integer, then N is a Decagonal Number.
- Else N is not a Decagonal Number.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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