Given an integer N, the task is to check if it is a Heptadecagonal Number or not. If the number N is an Heptadecagonal Number then print “Yes” else print “No”.
Heptadecagonal Number is class of figurate number. It has 17-sided polygon called heptadecagon. The N-th heptadecagonal number counts the seventeen number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptadecagonal numbers are 1, 17, 48, 94, 155, 231…
Examples:
Input: N = 17
Output: Yes
Explanation:
Second heptadecagonal number is 17.Input: N = 30
Output: No
Approach:
1. The Kth term of the heptadecagonal number is given as
2. As we have to check that the given number can be expressed as a heptadecagonal 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 Heptadecagonal Number.
4. Else N is not a Heptadecagonal Number.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to check if the number N// is a heptadecagonal numberbool isheptadecagonal(int N){ float n = (13 + sqrt(120 * N + 169)) / 30; // Condition to check if number N // is a heptadecagonal number return (n - (int)n) == 0;}// Driver Codeint main(){ // Given Number int N = 17; // Function call if (isheptadecagonal(N)) { cout << "Yes"; } else { cout << "No"; } return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{// Function to check if the number N// is a heptadecagonal numberstatic boolean isheptadecagonal(int N){ float n = (float) ((13 + Math.sqrt(120 * N + 169)) / 30); // Condition to check if number N // is a heptadecagonal number return (n - (int)n) == 0;}// Driver Codepublic static void main(String[] args){ // Given Number int N = 17; // Function call if (isheptadecagonal(N)) { System.out.print("Yes"); } else { System.out.print("No"); }}}// This code is contributed by Amit Katiyar |
Python3
# Python3 program for the above approach import numpy as np# Function to check if the number N # is a heptadecagonal number def isheptadecagonal(N): n = (13 + np.sqrt(120 * N + 169)) / 30 # Condition to check if number N # is a heptadecagonal number return (n - int(n)) == 0# Driver Code N = 17# Function call if (isheptadecagonal(N)): print("Yes") else: print("No") # This code is contributed by PratikBasu |
C#
// C# program for the above approachusing System;class GFG{// Function to check if the number N// is a heptadecagonal numberstatic bool isheptadecagonal(int N){ float n = (float) ((13 + Math.Sqrt(120 * N + 169)) / 30); // Condition to check if number N // is a heptadecagonal number return (n - (int)n) == 0;}// Driver Codepublic static void Main(string[] args){ // Given Number int N = 17; // Function call if (isheptadecagonal(N)) { Console.Write("Yes"); } else { Console.Write("No"); }}}// This code is contributed by rutvik_56 |
Javascript
<script>// Javascript program for the above approach// Function to check if the number N// is a heptadecagonal numberfunction isheptadecagonal(N){ let n = (13 + Math.sqrt(120 * N + 169)) / 30; // Condition to check if number N // is a heptadecagonal number return (n - parseInt(n)) == 0;}// Driver Code// Given Numberlet N = 17;// Function callif (isheptadecagonal(N)) { document.write("Yes");}else { document.write("No");}// This code is contributed by subham348.</script> |
Yes
Time Complexity: O(logN) because inbuilt sqrt function has been used
Auxiliary Space: O(1)
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