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, …
Examples:
Input: N = 10
Output: Yes
Explanation:
Second decagonal number is 10.
Input: N = 30
Output: No
Approach:
- 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:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to check if N is a// Decagonal Numberbool isdecagonal(int N){ float n = (3 + sqrt(16 * N + 9)) / 8; // Condition to check if the // number is a decagonal number return (n - (int)n) == 0;}// Driver Codeint main(){ // Given Number int N = 10; // Function call if (isdecagonal(N)) { cout << "Yes"; } else { cout << "No"; } return 0;} |
Java
// Java program for the above approach import java.lang.Math;class GFG{ // Function to check if N is a // decagonal number public static boolean isdecagonal(int N) { double n = (3 + Math.sqrt(16 * N + 9)) / 8; // Condition to check if the // number is a decagonal number return (n - (int)n) == 0; } // Driver code public static void main(String[] args){ // Given number int N = 10; // Function call if (isdecagonal(N)) { System.out.println("Yes"); } else { System.out.println("No"); } }}// This code is contributed by divyeshrabadiya07 |
Python3
# Python3 program for the above approachimport math# Function to check if N is a# decagonal numberdef isdecagonal(N): n = (3 + math.sqrt(16 * N + 9)) / 8 # Condition to check if the # number is a decagonal number return (n - int(n)) == 0 # Driver Codeif __name__=='__main__': # Given number N = 10 # Function Call if isdecagonal(N): print('Yes') else: print('No')# This code is contributed by rutvik_56 |
C#
// C# program for the above approachusing System;class GFG{ // Function to check if N // is a decagonal Numberstatic bool isdecagonal(int N){ double n = (3 + Math.Sqrt(16 * N + 9)) / 8; // Condition to check if the // number is a decagonal number return (n - (int)n) == 0;} // Driver Codestatic public void Main (){ // Given Number int N = 10; // Function call if (isdecagonal(N)) { Console.Write("Yes"); } else { Console.Write("No"); }}}// This code is contributed by ShubhamCoder |
Javascript
<script>// javascript program for the above approach// Function to check if N is a// Decagonal Numberfunction isdecagonal( N){ let n = (3 + Math.sqrt(16 * N + 9)) / 8; // Condition to check if the // number is a decagonal number return (n - parseInt(n)) == 0;}// Driver Code // Given Number let N = 10; // Function Call if (isdecagonal(N)) { document.write( "Yes"); } else { document.write( "No"); }// This code contributed by gauravrajput1 </script> |
Yes
Time Complexity: O(logN) since sqrt function is being used
Auxiliary Space: O(1)
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