Program to check if N is a Chiliagon Number Last Updated : 30 Dec, 2022 Comments Improve Suggest changes Like Article Like Report Given an integer N, the task is to check if N is a Chiliagon Number or not. If the number N is a Chiliagon Number then print "Yes" else print "No". Chiliagon Number is class of figurate number. It has 1000 – sided polygon called Chiliagon. The N-th Chiliagon Number counts the 1000 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few Chiliagon Numbers are 1, 1000, 2997, 5992, ... \Examples: Input: N = 1000 Output: Yes Explanation: Second chiliagon number is 1000Input: 35 Output: No Approach: The Kth term of the Chiliagon Number is given as K^{th} Term = \frac{998*K^{2} - 996*K}{2} As we have to check that the given number can be expressed as a Chiliagon Number or not. This can be checked as follows: => N = \frac{998*K^{2} - 996*K}{2} => K = \frac{996 + \sqrt{7984*N + 992016}}{1996} 3.If the value of K calculated using the above formula is an integer, then N is a Chiliagon Number. 4. Else N is not a Chiliagon Number. Below is the implementation of the above approach: C++ // C++ for the above approach #include <bits/stdc++.h> using namespace std; // Function to check that if N is // Chiliagon Number or not bool is_Chiliagon(int N) { float n = (996 + sqrt(7984 * N + 992016)) / 1996; // Condition to check if N is a // Chiliagon Number return (n - (int)n) == 0; } // Driver Code int main() { // Given Number int N = 1000; // Function call if (is_Chiliagon(N)) { cout << "Yes"; } else { cout << "No"; } return 0; } Java // Java program for the above approach class GFG{ // Function to check that if N is // Chiliagon Number or not static boolean is_Chiliagon(int N) { float n = (float)(996 + Math.sqrt(7984 * N + 992016)) / 1996; // Condition to check if N is a // Chiliagon Number return (n - (int) n) == 0; } // Driver Code public static void main(String s[]) { // Given Number int N = 1000; // Function call if (is_Chiliagon(N)) { System.out.print("Yes"); } else { System.out.print("No"); } } } // This code is contributed by rutvik_56 Python3 # Python3 for the above approach import math; # Function to check that if N is # Chiliagon Number or not def is_Chiliagon(N): n = (996 + math.sqrt(7984 * N + 992016)) // 1996; # Condition to check if N is a # Chiliagon Number return (n - int(n)) == 0; # Driver Code # Given Number N = 1000; # Function call if (is_Chiliagon(N)): print("Yes"); else: print("No"); # This code is contributed by Code_Mech C# // C# program for the above approach using System; class GFG{ // Function to check that if N is // Chiliagon Number or not static bool is_Chiliagon(int N) { float n = (float)(996 + Math.Sqrt(7984 * N + 992016)) / 1996; // Condition to check if N is a // Chiliagon Number return (n - (int) n) == 0; } // Driver Code public static void Main() { // Given Number int N = 1000; // Function call if (is_Chiliagon(N)) { Console.Write("Yes"); } else { Console.Write("No"); } } } // This code is contributed by Code_Mech JavaScript <script> // Javascript for the above approach // Function to check that if N is // Chiliagon Number or not function is_Chiliagon(N) { let n = (996 + Math.sqrt(7984 * N + 992016)) / 1996; // Condition to check if N is a // Chiliagon Number return (n - Math.floor(n)) == 0; } // Driver Code // Given Number let N = 1000; // Function call if (is_Chiliagon(N)) { document.write("Yes"); } else { document.write("No"); } // This code is contributed by Mayank Tyagi </script> Output: Yes Time Complexity: O(logN)Auxiliary Space: O(1) Comment More infoAdvertise with us Next Article Program to check if N is a Chiliagon Number spp____ Follow Improve Article Tags : Mathematical DSA series Practice Tags : Mathematicalseries Similar Reads DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. 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