Hexagonal Number
Given an integer n, the task is to find the nth hexagonal number . The nth hexagonal number Hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots when the hexagons are overlaid so that they share one vertex.{Source : wiki}
Input: n = 2 Output: 6 Input: n = 5 Output: 45 Input: n = 7 Output: 91
In general, a polygonal number (triangular number, square number, etc) is a number represented as dots or pebbles arranged in the shape of a regular polygon. The first few pentagonal numbers are 1, 5, 12, etc.
If s is the number of sides in a polygon, the formula for the nth s-gonal number P (s, n) is
nth s-gonal number P(s, n) = (s - 2)n(n-1)/2 + n If we put s = 6, we get n'th Hexagonal number Hn = 2(n*n)-n = n(2n - 1)
C++
// C++ program for above approach #include<bits/stdc++.h> using namespace std; // Finding the nth Hexagonal Number int hexagonalNum( int n){ return n*(2*n - 1); } // Driver program to test above function int main(){ int n = 10; cout << "10th Hexagonal Number is " << hexagonalNum(n) << endl; return 0; } // The code is contributed by Gautam goel (gautamgoel962) |
C
// C program for above approach #include <stdio.h> #include <stdlib.h> // Finding the nth Hexagonal Number int hexagonalNum( int n) { return n*(2*n - 1); } // Driver program to test above function int main() { int n = 10; printf ( "10th Hexagonal Number is = %d" , hexagonalNum(n)); return 0; } |
Java
// Java program for above approach class Hexagonal { int hexagonalNum( int n) { return n*( 2 *n - 1 ); } } public class BeginnerCode { public static void main(String[] args) { Hexagonal obj = new Hexagonal(); int n = 10 ; System.out.printf( "10th Hexagonal number is = " + obj.hexagonalNum(n)); } } |
Python3
# Python program for finding Hexagonal numbers def hexagonalNum( n ): return n * ( 2 * n - 1 ) # Driver code n = 10 print ( "10th Hexagonal Number is = " , hexagonalNum(n)) |
C#
// C# program for above approach using System; class GFG { static int hexagonalNum( int n) { return n * (2 * n - 1); } public static void Main() { int n = 10; Console.WriteLine( "10th Hexagonal" + " number is = " + hexagonalNum(n)); } } // This code is contributed by vt_m. |
PHP
<?php // PHP program for above approach // Finding the nth Hexagonal Number function hexagonalNum( $n ) { return $n * (2 * $n - 1); } // Driver program to test above function $n = 10; echo ( "10th Hexagonal Number is " . hexagonalNum( $n )); // This code is contributed by Ajit. ?> |
Javascript
<script> // Javascript program for above approach // centered pentadecagonal function function hexagonalNum(n) { return n * (2 * n - 1); } // Driver Code var n = 10; document.write( "10th Hexagonal number is = " + hexagonalNum(n)); // This code is contributed by Kirti </script> |
Output:
10th Hexagonal Number is = 190
Time complexity: O(1) since performing constant operations
Auxiliary space: O(1) since it is using constant variables
Reference:https://en.wikipedia.org/wiki/Hexagonal_number
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