Number of coloured 0’s in an N-level hexagon
Given an integer N, the task is to find the count of coloured 0s in an N-level hexagon when the 0s are coloured in the following way:
Examples:
Input: N = 2
Output: 5
Input: N = 3
Output: 12
Approach: For the values of N = 1, 2, 3, … it can be observed that a series will be formed as 1, 5, 12, 22, 35, …. It’s a difference series where differences are in AP as 4, 7, 10, 13, ….
Therefore the Nth term of will be 1 + {4 + 7 + 10 +13 +…..(n – 1) terms}
= 1 + (n – 1) * (2 * 4 + (n – 1 – 1) * 3) / 2
= 1 + (n – 1) * (8 + (n – 2) * 3) / 2
= 1 + (n – 1) * (8 + 3n – 6) / 2
= 1 + (n – 1) * (3n + 2) / 2
= n * (3 * n – 1) / 2
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to return the count of // coloured 0s in an n-level hexagon int count( int n) { return n * (3 * n - 1) / 2; } // Driver code int main() { int n = 3; cout << count(n); return 0; } |
Java
// Java implementation of the approach class GFG { // Function to return the count of // coloured 0s in an n-level hexagon static int count( int n) { return n * ( 3 * n - 1 ) / 2 ; } // Driver code public static void main(String[] args) { int n = 3 ; System.out.println(count(n)); } } // This code is contributed by Code_Mech |
Python3
# Python3 implementation of the approach # Function to return the count of # coloured 0s in an n-level hexagon def count(n) : return n * ( 3 * n - 1 ) / / 2 ; # Driver code if __name__ = = "__main__" : n = 3 ; print (count(n)); # This code is contributed by AnkitRai01 |
C#
// C# implementation of the approach using System; class GFG { // Function to return the count of // coloured 0s in an n-level hexagon static int count( int n) { return n * (3 * n - 1) / 2; } // Driver code public static void Main(String[] args) { int n = 3; Console.WriteLine(count(n)); } } // This code is contributed by 29AjayKumar |
Javascript
<script> // Javascript implementation of the approach // Function to return the count of // coloured 0s in an n-level hexagon function count(n) { return parseInt(n * (3 * n - 1) / 2); } // Driver code var n = 3; document.write(count(n)); </script> |
Output:
12
Time Complexity: O(1)
Auxiliary Space: O(1)
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