Java Program for Maximum height when coins are arranged in a triangle
We have N coins which need to arrange in form of a triangle, i.e. first row will have 1 coin, second row will have 2 coins and so on, we need to tell maximum height which we can achieve by using these N coins.
Examples:
Input : N = 7 Output : 3 Maximum height will be 3, putting 1, 2 and then 3 coins. It is not possible to use 1 coin left. Input : N = 12 Output : 4 Maximum height will be 4, putting 1, 2, 3 and 4 coins, it is not possible to make height as 5, because that will require 15 coins.
// Java program to find maximum height // of arranged coin triangle class GFG { /* Returns the square root of n. Note that the function */ static float squareRoot( float n) { /* We are using n itself as initial approximation.This can definitely be improved */ float x = n; float y = 1 ; // e decides the accuracy level float e = 0 .000001f; while (x - y > e) { x = (x + y) / 2 ; y = n / x; } return x; } // Method to find maximum height // of arrangement of coins static int findMaximumHeight( int N) { // calculating portion inside // the square root int n = 1 + 8 * N; int maxH = ( int )(- 1 + squareRoot(n)) / 2 ; return maxH; } // Driver code public static void main(String[] args) { int N = 12 ; System.out.print(findMaximumHeight(N)); } } // This code is contributed by Anant Agarwal. |
Output:
4
Please refer complete article on Maximum height when coins are arranged in a triangle for more details!
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