Java Program for Maximum sum rectangle in a 2D matrix | DP-27

Java Program for Maximum height when coins are arranged in a triangle

Last Updated : 05 Dec, 2018

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:

Please refer complete article on Maximum height when coins are arranged in a triangle for more details!

Java Program for Maximum sum rectangle in a 2D matrix | DP-27

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