Python 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.
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# Python3 program to find
# maximum height of arranged
# coin triangle
  
# Returns the square root of n.
# Note that the function 
def squareRoot(n):
   
    # We are using n itself as
        # initial approximation
    # This can definitely be improved 
    x =
    y = 1 
  
    e = 0.000001  # e decides the accuracy level 
    while (x - y > e):
        x = (x + y) / 2
        y = n/x
          
    return
   
  
# Method to find maximum height
# of arrangement of coins
def findMaximumHeight(N):
   
    # calculating portion inside the square root
    n = 1 + 8*
    maxH = (-1 + squareRoot(n)) / 2
    return int(maxH) 
   
  
# Driver code to test above method
N = 12 
print(findMaximumHeight(N))
  
# This code is contributed by
# Smitha Dinesh Semwal

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Output:



4

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




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