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# Program to find the maximum height when coins are arranged in triangle using Python

by | Aug 8, 2021 | Python Programs

Home » Python » Python Programs » Program to find the maximum height when coins are arranged in triangle using Python

## Introduction

Given N number of coins, the task is to construct a triangle of maximum height H and print the max height. ## Program

```def sq_root(val):

n = val

m = 1

# Accuracy

e = 0.000001

while (n - m > e):

n = (n + m) / 2

m = val/n

return n
def find(ip_num)

val = 1 + 8*ip_num

# Find max height and return

maxHeight = int((-1 + sq_root(val)) / 2)

print("The maximum height is: ",maxHeight)

ip_num = int(input("Enter the number of coins: "))

find(ip_num)```

## Output ## Explanation

Approach:

• Relation between number of coins N and height H : H2 + H – 2*N <= 0 (ignoring negative root). Therefore, the maximum height H obtained by formula: (-1 + √(1+8N) )/2.
• To solve √(1+8N), we have used Babylonian method (used in function sq_root).

## Author

• A Full Stack Developer with 10+ years of experience in technical content creation.

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