Table of Contents
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).
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