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

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

The problem is to find the maximum height h of a triangle formed by arranging n coins in consecutive rows where the first row contains a single coin, the second row contains two coins, the third row contains three coins, and so on.

For a triangle with height h, the total number of coins used will be the sum of the first h natural numbers, which is given by the formula:

n=2h(h+1)​

Given n coins, we want to find the maximum h such that:

n≥2h(h+1)​

Let's create a Python program to solve this:

def max_triangle_height(n): """ Given n coins, find the maximum height of the triangle that can be formed. """ # Initialize height of the triangle h = 0 # Use a while loop to keep adding coins to each level of the triangle while n >= h + 1: h += 1 # Increase the height n -= h # Deduct the coins used for the current height return h # Test the function n = 10 # Number of coins height = max_triangle_height(n) print(f"Maximum height of triangle with {n} coins is: {height}")

Explanation:

  1. Start with a height of 0.
  2. For each height increment, check if we have enough coins to form a complete row of that height.
  3. Increase the height by 1 and deduct the coins used for the current height from n.
  4. Continue until you don't have enough coins to form a complete row.

The function will return the maximum height of the triangle that can be formed using n coins.

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