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.

`# 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 ` `=` `n ` ` ` `y ` `=` `1` ` ` ` ` `e ` `=` `0.000001` `# e decides the accuracy level ` ` ` `while` `(x ` `-` `y > e):` ` ` `x ` `=` `(x ` `+` `y) ` `/` `2` ` ` `y ` `=` `n` `/` `x` ` ` ` ` `return` `x ` ` ` ` ` `# Method to find maximum height` `# of arrangement of coins` `def` `findMaximumHeight(N):` ` ` ` ` `# calculating portion inside the square root` ` ` `n ` `=` `1` `+` `8` `*` `N ` ` ` `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` |

**Output:**

4

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

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