Abstract

The functions and fractal trees problem from HackerRank.

Functions and Fractal Trees#

Overview#

Functions and Fractal Trees | HackerRank

If, like me, you passed Trigonometry the second time you took it in college, you might find this particular challenge to be a bit beyond what one can accomplish solely based on thorough knowledge of shell scripting, and in that case, you might find the list of trigonometric identities and the trigonometric functions handy.

Note

Submissions with the design hard-coded in them, will be rejected.

Example Output 1#

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Task#

Creating a Fractal Tree from Y-shaped branches

This challenge involves the construction of trees, in the form of ASCII Art.

We have to deal with real world constraints, so we cannot keep repeating the pattern infinitely. So, we will provide you a number of iterations, and you need to generate the ASCII version of the Fractal Tree for only those many iterations (or, levels of recursion). A few samples are provided below.

Iteration #1#

In the beginning, we simply create a Y. There are 63 rows and 100 columns in the grid below. The triangle is composed of underscores and ones as shown below. The vertical segment and the slanting segments are both 16 characters in length.

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Iteration #2#

At the top of the left and right branches of the first Y, we now add a pair of Y-shapes, which are half the size of the original Y.

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Input Format#

A single integer, \(N\).

Constraints#

\(N \leq 5\)

Output Format#

The \(N^{th}\) iteration of the Fractal Tree, as shown above. It should be a matrix of 63 rows and 100 columns. (i.e. 6300 printable characters) It should be composed entirely of underscores and ones, in a manner similar to the examples provided. Do not include any extra leading or trailing spaces.

Explanation#

Accomplishing this should require the use of a multi-dimensional array initialized to be a 63x100 rectangle containing exclusively underscores. With the array initialized, a recursive function will be used to implement the Fractal Tree[1] as described in the overview using the input \(N\) as the seed.