Question

Suppose the function \(f\) expects a string as its input and returns a new string as its output made by removing odd-position letters from the input string. What is the result returned by the function \(f(f\) ("programming"))?

Short answer

The result is "gm".

Step-by-step solution

Understand the Function f

The function \(f\) takes a string as input and removes characters that are in odd positions (considering the first character position as 1, which is odd). The remaining characters, which are initially in even positions, are returned as a new string.

Apply Function f on "programming"

Write the characters of "programming" and identify their positions: \(p_1, r_2, o_3, g_4, r_5, a_6, m_7, m_8, i_9, n_{10}, g_{11}\). Remove odd-positioned characters \(p, o, r, m, i, g\). The remaining characters are \("rgamn\)."

Apply Function f Again on Result

Take the string \("rgamn\)" and apply function \(f\) again. List positions: \(r_1, g_2, a_3, m_4, n_5\). Remove odd-positioned \(r, a, n\). The result is \("gm"\).

Key concepts

Function Application

The concept of function application is essential in computer science and mathematics. It represents the process of applying a function to its argument(s) to produce a result. In this specific problem, we are dealing with a function, denoted as \( f \), which operates on strings.

Here's a simple breakdown of function application with regard to this problem:

• A function \( f \) is defined to take an input - in this case, a string.
• The function processes this input by implementing a specific criterion - removing odd-positioned characters.
• Once the criterion is applied, the function returns an output, a new string, with only the characters at even positions retained.

In functional programming, such applications can be composed to achieve more complex operations by chaining functions together. Like in this exercise, applying \( f(f(\text{"programming"})) \), where the function is applied twice, first producing the result \("rgamn"\) and then \("gm"\). It showcases how functions can build on each other to refine outputs incrementally.

Character Removal

String manipulation often involves tasks such as inserting, replacing, or removing characters to transform strings. In this exercise, character removal is the central focus.

The function \( f \) is tasked with removing characters from a string based on their positional index, specifically targeting odd-positioned characters:

• Identify the positions: Start indexing from 1 as the first position is considered odd.
• Filter characters: Scan through the input string and omit characters that are in odd indices.

This method is a common technique in various algorithms, reducing the string to a simpler form or isolating desired elements.

By systematically eliminating characters based on conditions like position, it becomes possible to tailor string data precisely. This exercise particularly helps in understanding how strategic character removal transforms data outputs.

Positions in Strings

Understanding the positions in strings is crucial when it comes to manipulating them effectively. Strings in programming are a sequence of characters, each with its own index.

In the function \( f \) described in this problem:

• The indices start at 1 for human-friendliness, implying the first character is in an odd position.
• Every alternate position starting from 1 (i.e., 1, 3, 5, ...) is considered an odd position.

When the function \( f \) processes the string \("programming"\), characters at positions 1, 3, 5, 7, 9, and 11 are identified as odd and are thus removed.

Accurate index management is vital for string operations. Misinterpretation of positions can lead to logical errors, such as removing or retaining incorrect characters. This exercise highlights the importance of correct positioning in string manipulation scenarios, pivotal in both small-scale coding tasks and in crafting robust data-processing pipelines.