Question

Write an application that reads a five-letter word from the user and produces every possible three-letter string that can be derived from the letters of that word. For example, the three-letter words produced from the word "bathe" include "ate," "bat," "bet," "tab," "hat," "the" and "tea."

Short answer

Validate the input is five letters, generate all 3-letter combinations, remove duplicates, and output the unique combinations.

Step-by-step solution

Input Validation

Ensure the user has entered a five-letter word. If the word is not five letters, prompt the user to re-enter a valid word.

Generate Combinations

Use a method to generate all possible combinations of three letters from the five-letter word. This could be done using nested loops or a combinatorial function if available in the programming language being used.

Eliminate Duplicates

Some combinations may be identical if the word contains repeating letters. Remove any duplicate combinations from the list.

Output Results

Display all unique three-letter combinations to the user. Depending on the programming language, this might involve iterating over the list of combinations and printing them to the console.

Key concepts

Input Validation

Ensuring the user's input meets certain criteria is crucial in programming to avoid errors during execution. In the case of generating letter combinations, input validation is the first line of defense against invalid data. The goal here is simple: to confirm that the user has provided a word of exactly five letters, no more and no less.

Consider this scenario: if the application requires a five-letter word to work correctly, but the user inputs a four-letter word or a sentence, the subsequent steps designed to generate letter combinations would not perform as expected. To implement validation effectively, you might use a loop that checks the input's length and continuously prompts for re-entry until the user complies. It's a simple yet powerful way to enforce data integrity before moving forward to more complex operations like generating combinations.

Nested Loops

In computer programming, nested loops are loops placed inside other loops. They're like a Russian doll of repetitions – one loop runs within another, allowing programmers to perform multi-level tasks such as generating combinations of letters from a word.

Let's illustrate nested loops with an example: imagine you have an outer loop that iterates through each letter of the input word. Inside this loop, there's another loop, or two, which also go through the word's letters, selecting an additional letter each time. The result is a set of letter combinations, where each iteration of the innermost loop creates a different combination based on the current position of the outer loops. This process is integral to the exercise at hand, where three-letter strings are to be derived from a five-letter word. Without nested loops, systematically generating these combinations would be a complex and daunting task.

Combinatorial Functions

Moving beyond nested loops, combinatorial functions in programming allow for a more elegant and less error-prone solution to the problem of generating letter combinations. These functions, often found in libraries or built into languages, specifically handle the task of combination and permutation generation.

For example, a combinatorial function could take the five-letter word and the number three as arguments, and then return all possible three-letter combinations. This abstracts away the complexity of manually writing nested loops and directly provides the required list of combinations. Such functions often use algorithms optimized for performance and can simplify the code by removing the need for explicit loop management. When available, they're a preferred method for dealing with combinatorial problems like the one in the original exercise.

Duplicate Elimination

In the realm of combination generation, especially when dealing with words that may have repeating characters, you might end up with identical combinations. Duplicate elimination is thus an essential step to ensure each output is unique.

To undertake this task, you might employ data structures such as sets that inherently disallow duplicates. As the combinatorial function (or nested loops) produces combinations, each new string is added to the set. If a duplicate is encountered, it simply won't be added, as sets maintain only unique elements. This approach also streamlines the final output, as iterating over a set will display only the unique combinations, free from repetitions, and matching what would be expected in true combinatorial problems.