Question

(Telephone-Number Word Generator) Standard telephone keypads contain the digits zero through nine. The numbers two through nine each have three letters associated with them (Fig. 14.27 ). Many people find it difficult to memorize phone numbers, so they use the correspondence between digits and letters to develop seven-letter words that correspond to their phone numbers. For example, a person whose telephone number is \(686-2377\) might use the correspondence indicated in Fig. 14.27 to develop the seven-letter word "NUMBERS." Every seven-letter word corresponds to exactly one seven-digit telephone number. A restaurant wishing to increase its takeout business could surely do so with the number \(825-3688\) (i.e., "TAKEOUT"). Every seven-letter phone number corresponds to many different seven-letter words. Unfortunately, most of these words represent unrecognizable juxtapositions of letters. It is possible, however, that the owner of a barbershop would be pleased to know that the shop's telephone number, \(424-7288,\) corresponds to "HAIRCUT." The owner of a liquor store would, no doubt, be delighted to find that the store's number, \(233-7226,\) corresponds to "BEERCAN." A veterinarian with the phone number \(738-2273\) would be pleased to know that the number corresponds to the letters "PETCARE." An automotive dealership would be pleased to know that the dealership number, \(639-2277,\) corresponds to "NEWCARS." Write a program that, given a seven-digit number, uses a Printstream object to write to a file every possible seven-letter word combination corresponding to that number. There are \(2,187\left(3^{7}\right)\) such combinations. Avoid phone numbers with the digits 0 and 1

Short answer

Program reads a valid 7-digit number, generates all 2,187 combinations, and writes them to a file.

Step-by-step solution

Identify the Correspondence

First, we need to understand what letters correspond to each digit on a telephone keypad. Typically, the mapping on a standard telephone keypad is: - 2: A, B, C - 3: D, E, F - 4: G, H, I - 5: J, K, L - 6: M, N, O - 7: P, Q, R, S - 8: T, U, V - 9: W, X, Y, Z. Digits 0 and 1 are not associated with any letters and should be avoided.

Read and Validate Input

Read the seven-digit telephone number input from the user. Validate that it does not contain the digits 0 or 1 to ensure all digits have corresponding letters, as these digits do not map to any letters on the telephone keypad.

Generate All Combinations

For the given valid seven-digit number, use a recursive algorithm or iterative loops to generate all possible combinations of letters. This involves using a nested loop structure (or a recursive function) to iterate through each letter corresponding to each digit of the number. There are a total of \(3^7 = 2,187\) possible combinations.

Output Results to File

Use a PrintStream object in your program to write each generated seven-letter combination to a file. Ensure that each combination is formatted as a word and write one word per line in the file for easy readability.

Key concepts

Letter-Digit Correspondence

Understanding the letter-digit correspondence on a telephone keypad is essential for generating meaningful word representations of phone numbers. On a standard keypad:

• 2 corresponds to A, B, C,
• 3 corresponds to D, E, F,
• 4 corresponds to G, H, I,
• 5 corresponds to J, K, L,
• 6 corresponds to M, N, O,
• 7 corresponds to P, Q, R, S,
• 8 corresponds to T, U, V,
• 9 corresponds to W, X, Y, Z.

In this context, numbers 0 and 1 are excluded as they lack corresponding letters. These mappings are used by the program to translate each digit of a given telephone number into letters and form word combinations. Ensuring a solid grasp of this concept is crucial for developing an effective generator.

Recursive Algorithm

A recursive algorithm is a method of solving problems where the function calls itself as part of its solution process. In the case of the Telephone-Number Word Generator, recursion can help explicitly explore all possible letter combinations. The concept here is simple: for each digit in the phone number, select a letter and recursively proceed to the next digit, exploring all possible letter combinations for subsequent digits. Eventually, the recursive function will generate and return a complete word each time it reaches the last digit in the sequence. This approach is particularly effective in handling the extensive 2,187 letter combinations required to represent a seven-digit phone number.

Program Output to File

A crucial part of the Telephone-Number Word Generator is its ability to save or output the results to a file. By writing the generated seven-letter words to a file, the program makes it easier for users to review and use these combinations. To achieve this, the program typically employs a PrintStream object, which is part of Java's standard library for handling input and output tasks. Each combination is formatted as a word and written to the file one line at a time. This method of output ensures that users have a persistent, easily-accessible record of all possible word combinations. It is not only convenient but also ensures that no potential word is inadvertently overlooked.

Input Validation

Input validation is a critical step to ensure that the provided telephone number is suitable for processing. For the Telephone-Number Word Generator, the input must be a seven-digit number excluding any instances of the digits 0 and 1. These digits do not map to any letters, making them invalid for the purpose of generating letter combinations. To validate the input effectively, the program needs to:

• Check the length of the input to confirm it is seven digits long.
• Ensure that every digit is between 2 to 9.

If the input does not meet these criteria, the program should prompt the user to provide a new, valid number. Proper input validation not only prevents processing errors but also ensures that the program produces meaningful word combinations.