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Iterative Letter Combinations of a Phone Number


The goal of creating every possible combination of letters in a phone number is a fascinating issue in the field of algorithms and problem-solving. In addition to requiring a solid understanding of basic programming ideas, this challenge calls for an original method of assigning numbers to letters. The article will examine the iterative process of creating letter combinations for a given phone number, analyze its algorithmic complexities, and comprehend its relevance.

The current issue:

The aim is to generate all possible letter combinations that a typical phone keypad may represent given a string of numbers ranging from 2 to 9. The phone keypad convention is followed when mapping numbers to letters:

2: abc

3: def

4: ghi

5: jkl

6: mno

7: pqrs

8: tuv

9: wxyz

If the input is "23," for instance, the output should contain every possible combination of letters that can be created with "abc" and "def"; in this example, that would be ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].

The Iterative Method:

Taking one digit at a time, the iterative method of solving this problem entails creating letter combinations repeatedly. In essence, it processes each number and adds the matching letters to the preexisting combinations, eventually building up the combinations.

Steps in the Algorithm:


  • To start, create a blank list to hold the combinations that are generated.

Iterate Over Digits:

  • Every digit present in the input string is:
  • Obtain the letters that correspond to the given digit.

Generate Combinations:

  • For every letter that corresponds to the current digit:
  • Add the letter to every combination that already exists.
  • Make changes to the combination list.

Continue with Every Digit:

  • For each digit in the input string, repeat these steps.

Final Outcome:

  • The ultimate outcome is contained in the list of combinations.


  • Let's consider the input "23."
  • Begin with a blank list: combinations = []
  • The related letters for the initial digit, "2," are "abc."
  • Begin the list of combinations by adding the letters "a," "b," and "c."
  • The related letters for the second digit, "3," are "def."
  • Add each letter to every combination that already exists, making the final result ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].
  • The desired result is the list of combinations at the end.



Letter Combinations for "23":

In this C program:

  • The calculateCombinations function is called recursively by the letterCombinations function, which initializes the process and generates all possible combinations.
  • The calculateCombinations function investigates every combination that could be feasible for each digit by going backward.
  • To store the result array and specific combinations, memory is dynamically allocated.
  • After combinations are used, the memory allotted for them can be released using the freeCombinations function.

This program can be modified to accept a variety of inputs, and the printCombinations function makes it simple to see the combinations that are generated.

Significance and Applications:

  • Code Interview Challenges: In technical interviews, questions like phone number letter combinations are frequently asked. They evaluate a candidate's aptitude for using algorithms to work through problems and come up with effective solutions.
  • Applications for Phones: For developers working on applications that require user input, comprehending and putting these techniques into practice is essential. For example, autocomplete or predictive text capabilities frequently need the creation of letter combinations based on numerical input.
  • Thinking Algorithmically: Iteration and combination generation must be approached thoughtfully in order to solve this difficulty. It motivates programmers to think about how to methodically construct solutions piece by piece.
  • Abstraction of Problems: This problem is meant to practice abstracting real-world situations into tasks that can be solved computationally. It is analogous to the process of converting phone numbers, which are numerical inputs, into meaningful textual outputs (letter combinations).

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