LeetCode 17 Solution: Letter Combination of a Phone Number

The LeetCode 17 solution, which tackles the “Letter Combination of a Phone Number” problem, is a popular challenge that tests both beginners and experienced coders. In this blog post, we will break down the solution step-by-step, making the process easy to understand and implement. Whether you’re new to coding or seeking a more efficient approach, this guide will walk you through everything you need to solve this problem confidently.

Understanding the Problem

The problem “Letter Combination of a Phone Number” involves translating a string of digits into all possible letter combinations based on the mapping of numbers to letters on a traditional phone keypad. Each number between 2 and 9 corresponds to a specific set of letters:

• 2 maps to “abc”
• 3 maps to “def”
• 4 maps to “ghi”
• 5 maps to “jkl”
• 6 maps to “mno”
• 7 maps to “pqrs”
• 8 maps to “tuv”
• 9 maps to “wxyz”

For example, if the input is the string "23", we need to generate all possible combinations of letters that can be made from the letters corresponding to 2 (“abc”) and 3 (“def”). The result would be ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].

Constraints to Consider

To develop the solution, it’s important to consider the problem constraints:

• The input string can be between 0 and 4 digits long.
• Only digits between ‘2’ and ‘9’ are considered valid.
• If the input string is empty, the expected output should be an empty list.

Given that the maximum length of the input string is just 4, even brute force methods can work within the problem’s limits. The total number of combinations we would generate in the worst case is (4^4 = 256), which is manageable.

The Backtracking Approach to Solving the Problem

One of the most effective ways to solve this problem is by using a backtracking approach. Backtracking is a common technique used when we need to explore all possible combinations or permutations of a set of elements. In this case, we can think of the solution as exploring all possible “paths” where each path is a combination of letters that corresponds to the digits in the input.

The idea behind backtracking is simple: we try adding one letter at a time for each digit, and once we have a complete combination, we backtrack to try other possible letters. This approach ensures that we explore all valid letter combinations.

Here’s a breakdown of the solution:

• First, we create a dictionary that maps each digit (from 2 to 9) to its corresponding letters.
• Next, we define a recursive function that builds the combinations by processing one digit at a time. For each digit, the function will loop through all the corresponding letters and add them to the current combination.
• Once all digits have been processed, the current combination is complete, and we add it to the final result.
• If the input string is empty, we simply return an empty list as there are no possible combinations.

Python Code for LeetCode 17 Solution

Here’s the Python implementation of the backtracking approach to solve the “Letter Combination of a Phone Number” problem:

def letterCombinations(digits):
    if not digits:
        return []

    phone_map = {
        "2": "abc", "3": "def", "4": "ghi", "5": "jkl",
        "6": "mno", "7": "pqrs", "8": "tuv", "9": "wxyz"
    }

    result = []

    def backtrack(index, current_combination):
        if index == len(digits):
            result.append("".join(current_combination))
            return

        letters = phone_map[digits[index]]
        for letter in letters:
            current_combination.append(letter)
            backtrack(index + 1, current_combination)
            current_combination.pop()

    backtrack(0, [])
    return result

This code starts by checking if the input string is empty. If it is, the function immediately returns an empty list. The phone_map dictionary holds the mapping between digits and their corresponding letters. The backtrack function is where the magic happens—it builds the combinations by recursively exploring all possible letter choices for each digit.

Exploring Edge Cases

There are a few edge cases to be aware of:

1. Empty Input String: If the input is an empty string, the solution should return an empty list since there are no digits to generate combinations from.
2. Single Digit Input: If the input contains just one digit, like "2", the solution will return the list of letters corresponding to that digit. For "2", the output would be ["a", "b", "c"].
3. Handling Multiple Digits: For inputs like "23", the solution will correctly generate all possible combinations of letters.

Time and Space Complexity

The time complexity of this solution is (O(4^n)), where n is the number of digits in the input string. This is because each digit can map to up to 4 letters, and we need to generate all combinations of letters. The space complexity is also (O(4^n)) because we store all possible combinations in a list. Additionally, the recursion uses space proportional to the number of digits, which is (O(n)).

LeetCode 17 Solution: Summary

The “LeetCode 17: Letter Combination of a Phone Number” problem is a great example of how backtracking can be used to efficiently explore combinations. By breaking the problem down into manageable steps, we can use recursion to generate all possible letter combinations for the given digits. With this backtracking approach, you can confidently tackle similar problems that involve generating combinations or permutations.

This solution is optimized for clarity and performance, ensuring that even with the maximum input size, it runs efficiently. If you’re preparing for coding interviews or just looking to improve your algorithmic skills, mastering this type of problem is a great step forward.

Happy Coding!

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Looking for more LeetCode solutions? Stay tuned for upcoming guides on tackling other LeetCode challenges in Python. Whether you’re preparing for technical interviews or aiming to improve your coding skills, exploring a variety of problems will enhance your understanding and proficiency.

You can find this problem on LeedCode, click here.