How do you solve Letter Combinations of a Phone Number on LeetCode?

Letter Combinations of a Phone Number (LeetCode #17) can be solved using Brute Force or Optimal Solution (Backtracking). The optimal approach is Optimal Solution (Backtracking) with O(3^n * 4^m) time complexity and O(n) space complexity. Key insight: Recognizing that each digit corresponds to a fixed set of letters allows us to use a mapping structure, which simplifies the problem significantly.

What is the brute force solution for Letter Combinations of a Phone Number?

The brute force approach for Letter Combinations of a Phone Number is Brute Force, with O(3^n * 4^m) time complexity and O(n) space complexity. The brute force approach generates all possible combinations of letters for the given digits by treating each digit as an independent choice. We can use recursion to explore all possibilities, similar to how we might explore all paths in a maze. The optimal Optimal Solution (Backtracking) approach improves this to O(3^n * 4^m).

What algorithm or data structure is used to solve Letter Combinations of a Phone Number?

Letter Combinations of a Phone Number uses the following concepts: Hash Table, String, Backtracking. The recommended patterns to study are: Hash Map, Array, Two Pointers.

What are the interview tips for Letter Combinations of a Phone Number?

When you first see this problem, clarify the mapping of digits to letters and ensure you understand the constraints. Communicate your thought process clearly as you outline your approach, especially how you plan to handle combinations. Mention edge cases, such as an empty input string or strings with only one digit, to show your awareness of potential pitfalls.

What are common mistakes when solving Letter Combinations of a Phone Number?

Students often forget to handle the base case for recursion, which can lead to infinite loops or stack overflow errors. Not properly managing the path during backtracking, leading to incorrect combinations being generated.

#17

Letter Combinations of a Phone Number

Medium

Hash TableStringBacktrackingHash MapArrayTwo Pointers

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution (Backtracking)★
Time	O(3^n * 4^m)	O(3^n * 4^m)
Space	O(n)	O(n)

💡

Intuition

Time O(3^n * 4^m)Space O(n)

The optimal approach uses backtracking to efficiently explore all combinations of letters. This method allows us to build combinations incrementally and backtrack when we reach the end of a combination, ensuring we only store valid combinations.

⚙️

Algorithm

3 steps

1Step 1: Create a mapping of digits to their corresponding letters.
2Step 2: Define a backtracking function that builds combinations recursively.
3Step 3: Use a list to collect valid combinations and return it after exploring all possibilities.

solution.py28 lines

1# Full working Python code with comments
2
3def letter_combinations(digits):
4    if not digits:
5        return []
6
7    digit_to_letters = {
8        '2': 'abc', '3': 'def', '4': 'ghi', '5': 'jkl',
9        '6': 'mno', '7': 'pqrs', '8': 'tuv', '9': 'wxyz'
10    }
11
12    combinations = []
13
14    def backtrack(index, path):
15        if index == len(digits):
16            combinations.append(''.join(path))
17            return
18        letters = digit_to_letters[digits[index]]
19        for letter in letters:
20            path.append(letter)
21            backtrack(index + 1, path)
22            path.pop()
23
24    backtrack(0, [])
25    return combinations
26
27# Example usage
28print(letter_combinations('23'))

ℹ

Complexity note: The time complexity is similar to the brute force approach, but with a more structured way of generating combinations, making it efficient in terms of memory usage and clarity.

1Recognizing that each digit corresponds to a fixed set of letters allows us to use a mapping structure, which simplifies the problem significantly.
2Understanding that backtracking can be used to explore all combinations incrementally helps in efficiently generating the required outputs.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.