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Leetcode 784. Letter Case Permutation

Problem Statement

Given a string s, you can transform every letter individually to be lowercase or uppercase to create another string. Return a list of all possible strings we could create. You can return the output in any order.

Example:

Input: s = "a1b2"
Output: ["a1b2", "a1B2", "A1b2", "A1B2"]

Clarifying Questions

  1. Can the input string contain only letters and digits?
    • Yes, the string consists of alphanumeric characters (letters and digits).
  2. Do the digits in the input string affect the case permutations?
    • No, the digits remain unchanged in all permutations.
  3. Is there a limit to the length of the input string?
    • The constraints will typically be the normal competitive programming limits, which we can assume the length of the string may be up to (12 \leq \text{length of } s \leq 15).

Strategy

We need to generate all possible permutations of the input string s by toggling each letter between lowercase and uppercase. The digits remain unaffected. We can achieve this through a backtracking approach.

Backtracking Approach

  1. Recursive Function: Define a recursive function that will explore each character in the string.
  2. Base Case: When we reach the end of the string, add the current permutation to the result list.
  3. Decision Making: For each character:
    • If it is a digit, it remains unchanged.
    • If it is a letter, recursively explore both the lowercase and uppercase options.

Code

import java.util.ArrayList;
import java.util.List;

public class LetterCasePermutation {
    public List<String> letterCasePermutation(String s) {
        List<String> result = new ArrayList<>();
        backtrack(s.toCharArray(), 0, result);
        return result;
    }

    private void backtrack(char[] chars, int index, List<String> result) {
        if (index == chars.length) {
            result.add(new String(chars));
            return;
        }
        
        if (Character.isDigit(chars[index])) {
            backtrack(chars, index + 1, result);
        } else {
            // Lowercase branch
            chars[index] = Character.toLowerCase(chars[index]);
            backtrack(chars, index + 1, result);

            // Uppercase branch
            chars[index] = Character.toUpperCase(chars[index]);
            backtrack(chars, index + 1, result);
        }
    }

    public static void main(String[] args) {
        LetterCasePermutation solution = new LetterCasePermutation();
        String input = "a1b2";
        List<String> output = solution.letterCasePermutation(input);
        System.out.println(output);
    }
}

Time Complexity

The time complexity of this approach is (O(2^N)), where (N) is the number of letters in the string s. This is because each letter can be toggled between lowercase and uppercase, resulting in (2^N) possible permutations.

Space Complexity

The space complexity is also (O(2^N)) due to the storage of all permutations in the result list. The recursive call stack would also require space, contributing to the overall space usage.

This solution ensures that all possible permutations are effectively generated and collected.

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