The Question
Coding

Unique String Permutations with Duplicates

Given a string that may contain duplicate characters (e.g., 'google'), implement an efficient algorithm to generate all unique permutations of the string. The solution should avoid generating duplicate results and optimize for both time and space complexity, explaining how duplicates are handled during the recursion process.
Java
Backtracking
Pruning
Recursion
Array
Questions & Insights

Clarifying Questions

Input Constraints: What is the maximum length of the input string? (Assuming N \le 12 as the number of permutations grows factorially, N!).
Output Format: Should the solution return a list of all unique strings, or just the count of unique permutations? (Assuming a list of strings).
Character Set: Does the string only contain lowercase English letters, or should it support any Unicode character? (Assuming any character).
Duplicates: The word "google" contains duplicate characters ('g' and 'o'). Should the algorithm handle duplicates to ensure the output list contains only unique permutations? (Assuming yes, this is the core of the challenge).
Assumptions:
We need to generate all unique permutations of the input string "google".
The input string may contain duplicate characters.
The order of the output list does not matter, but each permutation must be unique.

Thinking Process

Backtracking with Pruning: To generate permutations, we use a recursive backtracking approach. To handle duplicates without using a Set (which is memory-intensive), we sort the input characters first. This allows us to skip identical characters at the same recursion depth.
Decision Tree: At each level of the recursion, we decide which character to place in the current position. If a character is the same as the previous one and the previous one hasn't been used in this specific path, we skip it to avoid generating the same permutation subtree twice.
State Management: We maintain a boolean[] used array to keep track of which indices of the original sorted array are currently included in the permutation we are building.
Efficiency: Sorting takes O(N \log N), and backtracking takes O(N \cdot N!) in the worst case (no duplicates). With duplicates like in "google", the number of calls is reduced to \frac{N!}{\prod (count_i !)}.
Implementation Breakdown

Problem Set

Functional Requirements:
Input: A string s.
Output: A List<String> containing all unique permutations.
Constraints:
Time Complexity: O(N \cdot N!).
Space Complexity: O(N) for the recursion stack and visited array (excluding the output list).

Approach

Algorithm: Backtracking with Sorting/Pruning.
Data Structure: char[] for processing, boolean[] for state tracking.
Complexity:
Time: O(N \cdot N!) where N is the length of the string.
Space: O(N) auxiliary space for recursion and the used array.

Implementation

Wrap Up

Advanced Topics

Iterative Approach (Next Permutation): Instead of recursion, one can implement the nextPermutation algorithm (similar to std::next_permutation in C++). This approach uses O(1) extra space and generates permutations in lexicographical order.
Space Optimization: If the goal is just to process (e.g., print) permutations rather than store them, the space complexity remains O(N). Storing N! strings in memory will lead to OutOfMemoryError for N > 12.
Parallelization: The backtracking tree can be partitioned. For example, each available character at the first level can be processed by a different thread to speed up generation on multi-core systems.