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Split a String Into the Max Number of Unique Substrings

Difficulty: Medium

Problem Description

Given a string s, return the maximum number of unique substrings that the given string can be split into. You can split string s into any list of non-empty substrings, where the concatenation of the substrings forms the original string. However, you must split the substrings such that all of them are unique. A substring is a contiguous sequence of characters within a string.

Key Insights

  • The problem requires generating all possible substrings of a given string.
  • We need to keep track of unique substrings to maximize the count.
  • A backtracking approach can be utilized to explore all split possibilities.
  • Hash tables (or sets) can help maintain uniqueness and allow for efficient lookups.

Space and Time Complexity

Time Complexity: O(2^n) - In the worst case, we may explore every possible way to split the string. Space Complexity: O(n) - Space used for storing substrings in a set during the process.

Solution

To solve this problem, we will use a backtracking approach. We will iterate through the string and generate all possible substrings. At each step, we will check if the substring is unique by using a hash set. If it is unique, we will add it to the set and recursively call the function to continue splitting the remaining string. If we reach the end of the string, we will update our maximum count of unique substrings found. This approach efficiently manages uniqueness and explores all possible splits.

Code Solutions

def maxUniqueSplit(s: str) -> int:
    def backtrack(start: int, seen: set) -> int:
        if start == len(s):
            return len(seen)
        
        max_count = 0
        for end in range(start + 1, len(s) + 1):
            substring = s[start:end]
            if substring not in seen:
                seen.add(substring)
                max_count = max(max_count, backtrack(end, seen))
                seen.remove(substring)  # backtrack
        return max_count

    return backtrack(0, set())
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