Split a String Into the Max Number of Unique Substrings

Split a String Into the Max Number of Unique Substrings

What is this problem about?

The Split a String Into the Max Number of Unique Substrings interview question is significantly more challenging than the previous one. Here, the goal is to split a string into the maximum number of non-empty substrings such that every substring in the split is unique. This means you cannot have the same substring appearing twice in your final collection.

Why is this asked in interviews?

This Split a String Into the Max Number of Unique Substrings coding problem is frequently asked by Microsoft and Bloomberg because it requires Backtracking. Unlike the "Balanced Strings" problem, a greedy approach does not work here. A choice made early on might prevent a much better split later. It tests a candidate's ability to explore a decision tree and prune paths that don't lead to a better solution.

Algorithmic pattern used

The Backtracking interview pattern combined with a Hash Table (Set) is the standard approach.

1. Start at the beginning of the string.
2. Try every possible prefix as a substring.
3. If the prefix is not in your "seen" set, add it and move recursively to the rest of the string.
4. If it's already "seen," you cannot use it; try a longer prefix.
5. After the recursive call returns, "backtrack" by removing the substring from the set to explore other possibilities.
6. Keep track of the maximum number of unique substrings found across all paths.

Example explanation

String: abab

• Choice 1: "a", then "b", then "ab". (3 unique substrings: {"a", "b", "ab"})
• Choice 2: "ab", then "a", then "b". (3 unique substrings: {"ab", "a", "b"})
• Choice 3: "aba", then "b". (2 unique substrings: {"aba", "b"})
• Choice 4: "a", then "bab". (2 unique substrings: {"a", "bab"}) Max result: 3.

Common mistakes candidates make

• Greedy Approach: Trying to take the shortest possible unique substring at each step, which can lead to a sub-optimal global result.
• Missing the Base Case: Not correctly handling the end of the string in the recursion.
• Forget to Backtrack: Adding substrings to the set but failing to remove them when the recursion returns, corrupting subsequent searches.
• Efficiency: Not pruning the search when the remaining characters are too few to beat the current maximum result.

Interview preparation tip

When you see a problem asking for the "maximum number" where early choices affect later possibilities, and the input size is relatively small (like string length < 20), it's a huge hint that Backtracking is the intended solution. Practice implementing backtracking with a Set to keep track of used items efficiently.