Longest Uncommon Subsequence I

Longest Uncommon Subsequence I

What is this problem about?

The Longest Uncommon Subsequence I is a famous "trick" question. You are given two strings, a and b. You need to find the length of the longest uncommon subsequence between them. An uncommon subsequence is defined as a sequence of characters that is a subsequence of one string but not the other. If no such sequence exists, you return -1.

Why is this asked in interviews?

This problem is a brainteaser. Interviewers ask it to test a candidate's analytical thinking and to see if they will blindly jump into writing a massive Dynamic Programming algorithm without stopping to understand the core logic. It evaluates whether you can step back, analyze the constraints, and realize that a mathematically simple $O(1)$ or $O(N)$ logical check solves the entire problem.

Algorithmic pattern used

There is no complex algorithmic pattern here; it relies purely on Logical Deduction. Let's analyze the strings:

1. If string a is identical to string b (e.g., a = "abc", b = "abc"), then every subsequence of a is also a subsequence of b. It is impossible to find an uncommon one. Return -1.
2. If the strings are different, the longest possible sequence unique to one string is simply the longest string itself! If a = "abcd" and b = "abc", the string "abcd" cannot be a subsequence of "abc" because it is too long. Therefore, the longer string is the answer.

Example explanation

Example 1: a = "aba", b = "cdc" Are they equal? No. What is the length of the longer string? Both are length 3. Since they are different, the entire string "aba" is not a subsequence of "cdc". Thus, the longest uncommon subsequence is 3.

Example 2: a = "aaa", b = "aaa" Are they equal? Yes. They are exactly the same. No uncommon subsequence can exist. Return -1.

Example 3: a = "abcd", b = "a" Are they equal? No. The length of a is 4, length of b is 1. The string "abcd" is definitely not a subsequence of "a". Max length is 4.

Common mistakes candidates make

The absolute most common mistake is treating this like the "Longest Common Subsequence" problem. Candidates will spend 20 minutes writing out a 2D DP matrix to find overlapping characters, totally overengineering the solution and missing the elegant logic trap. The interviewer wants to see you write the 3-line solution, not a 30-line DP matrix.

Interview preparation tip

When faced with the Longest Uncommon Subsequence I interview question, always read the problem definitions carefully. Words like "Uncommon Subsequence" sound like standard algorithms, but if you evaluate edge cases (e.g., strings of different lengths), the logic unravels beautifully. Always ask yourself: "Is there a mathematical or logical shortcut?" before typing out a DP grid.