String Compression II

String Compression II

What is this problem about?

The String Compression II interview question is a challenging problem that focuses on finding the minimum length of a run-length encoded string after removing at most a certain number of characters. In run-length encoding, a string is represented by characters followed by the number of times they repeat consecutively (if the count is greater than one). For example, "aaabcc" becomes "a3bc2". The goal is to determine the optimal characters to delete from the original string so that the compressed version of the remaining string is as short as possible. This requires balancing the removal of characters that contribute most to the compressed length.

Why is this asked in interviews?

Companies like Toptal, Microsoft, and Amazon ask this question because it tests a candidate's ability to handle complex string manipulation combined with optimization. It is not a straightforward greedy problem; simply removing the most frequent characters or the least frequent ones won't always yield the best result. Instead, it requires a deep understanding of dynamic programming to explore various states and transitions. It evaluates how well a candidate can break down a hard problem into smaller subproblems and manage multiple state variables, such as the current index in the string and the number of deletions remaining.

Algorithmic pattern used

The primary pattern for this coding problem is Dynamic Programming (DP). Specifically, it often involves a 2D or 3D DP table where the states represent the current position in the string and the number of deletions still available (k). Because the compressed length depends on the count of consecutive characters, the DP transition must account for merging characters of the same type even if they were originally separated by characters that have since been deleted. This makes the state transition more intricate than standard DP problems.

Example explanation (use your own example)

Consider the string "aabbbc" and we are allowed to delete k = 2 characters.

• If we delete nothing (k=0), the compressed string is "a2b3c", length 5.
• If we delete "c", the string is "aabbb", compressed to "a2b3", length 4.
• If we delete "aa", the string is "bbbc", compressed to "b3c", length 3.
• If we delete one "b" and "c", the string is "aabb", compressed to "a2b2", length 4. In this case, deleting "aa" gives the minimum length of 3. The challenge is to find the best combination of removals for much larger strings and larger values of k.

Common mistakes candidates make

One common mistake is trying to use a greedy approach, such as always deleting characters that appear only once. While this might seem intuitive, it fails because deleting a character might allow two blocks of the same character to merge, significantly reducing the compressed length. Another mistake is failing to correctly account for the length of the count in the compressed format (e.g., a count of 10 takes two digits, whereas a count of 9 takes only one). Candidates also often struggle with the DP transition logic, specifically how to handle the "skip" vs. "keep" decisions.

Interview preparation tip

To excel in the String Compression II interview pattern, practice problems that involve "deleting k characters" to optimize a property. Focus on identifying the state variables early. If you find yourself stuck, try to write out the recurrence relation on paper before coding. Understanding how run-length encoding changes when character counts cross thresholds (like 1, 9, 99) is crucial for this specific problem.