Interview Problem Explained: Minimize String Length (LeetCode 2716)

Minimize String Length: Problem Statement

Given a string s, your task is to minimize its length by performing certain operations as many times as you wish (including zero times):

1. Choose an index i in the string. If there is another character c to the left of index i that matches the character at i, delete the closest such c.

2. Choose an index i in the string. If there is another character c to the right of index i that matches the character at i, delete the closest such c.

Your goal is to perform these operations to reduce the string's length as much as possible and return the minimum possible length as an integer.

If you examine the rules closely, you’ll notice that whenever a character appears more than once, you can always remove duplicates using one of the two operations. In other words, as long as there are duplicate characters, you can always remove one of them.

For example, if the string contains ...x...x..., you can:

• Delete the right x by referencing the left one, or

• Delete the left x by referencing the right one.

Ultimately, this problem is equivalent to counting the number of unique characters in string s.

Problem Requirements

1. Input: A string s.

2. Output: Return the number of unique characters in s after all possible operations.

Tip: This is LeetCode Problem 2716.

LeetCode’s explanation may be brief or unclear to some readers while Codetree provides more context and examples to improve your understanding.

Step 1. Naive Approach

Idea

Understanding the true goal of the problem is crucial. While the two operations (operation1 and operation2) may seem confusing, the essence is to determine the length of the string after all duplicates are removed. This is the same as counting the number of unique characters in the original string.

The most basic approach is to implement logic that removes duplicate characters.

Logic Breakdown

1. Iterate through the string character by character.

2. For each character, do the following: a. If the character hasn’t appeared before, b. Record it in a separate list that keeps track of unique characters.

3. After the iteration, return the length of the list of unique characters.

Code Implementation

def minimizedStringLength(s):
    """
    :type s: str
    :rtype: int
    """
    seen = []  # array to store characters we've already seen

    for ch in s:  # traverse the string one character at a time
        if ch not in seen:  # if it's the first time we see this character
            seen.append(ch)  # record it

    return len(seen)

Time & Space Complexity Analysis

Let L be the length of the string.

• Time Complexity: For each character, checking if it is in seen takes O(L) time, repeated for L characters, resulting in O(L²).

• Space Complexity: In the worst case (all unique characters), O(L) space is needed.

While straightforward, this approach becomes inefficient for long strings due to its O(L²) time complexity. Let’s see how to optimize this.

Step 2. Using a Set

Idea

When solving problems that involve removing duplicates, Python’s built-in set data structure is a perfect fit. A set automatically stores only unique elements. So by converting the string to a set, we get all the unique characters at once.

For more on sets, see Codetree’s set introduction.

Logic Breakdown

1. Convert the input string s to a Python set. This automatically removes duplicates.

2. Return the length of the set, which is the number of unique characters.

Code Implementation

def minimizedStringLength(self, s):
    """
    :type s: str
    :rtype: int
    """
    return len(set(s))

Time & Space Complexity Analysis

• Time Complexity: Each character is added to the set in average O(1) time, so the total is O(L).

• Space Complexity: In the worst case (all unique), O(L) space is needed.

This is one of the fastest and most concise ways to remove duplicates and count unique characters.

Frequently Asked Questions

Q: Can we use other data structures besides set? What’s the difference?

A: Yes. You could use a hashmap(dict) to track character occurrences, or even sort the string and manually remove duplicates. But using a set is generally the most intuitive and concise solution.

Q: Does the order of operations matter in this problem?

A: No. Regardless of which operation or sequence you use, the result always boils down to counting the number of unique characters in the string.

How to Prepare for Interviews with the Minimize String Length Problem

Problems like "Minimize String Length" may appear complex due to their detailed rules, but once you identify the core, they can be solved concisely. These problems are effective for assessing your ability to understand the problem, think analytically, and select the right data structure.

Interview Tips:

1. Identify the Core of the Problem

   • After reading the problem, try to restate it in one or two sentences. For example: “Is this problem really asking for the number of unique characters in the string?”

   • Practice simplifying complex operations to their essential effect.

2. Choose and Use the Optimal Data Structure

   • Know which data structures (e.g., Set, HashMap/Dictionary, Array, List) are best for tasks like duplicate removal, frequency counting, or searching.

   • In this problem, recognizing that a set is the optimal choice leads to a fast, elegant solution. Be ready to explain your choice and discuss alternatives and their trade-offs.

Similar Problems to Practice

• Contains Duplicate

• Intersection of Two Arrays

• Distinct Numbers

All of these problems are well-suited for practicing how to identify simple rules, discover mathematical patterns, and generalize them through mathematical reasoning.

How to Review After Solving This Problem

1. Collecting similar problems that require identifying the core and selecting the optimal data structure.

2. Summarizing the key steps (interpreting the operation, extracting unique values with a set) in your own words.