To solve the problem, use dynamic programming combined with greedy strategies to minimize changes. Consider the adjacent character conditions and apply a state transition approach. The challenge lies in efficiently selecting the optimal transformations to ensure no adjacent almost-equal characters remain.
Problem Statement
Given a string word, you must determine the minimum number of operations required to transform it such that no two adjacent characters are almost-equal. In one operation, you can change any character in the string to any lowercase English letter.
The goal is to minimize the number of operations necessary to break all adjacent almost-equal pairs in the string, where characters are almost-equal if they are adjacent in the alphabet. The solution should efficiently handle word strings up to 100 characters long.
Examples
Example 1
Input: word = "aaaaa"
Output: 2
We can change word into "acaca" which does not have any adjacent almost-equal characters. It can be shown that the minimum number of operations needed to remove all adjacent almost-equal characters from word is 2.
Example 2
Input: word = "abddez"
Output: 2
We can change word into "ybdoez" which does not have any adjacent almost-equal characters. It can be shown that the minimum number of operations needed to remove all adjacent almost-equal characters from word is 2.
Example 3
Input: word = "zyxyxyz"
Output: 3
We can change word into "zaxaxaz" which does not have any adjacent almost-equal characters. It can be shown that the minimum number of operations needed to remove all adjacent almost-equal characters from word is 3.
Constraints
- 1 <= word.length <= 100
- word consists only of lowercase English letters.
Solution Approach
State Transition Dynamic Programming
The main approach is to use dynamic programming to track the minimum changes needed for each character while considering adjacent almost-equal character pairs. You maintain a state that reflects the previous character's change and ensure each transition results in an optimal transformation.
Greedy Character Selection
During each transition, you must choose a new character for the current index. A greedy approach can be applied by selecting the character that minimizes the number of adjacent almost-equal pairs while considering the prior characters. This ensures each change optimally reduces operations.
Optimized Space Complexity
Efficient implementation reduces space complexity by utilizing a limited state-space for dynamic programming, avoiding unnecessary storage. By considering only adjacent character pairs and minimizing extra computation, the space required for storing the states can be optimized.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity depends on the approach used for state transitions and greedy character selection. It is generally O(n) for the optimized dynamic programming approach, where n is the length of the word. The space complexity is also O(n) due to the need to store state information for each character in the word.
What Interviewers Usually Probe
- Strong understanding of dynamic programming is required to identify and manage state transitions.
- Greedy strategies must be applied carefully to ensure optimal character transformations.
- The ability to minimize space complexity while solving the problem shows an efficient solution approach.
Common Pitfalls or Variants
Common pitfalls
- Failing to properly account for all adjacent almost-equal character pairs during transformations can lead to suboptimal solutions.
- Incorrect greedy character selection might result in more operations than necessary, especially in longer strings.
- Excessive space complexity due to improper state tracking or inefficient memory management can negatively impact performance.
Follow-up variants
- Consider variations where the allowed transformations could involve changing characters to any set of characters, not just lowercase English letters.
- Explore the scenario where adjacent characters have varying levels of 'almost-equality,' requiring more complex state transitions.
- Analyze the problem with longer strings, where the dynamic programming approach's time complexity becomes more critical.
How GhostInterview Helps
- GhostInterview helps by providing structured approaches to solve dynamic programming problems like this, emphasizing efficient state transitions.
- By focusing on greedy techniques and dynamic programming, GhostInterview offers guidance on optimal decision-making for character transformations.
- GhostInterview assists in understanding the balance between time complexity and space usage, ensuring a solution that is both efficient and scalable.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the primary approach to solving the Remove Adjacent Almost-Equal Characters problem?
The primary approach involves using dynamic programming to track and minimize operations required to remove adjacent almost-equal character pairs in the string.
How do greedy techniques apply in the Remove Adjacent Almost-Equal Characters problem?
Greedy techniques are used to select the optimal character for each position, ensuring that adjacent almost-equal pairs are removed while minimizing operations.
What does 'almost-equal' mean in the context of this problem?
'Almost-equal' refers to two characters that are adjacent in the alphabet, such as 'a' and 'b' or 'y' and 'z'. These pairs need to be broken up to solve the problem.
How can space complexity be optimized in this problem?
Space complexity can be optimized by using a limited state-space for dynamic programming, tracking only necessary transitions and minimizing memory usage.
What are the time and space complexities of the optimal solution?
The time complexity of the optimal solution is generally O(n), and the space complexity is also O(n), where n is the length of the string.
Need direct help with Remove Adjacent Almost-Equal Characters instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Remove Adjacent Almost-Equal Characters from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Find the longest alternating subsequence in a string array based on a binary group array.
Open problem page#2712 Minimum Cost to Make All Characters EqualFind the minimum cost to make all characters of a binary string equal by performing two types of operations.
Open problem page#3260 Find the Largest Palindrome Divisible by KCompute the largest n-digit integer divisible by k that forms a palindrome using state transition dynamic programming techniques.
Open problem page