#2957

Medium

auto_awesomeState transition dynamic programming

LeetCode Problem Workspace

Remove Adjacent Almost-Equal Characters

Minimize operations to remove adjacent almost-equal characters using dynamic programming and greedy methods.

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.

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.

terminal

Solution

Solution 1: Greedy

We start traversing the string `word` from index $1$. If `word[i]` and `word[i - 1]` are approximately equal, we greedily replace `word[i]` with a character that is not equal to both `word[i - 1]` and `word[i + 1]` (we can choose not to perform the replacement operation, just record the number of operations). Then, we skip `word[i + 1]` and continue to traverse the string `word`.

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class Solution:
    def removeAlmostEqualCharacters(self, word: str) -> int:
        ans = 0
        i, n = 1, len(word)
        while i < n:
            if abs(ord(word[i]) - ord(word[i - 1])) < 2:
                ans += 1
                i += 2
            else:
                i += 1
        return ans

Continue Practicing

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