Solving the Longest Substring Without Repeating Characters Problem in Java | O(n) Time Complexity

Problem Definition

Given a string, find the length of the longest substring without repeating characters.

Input: A single string s.

Output: An integer representing the length of the longest substring without repeating characters.

Constraints:

• 0 ≤ s.length ≤ 5 * 104
• The string s consists of English letters, digits, symbols, and spaces.

Example:

    Input: s = "abcabcbb"
    Output: 3
    Explanation: The answer is "abc", with the length of 3.
    

Understanding the Problem

The core challenge of this problem is to find the longest substring without repeating characters. This is a common problem in string manipulation and has applications in various fields such as text processing, data compression, and more.

One potential pitfall is to misunderstand the requirement of the substring being contiguous. Another common misconception is to think that the problem can be solved by simply counting unique characters, which is not the case.

Approach

To solve this problem, we need to consider different approaches:

Naive Solution

The naive solution involves checking all possible substrings and ensuring no characters repeat. This approach is not optimal as it has a time complexity of O(n³), where n is the length of the string.

Optimized Solution

A more efficient approach is to use the sliding window technique with a hash set to keep track of characters in the current window. This approach has a time complexity of O(n).

Here is the thought process for the optimized solution:

• Use two pointers to represent the current window of characters.
• Expand the window by moving the right pointer and add characters to the set.
• If a character is already in the set, move the left pointer to shrink the window until the character is removed from the set.
• Keep track of the maximum length of the window during this process.

Algorithm

Let's break down the optimized algorithm step-by-step:

1. Initialize a set to store characters and two pointers (left and right) to represent the window.
2. Iterate through the string using the right pointer.
3. If the character at the right pointer is not in the set, add it to the set and update the maximum length.
4. If the character is in the set, remove the character at the left pointer from the set and move the left pointer to the right.
5. Continue this process until the right pointer reaches the end of the string.

Code Implementation

public class Solution {
    public int lengthOfLongestSubstring(String s) {
        // HashSet to store the characters in the current window
        Set<Character> set = new HashSet<>();
        int left = 0, right = 0, maxLength = 0;

        // Iterate through the string with the right pointer
        while (right < s.length()) {
            // If the character is not in the set, add it and update maxLength
            if (!set.contains(s.charAt(right))) {
                set.add(s.charAt(right));
                maxLength = Math.max(maxLength, right - left + 1);
                right++;
            } else {
                // If the character is in the set, remove the leftmost character and move left pointer
                set.remove(s.charAt(left));
                left++;
            }
        }
        return maxLength;
    }
}

Complexity Analysis

The time complexity of the optimized solution is O(n) because each character is processed at most twice (once by the right pointer and once by the left pointer). The space complexity is O(min(n, m)), where n is the length of the string and m is the size of the character set (in this case, 128 for ASCII characters).

Edge Cases

Consider the following edge cases:

• Empty string: The output should be 0.
• String with all unique characters: The output should be the length of the string.
• String with all identical characters: The output should be 1.

Examples:

    Input: s = ""
    Output: 0

    Input: s = "abcdef"
    Output: 6

    Input: s = "aaaaaa"
    Output: 1
    

Testing

To test the solution comprehensively, consider a variety of test cases:

• Simple cases with short strings.
• Cases with mixed characters (letters, digits, symbols).
• Edge cases as discussed above.

Using a testing framework like JUnit can help automate and manage these tests effectively.

Thinking and Problem-Solving Tips

When approaching such problems, consider the following tips:

• Break down the problem into smaller parts and understand each requirement.
• Think about different approaches and their trade-offs.
• Practice similar problems to improve your problem-solving skills.

Conclusion

In this blog post, we discussed how to solve the Longest Substring Without Repeating Characters problem in Java using an optimized approach with O(n) time complexity. We covered the problem definition, understanding the problem, different approaches, detailed algorithm, code implementation, complexity analysis, edge cases, and testing.

Understanding and solving such problems is crucial for improving your coding and problem-solving skills. Keep practicing and exploring further to master these concepts.

Additional Resources

For further reading and practice, consider the following resources:

• LeetCode Problem
• GeeksforGeeks Article
• Coursera Algorithms Course