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Copy file name to clipboardExpand all lines: CodingChallenges/LeetCode/longest-substring-without-repeating-characters/insight.md
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@@ -26,4 +26,58 @@ Given a string `s`, find the length of the longest **substring** (A substring is
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### Constraints
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-`0 <= s.length <= 5 * 104`
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-`s` consists of English letters, digits, symbols and spaces.
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-`s` consists of English letters, digits, symbols, and spaces.
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## Problem Breakdown
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This problem is a classic example that utilizes the Sliding Window technique, which is particularly effective for challenges involving contiguous sequences of elements such as substrings or subarrays.
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### Understanding the Problem
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The goal is to identify the longest substring of `s` that contains no repeating characters. Key considerations include handling strings of varying lengths and compositions, from completely unique strings to those with repetitive characters.
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### Edge Cases
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-**Empty string**: Returns a length of 0.
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-**Uniform character string**: Such as "aaaa", should return 1 because there is only one unique character.
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-**All unique characters**: Returns the length of the string itself.
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## Approach: Sliding Window
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This technique involves two pointers to define a moving window of characters that expands and contracts based on the uniqueness of characters within it.
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### Solution Explanation
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-**Initialization**: Two pointers, `left` and `right`, start at the beginning of the string, with a set to track characters within the current window.
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-**Expansion**: The `right` pointer moves to the right, adding new characters to the set.
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-**Contraction**: When a duplicate character is found, the `left` pointer moves right until the duplicate is removed from the set, thereby making the substring unique again.
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-**Tracking Maximum**: The maximum length of the substring without repeating characters is updated continuously as the window adjusts.
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### Example Walkthrough
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-**Input**: "abcabcbb"
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- Expands to "abc", then encounters a duplicate 'a'.
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- Contracts by moving the left pointer to just past the first 'a'.
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- Continues until the end, updating the maximum length found.
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## Applied Data Structure and Algorithm
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-**Data Structure**: Uses a set to efficiently check for duplicates and to quickly clear items when necessary.
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-**Algorithm**: Implements the Sliding Window technique with dynamic adjustment of window boundaries based on the condition of uniqueness.
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## Complexity Analysis
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-**Time Complexity**: O(n), where `n` is the length of the string. Each character is processed at most twice (once added and once removed).
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-**Space Complexity**: O(min(m, n)), where `m` is the size of the character set, and `n` is the length of the string.
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## What We've Learned
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- The sliding window technique is incredibly effective for problems involving substrings or subarrays where the condition of the window changes dynamically based on the sequence content.
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- Using a set facilitates O(1) time complexity for adding and removing characters, making the solution efficient even for large strings.
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## Key Notes
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- The solution gracefully handles all types of strings by dynamically adjusting the window size.
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- It’s essential to consider how the data structure used (in this case, a set) can significantly impact the efficiency of the solution.
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