Longest Substring Without Repeating Characters
To find the length of the longest substring without repeating characters in a given string, you can use the sliding window technique. Here’s a code that does this:


Here’s a brief explanation of how it works:
 Use two pointers,
start
andend
, to define a sliding window of unique characters.  Move the
end
pointer to the right and check if the character is in thechar_index_map
.  If the character is found and its last occurrence is within the current window, move the
start
pointer to the right of that occurrence.  Keep track of the maximum length of the window, which gives you the length of the longest substring without repeating characters.
Abstract Representation of the Problem
In an abstract sense, this problem is about finding the longest contiguous subsequence in a given sequence where all elements are unique. The sequence can contain various types of elements such as letters, digits, symbols, and spaces. The measure of the solution is the length of this longest subsequence.
Key elements:
 A sequence (array or string) of elements.
 A subsequence that has unique elements.
 Length as the measure of the solution.
Constraints:
 Length of the sequence is within a certain limit.
 Elements in the sequence can be from a specified set (English letters, digits, symbols, spaces).
The goal is to identify this subsequence and report its length.
Problem Classification
This problem falls under the category of sequence analysis. Specifically, it involves analyzing a sequence of characters to find a particular kind of subsequence (substring in this case) that satisfies certain uniqueness conditions. Sequence analysis is common in computer science and bioinformatics but can be applied in various other domains as well.
Cues
I have identified the following two elements as the cues from analyzing the problem:
 Subsequence Extraction
 Validate Uniqueness of Characters
These two elements serve as cues for approaching the problem.
Subsequence Extraction: The goal is to extract a substring, which is a contiguous sequence of characters from the given string.
Validate Uniqueness of Characters: While extracting, you need to ensure that the characters in the substring are unique.
Understanding these cues can guide your problemsolving strategy. For instance, you might decide to employ a sliding window technique to handle subsequence extraction while using a data structure like a set to validate the uniqueness of characters within that window.
This is about Subsequence Extraction where the characters must be unique and the longest we could find in the given input.
The problem is focused on subsequence extraction, but with the constraint that the characters in the subsequence must be unique. Furthermore, the objective is to find the longest such subsequence within the given input string. This is a more specialized form of sequence analysis, aimed at maximizing the length while maintaining character uniqueness.
Loop Invariant Structure for the Problem
Initialization
Before the loop starts, we create a set to store unique characters and two pointers start
and end
to indicate the boundaries of our current substring. At this point, the set is empty, and both pointers are at the 0th index. Our loop invariant is that the set contains all unique characters between start
and end
.
Maintenance
During each iteration, we move the end
pointer one step forward and add the new character to our set. If we find a duplicate, we remove the character at the start
pointer from the set and move start
one step forward. This maintains the loop invariant: the set contains unique characters between start
and end
.
Termination
When the loop ends, the set will contain unique characters from the longest substring without repeating characters. The distance between start
and end
will give us the length of this substring, ensuring the problem is solved correctly.
By following these steps, we prove that our loop invariant holds at Initialization, is maintained during each iteration, and gives us a useful property (the longest substring without repeating characters) at Termination.
Tabular Representation
Here’s a table illustrating these steps for the string “pwwkew”:
Step No  Start  End  Current Char  Set  Action  Longest Substring 

1  0  0  p  {p}  Add ‘p’  p 
2  0  1  w  {p, w}  Add ‘w’  pw 
3  0  2  w  {p}  Remove ‘p’, Move Start  pw 
4  1  2  w  {w}  Remove ‘w’, Move Start  pw 
5  2  2  w  {w}  Add ‘w’  w 
6  2  3  k  {w, k}  Add ‘k’  wk 
7  2  4  e  {w, k, e}  Add ’e’  wke 
8  2  5  w  {k, e}  Remove ‘w’, Move Start  wke 
9  3  5  w  {k, e, w}  Add ‘w’  kew 
The “Longest Substring” column keeps track of the longest substring without repeating characters that we’ve seen so far. In this case, “wke” is the longest substring without repeating characters, and its length is 3.