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docs(docs): add longest‑substring problem page and sliding‑window reference with SVG illustrations
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Prad Nukala
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---
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title: '3. Longest Substring Without Repeating Characters'
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description: Given a string s, find the length of the longest substring without duplicate characters
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sidebar:
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label: 'Longest Substring Without Repeating Characters'
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badge: 'Medium'
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---
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<Badge variant="accent">Sliding Window</Badge>
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### Example 1:
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- Input: `s = "abcabcbb"`
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- Output: `3`
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- Explanation: The answer is "abc", with the length of `3`. Note that "bca" and "cab" are also correct answers.
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### Example 2:
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- Input: `s = "bbbbb"`
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- Output: `1`
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- Explanation: The answer is "b", with the length of `1`.
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### Example 3:
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- Input: `s = "pwwkew"`
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- Output: `3`
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- Explanation: The answer is "wke", with the length of `3`. Notice that the answer must be a substring, "pwke" is a subsequence and not a substring.
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### Constraints:
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- `0 <= s.length <= 10^5`
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- `s` consists of English letters, digits, symbols and spaces.
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## Solution
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```py
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class Solution:
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def lengthOfLongestSubstring(self, s: str) -> int:
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left = 0
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ans = 0
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seen = set()
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for right, c in enumerate(s):
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while c in seen:
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seen.remove(s[left])
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left += 1
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seen.add(c)
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ans = max(ans, right - left + 1)
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return ans
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```
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---
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title: Sliding Window
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description: 'Sliding window is a specialized two-pointer family where the pointers define a contiguous interval and you maintain information about that entire interval as it moves.'
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---
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:::warning
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This is the family where invariants matter the most
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:::
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## What Makes Sliding Window Different?
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Many problems have two moving boundaries. That alone does not make them sliding window problems.
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A problem belongs to this family when:
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- the answer depends on the subarray or substring between left and right
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- you can update the window state incrementally as elements enter or leave
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- you maintain a condition that tells you whether the window is valid
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## What is an Invariant?
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An invariant is a statement that stays true before and after every iteration.
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For sliding window, the invariant often looks like one of these:
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- "the current window is valid"
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- "the current window contains no duplicates"
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- "the current window sum is at most the target"
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- "the frequency map matches the characters currently inside the window"
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The invariant gives the loop its structure:
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- expand the window by moving right
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- update the window state
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- if the invariant breaks, shrink from the left until it holds again
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- update the answer only when you know the invariant is satisfied
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## Why Invariants Matter
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Without an invariant, shrinking the window becomes arbitrary. You no longer know:
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- when the window is valid
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- when to update the answer
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- why the left pointer should stop moving
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- The invariant is the reason the algorithm is correct.
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## The Main Subtypes
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### 1. Fixed-size windows
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:::tip
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The window size never changes. The main task is updating the window state efficiently when one element enters and one leaves.
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:::
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### 2. Flexible-size windows with a validity rule
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:::tip
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Here the window expands until invalid, then shrinks until valid again.
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:::
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### 3. Frequency-tracking windows
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:::tip
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The difficulty comes from keeping the bookkeeping correct as characters enter and leave.
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:::
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## How Sliding Window Differs From Other Two-Pointer Families
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Compare it with Container With Most Water:
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- In sliding window, the interval itself has meaning.
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- In container, the interval is just the remaining search space.
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Compare it with Remove Duplicates:
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- In sliding window, both pointers describe a live window.
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- In compaction, the left part of the array is already the answer prefix.
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## A Practical Template
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A common variable-size sliding window has this shape:
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1. Add the new rightmost element.
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2. Update the window state.
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3. While the invariant is broken, remove elements from the left.
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4. Once the invariant is restored, update the answer.
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The exact data structure changes from problem to problem, but the logic stays the same.
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As you work through this section, keep asking:
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:::warning
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What invariant does my window maintain, and at what moment is it safe to update the answer?
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:::
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@@ -0,0 +1,66 @@
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<svg viewBox="0 0 800 450" xmlns="http://www.w3.org/2000/svg">
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<!-- Background (REQUIRED) -->
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<rect width="800" height="450" fill="#f8f9fa" rx="10"/>
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<!-- Title and Subtitle -->
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<text x="400" y="45" font-family="Arial, sans-serif" font-size="26" font-weight="bold" fill="#2c3e50" text-anchor="middle">Sliding Window: Fixed Size</text>
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<text x="400" y="75" font-family="Arial, sans-serif" font-size="16" fill="#7f8c8d" text-anchor="middle">Window of size K=3 moving through the array.</text>
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<!-- Step 1: Initial window -->
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<g transform="translate(150, 130)">
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<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">1. Current window (Sum = 10)</text>
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<!-- Array -->
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<g transform="translate(0, 20)">
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<rect x="0" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">2</text>
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<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">3</text>
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<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">5</text>
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<rect x="210" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
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<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">1</text>
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<rect x="280" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
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<text x="310" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">8</text>
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<!-- Bracket -->
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<path d="M 0,60 L 0,70 L 200,70 L 200,60" fill="none" stroke="#10b981" stroke-width="2"/>
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</g>
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</g>
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<!-- Transition -->
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<g transform="translate(400, 260)">
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<path d="M 0,0 L 0,30" stroke="#dee2e6" stroke-width="2" fill="none"/>
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<text x="10" y="20" font-family="Arial, sans-serif" font-size="14" font-style="italic" fill="#7f8c8d">Slide window: -2, +1</text>
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</g>
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<!-- Step 2: Slid window -->
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<g transform="translate(150, 340)">
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<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">2. Next window (Sum = 9)</text>
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<!-- Array -->
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<g transform="translate(0, 20)">
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<rect x="0" y="0" width="60" height="50" fill="#e5e7eb" stroke="#94a3b8" stroke-width="2" rx="3"/>
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<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#94a3b8">2</text>
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<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">3</text>
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<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">5</text>
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<rect x="210" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">1</text>
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<rect x="280" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
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<text x="310" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">8</text>
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<!-- Bracket -->
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<path d="M 70,60 L 70,70 L 270,70 L 270,60" fill="none" stroke="#10b981" stroke-width="2"/>
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</g>
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</g>
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</svg>
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After Width: | Height: | Size: 3.7 KiB |
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<svg viewBox="0 0 800 450" xmlns="http://www.w3.org/2000/svg">
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<!-- Background (REQUIRED) -->
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<rect width="800" height="450" fill="#f8f9fa" rx="10"/>
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<!-- Title and Subtitle -->
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<text x="400" y="45" font-family="Arial, sans-serif" font-size="26" font-weight="bold" fill="#2c3e50" text-anchor="middle">Sliding Window: Flexible Size</text>
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<text x="400" y="75" font-family="Arial, sans-serif" font-size="16" fill="#7f8c8d" text-anchor="middle">Window expands until invalid, then shrinks until valid again.</text>
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<!-- Step 1: Invalid state -->
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<g transform="translate(150, 130)">
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<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">1. Expansion breaks invariant</text>
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<!-- Array -->
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<g transform="translate(0, 20)">
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<rect x="0" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="3" rx="3"/>
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<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
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<polygon points="30,60 25,70 35,70" fill="#27ae60"/>
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<text x="30" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#27ae60" text-anchor="middle">L</text>
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<rect x="70" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="3" rx="3"/>
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<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">b</text>
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<rect x="140" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="3" rx="3"/>
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<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">c</text>
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<rect x="210" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="4" rx="3"/>
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<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
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<polygon points="240,60 235,70 245,70" fill="#3498db"/>
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<text x="240" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#3498db" text-anchor="middle">R</text>
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<text x="300" y="32" font-family="Arial, sans-serif" font-size="14" fill="#ef4444" font-weight="bold">Duplicate 'a'!</text>
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</g>
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</g>
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<!-- Transition -->
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<g transform="translate(400, 260)">
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<path d="M 0,0 L 0,30" stroke="#dee2e6" stroke-width="2" fill="none"/>
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<text x="10" y="20" font-family="Arial, sans-serif" font-size="14" font-style="italic" fill="#7f8c8d">Shrink from left</text>
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</g>
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<!-- Step 2: Valid again -->
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<g transform="translate(150, 340)">
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<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">2. Invariant restored</text>
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<!-- Array -->
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<g transform="translate(0, 20)">
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<rect x="0" y="0" width="60" height="50" fill="#e5e7eb" stroke="#94a3b8" stroke-width="2" rx="3"/>
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<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#94a3b8">a</text>
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<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">b</text>
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<polygon points="100,60 95,70 105,70" fill="#27ae60"/>
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<text x="100" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#27ae60" text-anchor="middle">L</text>
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<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">c</text>
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<rect x="210" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
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<polygon points="240,60 235,70 245,70" fill="#3498db"/>
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<text x="240" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#3498db" text-anchor="middle">R</text>
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<text x="300" y="32" font-family="Arial, sans-serif" font-size="14" fill="#10b981" font-weight="bold">Valid again!</text>
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</g>
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</g>
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</svg>
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After Width: | Height: | Size: 4.1 KiB |
@@ -0,0 +1,54 @@
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<svg viewBox="0 0 800 450" xmlns="http://www.w3.org/2000/svg">
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<!-- Background (REQUIRED) -->
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<rect width="800" height="450" fill="#f8f9fa" rx="10"/>
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<!-- Title and Subtitle -->
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<text x="400" y="45" font-family="Arial, sans-serif" font-size="26" font-weight="bold" fill="#2c3e50" text-anchor="middle">Sliding Window: Frequency Tracking</text>
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<text x="400" y="75" font-family="Arial, sans-serif" font-size="16" fill="#7f8c8d" text-anchor="middle">Maintaining a character frequency map for the current window.</text>
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<!-- Left: Window -->
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<g transform="translate(100, 150)">
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<text x="0" y="-30" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">Current Window</text>
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<!-- Array -->
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<g transform="translate(0, 20)">
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<rect x="0" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
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<polygon points="30,60 25,70 35,70" fill="#27ae60"/>
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<text x="30" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#27ae60" text-anchor="middle">L</text>
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<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">b</text>
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<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
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<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
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||||
<polygon points="170,60 165,70 175,70" fill="#3498db"/>
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<text x="170" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#3498db" text-anchor="middle">R</text>
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||||
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<rect x="210" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
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<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">c</text>
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</g>
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</g>
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<!-- Right: Frequency Map -->
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<g transform="translate(500, 150)">
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<text x="0" y="-30" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">Frequency Map</text>
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<!-- Map Container -->
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<rect x="0" y="0" width="150" height="120" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="8"/>
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<!-- Entries -->
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<g transform="translate(25, 35)">
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<text x="0" y="0" font-family="monospace" font-size="18" fill="#2c3e50">'a' : 2</text>
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<text x="0" y="30" font-family="monospace" font-size="18" fill="#2c3e50">'b' : 1</text>
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<text x="0" y="60" font-family="monospace" font-size="18" fill="#7f8c8d">'c' : 0</text>
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</g>
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<!-- Invariant label -->
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<rect x="-20" y="140" width="190" height="40" fill="#e3f2fd" stroke="#3498db" stroke-width="1" rx="5"/>
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<text x="75" y="165" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#1565c0" text-anchor="middle">INVARIANT: SYNCED STATE</text>
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</g>
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<!-- Connector -->
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<path d="M 380,195 L 480,195" stroke="#dee2e6" stroke-width="2" stroke-dasharray="5,5" fill="none"/>
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</svg>
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|
After Width: | Height: | Size: 3.1 KiB |
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