feat: refactored docs structure

docs/(01-linear-structures)/sliding-window/(problems)/1004_max-consecutive-ones-iii.mdx

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+---
+title: '1004. Max Consecutive Ones III'
+description: Given a binary array nums and an integer k, return the maximum number of consecutive 1's in the array if you can flip at most k 0's
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Binary Search", slug: "binary-search" }
+  - { name: "Sliding Window", slug: "sliding-window" }
+  - { name: "Prefix Sum", slug: "prefix-sum" }
+issue: "https://github.com/prdlk/leetcode/issues/56"
+sidebar:
+  label: 'Max Consecutive Ones III'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `nums = [1,1,1,0,0,0,1,1,1,1,0], k = 2`
+- Output: `6`
+- Explanation: `[1,1,1,0,0,1,1,1,1,1,1]` Bolded numbers were flipped from `0` to `1`. The longest subarray is underlined.
+
+### Example 2:
+- Input: `nums = [0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,1,1], k = 3`
+- Output: `10`
+- Explanation: `[0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1]` Bolded numbers were flipped from `0` to `1`. The longest subarray is underlined.
+
+### Constraints:
+
+- `1 <= nums.length <= 10^5`
+- `nums[i]` is either 0 or 1.
+- `0 <= k <= nums.length`
+
+## Solution
+
+```py
+class Solution:
+    def longestOnes(self, nums: list[int], k: int) -> int:
+        left = 0
+        cur = 0
+        ans = 0
+
+        for right in range(len(nums)):
+            if nums[right] == 0:
+                cur += 1
+            while cur > k:
+                if nums[left] == 0:
+                    cur -= 1
+                left += 1
+
+            ans = max(ans, right - left + 1)
+
+        return ans
+```

docs/(01-linear-structures)/sliding-window/(problems)/121_best-time-to-buy-and-sell-stock.mdx

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+---
+title: '121. Best Time to Buy and Sell Stock'
+description: You are given an array prices where prices[i] is the price of a given stock on the i^th day
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Dynamic Programming", slug: "dynamic-programming" }
+video: "1pkOgXD63yU"
+issue: "https://github.com/prdlk/leetcode/issues/50"
+sidebar:
+  label: 'Best Time to Buy and Sell Stock'
+  badge: 'Easy'
+---
+
+### Example 1:
+- Input: `prices = [7,1,5,3,6,4]`
+- Output: `5`
+- Explanation: Buy on day `2` (price = `1`) and sell on day `5` (price = `6`), profit = `6-1 = 5`. Note that buying on day `2` and selling on day `1` is not allowed because you must buy before you sell.
+
+### Example 2:
+- Input: `prices = [7,6,4,3,1]`
+- Output: `0`
+- Explanation: In this case, no transactions are done and the max profit = `0`.
+
+### Constraints:
+
+- `1 <= prices.length <= 10^5`
+- `0 <= prices[i] <= 10^4`
+
+## Approach
+
+::::warning
+The diagram traces the code below literally. That code does not run: `curr` and `ans` are never initialised, so the first `curr > left` test raises `NameError`, and `left` holds a price rather than an index, so `prices[left]` indexes by value.
+::::
+
+```mermaid
+flowchart TD
+  S(["maxProfit(prices)"]) --> I["left = min(prices)"]
+  I --> F{"more right in range(len(prices))?"}
+  F -- no --> E(["return ans"])
+  F -- yes --> W{"curr > left?"}
+  W -- yes --> P["curr -= prices[left]; left += 1"]
+  P --> W
+  W -- no --> M["ans = max(ans, curr)"]
+  M --> F
+```
+
+## Solution
+
+```py
+class Solution:
+    def maxProfit(self, prices: List[int]) -> int:
+        left = min(prices)
+        for right in range(len(prices)):
+            while curr > left:
+                curr -= prices[left]
+                left += 1
+            ans = max(ans, curr)
+        return ans
+```

docs/(01-linear-structures)/sliding-window/(problems)/209_minimum-size-subarray-sum.mdx

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+---
+title: '209. Minimum Size Subarray Sum'
+description: Given an array of positive integers nums and a positive integer target, return the minimal length of a subarray whose sum is greater than or equal to target. If there is no such subarray, return 0 instead
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Binary Search", slug: "binary-search" }
+  - { name: "Sliding Window", slug: "sliding-window" }
+  - { name: "Prefix Sum", slug: "prefix-sum" }
+issue: "https://github.com/prdlk/leetcode/issues/54"
+sidebar:
+  label: 'Minimum Size Subarray Sum'
+  badge: 'Medium'
+---
+
+::::warning
+If you have figured out the O(n) solution, try coding another solution of which the time complexity is O(n log(n)).
+::::
+
+### Example 1:
+- Input: `target = 7, nums = [2,3,1,2,4,3]`
+- Output: `2`
+- Explanation: The subarray `[4,3]` has the minimal length under the problem constraint.
+
+### Example 2:
+- Input: `target = 4, nums = [1,4,4]`
+- Output: `1`
+
+### Example 3:
+- Input: `target = 11, nums = [1,1,1,1,1,1,1,1]`
+- Output: `0`
+
+### Constraints:
+
+- `1 <= target <= 10^9`
+- `1 <= nums.length <= 10^5`
+- `1 <= nums[i] <= 10^4`
+
+## Solution
+
+```py
+class Solution:
+    def minSubArrayLen(self, target: int, nums: list[int]) -> int:
+        window_sum = 0
+        length = len(nums) + 1
+        left = 0
+
+        for right in range(len(nums)):
+            window_sum += nums[right]
+            while window_sum >= target:
+                length = min(length, right - left + 1)
+                window_sum -= nums[left]
+                left += 1
+        if length > len(nums):
+            return 0
+        return length
+```

docs/(01-linear-structures)/sliding-window/(problems)/3_longest-substring-without-repeating-characters.mdx

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+---
+title: '3. Longest Substring Without Repeating Characters'
+description: Given a string s, find the length of the longest substring without duplicate characters
+icon: dot
+topics:
+  - { name: "Hash Table", slug: "hash-table" }
+  - { name: "String", slug: "string" }
+  - { name: "Sliding Window", slug: "sliding-window" }
+video: "wiGpQwVHdE0"
+issue: "https://github.com/prdlk/leetcode/issues/51"
+sidebar:
+  label: 'Longest Substring Without Repeating Characters'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `s = "abcabcbb"`
+- Output: `3`
+- Explanation: The answer is "abc", with the length of `3`. Note that "bca" and "cab" are also correct answers.
+
+### Example 2:
+- Input: `s = "bbbbb"`
+- Output: `1`
+- Explanation: The answer is "b", with the length of `1`.
+
+### Example 3:
+- Input: `s = "pwwkew"`
+- Output: `3`
+- 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.
+
+### Constraints:
+
+- `0 <= s.length <= 10^5`
+- `s` consists of English letters, digits, symbols and spaces.
+
+## Approach
+
+```mermaid
+flowchart TD
+  S(["lengthOfLongestSubstring(s)"]) --> I["left = 0, ans = 0, window = set()"]
+  I --> L{"more (right, c) in s?"}
+  L -- no --> E(["return ans"])
+  L -- yes --> W{"c already in window?"}
+  W -- yes --> P["window.remove(s[left]); left += 1 — shrink until c is free"]
+  P --> W
+  W -- no --> A["window.add(c)"]
+  A --> M["ans = max(ans, right - left + 1)"]
+  M --> L
+```
+
+## Solution
+
+```py
+class Solution:
+    def lengthOfLongestSubstring(self, s: str) -> int:
+        left = 0
+        ans = 0
+        window = set()
+        for right, c in enumerate(s):
+            while c in window:
+                window.remove(s[left])
+                left += 1
+            window.add(c)
+            ans = max(ans, right - left + 1)
+
+        return ans
+```

docs/(01-linear-structures)/sliding-window/(problems)/424_longest-repeating-character-replacement.mdx

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+---
+title: '424. Longest Repeating Character Replacement'
+description: You are given a string s and an integer k. You can choose any character of the string and change it to any other uppercase English character. You can perform this operation at most k times
+icon: dot
+topics:
+  - { name: "Hash Table", slug: "hash-table" }
+  - { name: "String", slug: "string" }
+  - { name: "Sliding Window", slug: "sliding-window" }
+video: "gqXU1UyA8pk"
+issue: "https://github.com/prdlk/leetcode/issues/52"
+sidebar:
+  label: 'Longest Repeating Character Replacement'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `s = "ABAB", k = 2`
+- Output: `4`
+- Explanation: Replace the two 'A's with two 'B's or vice versa.
+
+### Example 2:
+- Input: `s = "AABABBA", k = 1`
+- Output: `4`
+- Explanation: Replace the one 'A' in the middle with 'B' and form "AABBBBA". The substring "BBBB" has the longest repeating letters, which is `4`. There may exists other ways to achieve this answer too.
+
+### Constraints:
+
+- `1 <= s.length <= 10^5`
+- `s` consists of only uppercase English letters.
+- `0 <= k <= s.length`
+
+## Approach
+
+```mermaid
+flowchart TD
+  S(["characterReplacement(s, k)"]) --> I["count = {}, res = 0, l = 0, maxF = 0"]
+  I --> L{"more (r, c) in s?"}
+  L -- no --> E(["return res"])
+  L -- yes --> A["count[c] += 1; maxF = max(maxF, count[c])"]
+  A --> W{"(r - l + 1) - maxF > k? — too many chars to replace"}
+  W -- yes --> P["count[s[l]] -= 1; l += 1 — shrink from the left"]
+  P --> W
+  W -- no --> M["res = max(res, r - l + 1)"]
+  M --> L
+```
+
+## Solution
+
+```py
+class Solution:
+    def characterReplacement(self, s: str, k: int) -> int:
+        count = {}
+        res = 0
+
+        l = 0
+        maxF = 0
+        for r, c in enumerate(s):
+            count[c] = 1 + count.get(c, 0)
+            maxF = max(maxF, count[c])
+
+            while (r - l + 1) - maxF > k:
+                count[s[l]] -= 1
+                l += 1
+
+            res = max(res, r - l + 1)
+        return res
+```

docs/(01-linear-structures)/sliding-window/(problems)/567_permutation-in-string.mdx

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+---
+title: '567. Permutation in String'
+description: Given two strings s1 and s2, return true if s2 contains a permutation of s1, or false otherwise
+icon: dot
+topics:
+  - { name: "Hash Table", slug: "hash-table" }
+  - { name: "Two Pointers", slug: "two-pointers" }
+  - { name: "String", slug: "string" }
+  - { name: "Sliding Window", slug: "sliding-window" }
+video: "UbyhOgBN834"
+issue: "https://github.com/prdlk/leetcode/issues/53"
+sidebar:
+  label: 'Permutation in String'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `s1 = "ab", s2 = "eidbaooo"`
+- Output: `true`
+- Explanation: `s2` contains one permutation of `s1` ("ba").
+
+### Example 2:
+- Input: `s1 = "ab", s2 = "eidboaoo"`
+- Output: `false`
+
+### Constraints:
+
+- `1 <= s1.length, s2.length <= 10^4`
+- `s1` and `s2` consist of lowercase English letters.
+
+## Approach
+
+```mermaid
+flowchart TD
+  S(["checkInclusion(s1, s2)"]) --> G{"k = len(s1) > len(s2)?"}
+  G -- yes --> X(["return False"])
+  G -- no --> I["need = Counter(s1), window = Counter()"]
+  I --> L{"more (right, c) in s2?"}
+  L -- no --> E(["return False"])
+  L -- yes --> A["window[c] += 1"]
+  A --> B{"right >= k? — window is now longer than k"}
+  B -- yes --> C["drop s2[right - k] from window, deleting the key at 0"]
+  B -- no --> Q
+  C --> Q{"window == need?"}
+  Q -- yes --> R(["return True"])
+  Q -- no --> L
+```
+
+## Solution
+
+```py
+from collections import Counter
+
+
+class Solution:
+    def checkInclusion(self, s1: str, s2: str) -> bool:
+        k = len(s1)
+        if k > len(s2):
+            return False
+
+        need = Counter(s1)
+        window = Counter()
+
+        for right, c in enumerate(s2):
+            window[c] += 1
+            if right >= k:
+                left_char = s2[right - k]
+                window[left_char] -= 1
+                if window[left_char] == 0:
+                    del window[left_char]
+            if window == need:
+                return True
+
+        return False
+```

docs/(01-linear-structures)/sliding-window/(problems)/643_maximum-average-subarray-i.mdx

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+---
+title: '643. Maximum Average Subarray I'
+description: You are given an integer array nums consisting of n elements, and an integer k
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Sliding Window", slug: "sliding-window" }
+issue: "https://github.com/prdlk/leetcode/issues/55"
+sidebar:
+  label: 'Maximum Average Subarray I'
+  badge: 'Easy'
+---
+
+### Example 1:
+- Input: `nums = [1,12,-5,-6,50,3], k = 4`
+- Output: `12.75000`
+- Explanation: Maximum average is `(12 - 5 - 6 + 50`) / `4 = 51 / 4 = 12.75`
+
+### Example 2:
+- Input: `nums = [5], k = 1`
+- Output: `5.00000`
+
+### Constraints:
+
+- `n == nums.length`
+- `1 <= k <= n <= 10^5`
+- `-10^4 <= nums[i] <= 10^4`
+
+## Solution
+
+```py
+class Solution:
+    def findMaxAverage(self, nums: list[int], k: int) -> float:
+        window_sum = 0
+        for i in range(k):
+            window_sum += nums[i]
+        largest = window_sum
+
+        for right in range(k, len(nums)):
+            left = right - k
+            window_sum -= nums[left]
+            window_sum += nums[right]
+            largest = max(largest, window_sum)
+
+        return largest / k
+```

docs/(01-linear-structures)/sliding-window/index.mdx

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+---
+title: Sliding Window
+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.'
+hidden: true
+---
+
+
+<YouTube id="tSTO9w3piAo" title="Sliding Window" />
+
+
+Many problems have two moving boundaries. That alone does not make them sliding window problems.
+
+A problem belongs to this family when:
+
+- the answer depends on the subarray or substring between left and right
+- you can update the window state incrementally as elements enter or leave
+- you maintain a condition that tells you whether the window is valid
+
+:::tip
+The rule for all three: every element enters once and leaves once, so the whole thing runs in O(n).
+:::
+
+<Accordion>
+  <AccordionItem title="What is an invariant?">
+    An invariant is a statement that stays true before and after every iteration. In a sliding window, that statement usually describes the window itself, such as “the window is valid,” “it has no duplicates,” or “its sum is at most the target.” It can also describe a helper structure, such as “the frequency map matches the characters currently inside the window.”
+  </AccordionItem>
+  <AccordionItem title="Why invariants matter?">
+    Without an invariant, shrinking the window is just a guess. You no longer know when the window is valid, when to update the answer, or why the left pointer should stop. The invariant is what makes the algorithm correct.
+  </AccordionItem>
+  <AccordionItem title="How sliding window differs from other two-pointer families?">
+    Sliding window is not the same as every other two-pointer pattern. In Container With Most Water, the interval is only the remaining search space. In sliding window, the interval itself is the thing you care about. In Remove Duplicates, the left side is already the finished answer prefix. In sliding window, both pointers describe a live window that is still being checked.
+  </AccordionItem>
+</Accordion>
+
+
+## 1. Fixed-size windows
+
+:::tip
+The window size never changes. The main task is updating the window state efficiently when one element enters and one leaves.
+:::
+
+
+<Frame caption="Sliding Window Fixed" hint="">
+
+![](/sliding-window-fixed-size.svg)
+
+</Frame>
+
+
+```python
+def sliding_window_fixed(input, window_size):
+    ans = window = input[0:window_size]
+    for right in range(window_size, len(input)):
+        left = right - window_size
+        remove input[left] from window
+        append input[right] to window
+        ans = optimal(ans, window)
+    return ans
+```
+
+<Steps>
+  <Step title="">
+  Add `nums[right]` to the window.
+  </Step>
+  <Step title="">
+    If the window has `k` elements, record the answer.
+  </Step>
+  <Step title="">
+    Remove the leftmost element so the window stays at size `k`.
+  </Step>
+</Steps>
+
+
+## 2. Flexible-size windows with a validity rule
+
+:::tip
+Here the window expands until invalid, then shrinks until valid again.
+:::
+
+<Frame caption="Sliding Window Flexible" hint="">
+
+![](/sliding-window-flexible.svg)
+
+</Frame>
+
+
+<Tabs inline>
+  <Tab title="Longest Window">
+
+```python
+def sliding_window_flexible_longest(input):
+    initialize window, ans
+    left = 0
+    for right in range(len(input)):
+        append input[right] to window
+        while invalid(window):        # update left until window is valid again
+            remove input[left] from window
+            left += 1
+        ans = max(ans, window)        # window is guaranteed to be valid here
+    return ans
+
+```
+
+  </Tab>
+  <Tab title="Shortest Window">
+
+```python
+def sliding_window_flexible_shortest(input):
+    initialize window, ans
+    left = 0
+    for right in range(len(input)):
+        append input[right] to window
+        while valid(window):
+            ans = min(ans, window)      # window is guaranteed to be valid here
+            remove input[left] from window
+            left += 1
+    return ans
+```
+
+  </Tab>
+</Tabs>
+
+<Steps>
+  <Step title="">
+  Add `nums[right]` to the window.
+  </Step>
+  <Step title="">
+    While the window is invalid, remove `nums[left]` and move `left` up.
+  </Step>
+  <Step title="">
+    The window is now valid. Record its size.
+  </Step>
+</Steps>
+
+---
+
+## 3. Frequency-tracking windows
+
+:::tip
+The difficulty comes from keeping the bookkeeping correct as characters enter and leave.
+:::
+
+
+<Frame caption="Frequency-tracking windows" hint="">
+
+![](/sliding-window-frequency.svg)
+
+</Frame>
+
+```python
+from collections import defaultdict
+
+def frequency_window(s):
+    left = 0
+    counts = defaultdict(int)
+    best = 0
+
+    for right in range(len(s)):
+        counts[s[right]] += 1                # character enters
+
+        while counts[s[right]] > 1:          # rule: no repeats
+            counts[s[left]] -= 1             # character leaves
+            left += 1
+
+        best = max(best, right - left + 1)
+
+    return best
+```
+
+<Steps>
+  <Step title="">
+  Add `s[right]` to the window.
+  </Step>
+  <Step title="">
+    While the window has more than one character, remove `s[left]` and move `left` up.
+  </Step>
+  <Step title="">
+    The window is now valid. Record its size.
+  </Step>
+</Steps>
+
+---
+
+For anagram or "minimum window substring" problems, you also keep a target count. Track how many characters currently match the target with one integer (`matched`). Update it only when a count crosses the target value. This keeps each step `O(1)`.
+
+```python
+def anagram_window(s, p):
+    need = defaultdict(int)
+    for c in p:
+        need[c] += 1
+
+    counts = defaultdict(int)
+    matched = 0                  # how many chars have counts[c] == need[c]
+    result = []
+    k = len(p)
+
+    for right in range(len(s)):
+        c = s[right]
+        counts[c] += 1
+        if counts[c] == need[c]:
+            matched += 1
+
+        if right >= k:                       # window too big, remove left
+            d = s[right - k]
+            if counts[d] == need[d]:
+                matched -= 1
+            counts[d] -= 1
+
+        if matched == len(need):
+            result.append(right - k + 1)
+
+    return result
+```
+