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chore: clean up content phase organization
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---
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title: '121. Best Time to Buy and Sell Stock'
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description: You are given an array prices where prices[i] is the price of a given stock on the i^th day
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sidebar:
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label: 'Best Time to Buy and Sell Stock'
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badge: 'Easy'
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---
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<Badge variant="accent">Array</Badge>
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### Example 1:
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- Input: `prices = [7,1,5,3,6,4]`
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- Output: `5`
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- 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.
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### Example 2:
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- Input: `prices = [7,6,4,3,1]`
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- Output: `0`
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- Explanation: In this case, no transactions are done and the max profit = `0`.
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### Constraints:
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- `1 <= prices.length <= 10^5`
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- `0 <= prices[i] <= 10^4`
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## Approach
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::::warning
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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.
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::::
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```mermaid
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flowchart TD
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S(["maxProfit(prices)"]) --> I["left = min(prices)"]
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I --> F{"more right in range(len(prices))?"}
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F -- no --> E(["return ans"])
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F -- yes --> W{"curr > left?"}
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W -- yes --> P["curr -= prices[left]; left += 1"]
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P --> W
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W -- no --> M["ans = max(ans, curr)"]
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M --> F
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```
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## Solution
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```py
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class Solution:
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def maxProfit(self, prices: List[int]) -> int:
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left = min(prices)
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for right in range(len(prices)):
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while curr > left:
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curr -= prices[left]
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left += 1
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ans = max(ans, curr)
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return ans
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```
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## Explanation
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<YouTube id="1pkOgXD63yU" title="Sliding Window: Best Time to Buy and Sell Stock - Leetcode 121 - Python" />
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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">Hash Table</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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## Approach
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```mermaid
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flowchart TD
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S(["lengthOfLongestSubstring(s)"]) --> I["left = 0, ans = 0, window = set()"]
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I --> L{"more (right, c) in s?"}
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L -- no --> E(["return ans"])
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L -- yes --> W{"c already in window?"}
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W -- yes --> P["window.remove(s[left]); left += 1 — shrink until c is free"]
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P --> W
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W -- no --> A["window.add(c)"]
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A --> M["ans = max(ans, right - left + 1)"]
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M --> L
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```
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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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window = set()
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for right, c in enumerate(s):
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while c in window:
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window.remove(s[left])
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left += 1
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window.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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## Explanation
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<YouTube id="wiGpQwVHdE0" title="Longest Substring Without Repeating Characters - Leetcode 3 - Python" />
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---
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title: '424. Longest Repeating Character Replacement'
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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
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sidebar:
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label: 'Longest Repeating Character Replacement'
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badge: 'Medium'
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---
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<Badge variant="accent">Hash Table</Badge>
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### Example 1:
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- Input: `s = "ABAB", k = 2`
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- Output: `4`
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- Explanation: Replace the two 'A's with two 'B's or vice versa.
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### Example 2:
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- Input: `s = "AABABBA", k = 1`
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- Output: `4`
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- 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.
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### Constraints:
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- `1 <= s.length <= 10^5`
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- `s` consists of only uppercase English letters.
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- `0 <= k <= s.length`
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## Approach
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```mermaid
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flowchart TD
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S(["characterReplacement(s, k)"]) --> I["count = {}, res = 0, l = 0, maxF = 0"]
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I --> L{"more (r, c) in s?"}
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L -- no --> E(["return res"])
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L -- yes --> A["count[c] += 1; maxF = max(maxF, count[c])"]
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A --> W{"(r - l + 1) - maxF > k? — too many chars to replace"}
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W -- yes --> P["count[s[l]] -= 1; l += 1 — shrink from the left"]
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P --> W
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W -- no --> M["res = max(res, r - l + 1)"]
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M --> L
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```
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## Solution
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```py
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class Solution:
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def characterReplacement(self, s: str, k: int) -> int:
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count = {}
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res = 0
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l = 0
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maxF = 0
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for r, c in enumerate(s):
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count[c] = 1 + count.get(c, 0)
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maxF = max(maxF, count[c])
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while (r - l + 1) - maxF > k:
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count[s[l]] -= 1
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l += 1
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res = max(res, r - l + 1)
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return res
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```
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## Explanation
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<YouTube id="gqXU1UyA8pk" title="Longest Repeating Character Replacement - Leetcode 424 - Python" />
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---
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title: '567. Permutation in String'
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description: Given two strings s1 and s2, return true if s2 contains a permutation of s1, or false otherwise
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sidebar:
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label: 'Permutation in String'
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badge: 'Medium'
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---
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<Badge variant="accent">Hash Table</Badge>
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### Example 1:
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- Input: `s1 = "ab", s2 = "eidbaooo"`
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- Output: `true`
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- Explanation: `s2` contains one permutation of `s1` ("ba").
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### Example 2:
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- Input: `s1 = "ab", s2 = "eidboaoo"`
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- Output: `false`
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### Constraints:
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- `1 <= s1.length, s2.length <= 10^4`
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- `s1` and `s2` consist of lowercase English letters.
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## Approach
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```mermaid
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flowchart TD
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S(["checkInclusion(s1, s2)"]) --> G{"k = len(s1) > len(s2)?"}
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G -- yes --> X(["return False"])
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G -- no --> I["need = Counter(s1), window = Counter()"]
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I --> L{"more (right, c) in s2?"}
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L -- no --> E(["return False"])
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L -- yes --> A["window[c] += 1"]
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A --> B{"right >= k? — window is now longer than k"}
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B -- yes --> C["drop s2[right - k] from window, deleting the key at 0"]
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B -- no --> Q
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C --> Q{"window == need?"}
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Q -- yes --> R(["return True"])
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Q -- no --> L
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```
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## Solution
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```py
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from collections import Counter
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class Solution:
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def checkInclusion(self, s1: str, s2: str) -> bool:
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k = len(s1)
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if k > len(s2):
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return False
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need = Counter(s1)
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window = Counter()
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for right, c in enumerate(s2):
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window[c] += 1
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if right >= k:
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left_char = s2[right - k]
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window[left_char] -= 1
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if window[left_char] == 0:
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del window[left_char]
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if window == need:
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return True
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return False
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```
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## Explanation
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<YouTube id="UbyhOgBN834" title="Permutation in String - Leetcode 567 - Python" />
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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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hidden: true
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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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import { defineMeta } from "blume";
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export default defineMeta({ title: "Sliding Window", order: 4, icon: "app-window", display: "group" });
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