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  1. Problem Statement (Simple Explanation) You’re given: A  rotated  array nums that was originally sorted in  non-decreasing  order. The array may contain  duplicates . An integer target. You must return: true if target exists in nums false otherwise. Rotation: Original sorted: e.g. [0,1,2,4,4,4,5,6,6,7] Rotated at pivot k: e.g. [4,5,6,6,7,0,1,2,4,4] Goal: Decrease operations as much as possible (use a  modified binary search ). 2. Examples Example 1: Input: nums = [2,5,6,0,0,1,2], target = 0 0 is in the array. Output: true Example 2: Input: nums = [2,5,6,0,0,1,2], target = 3 3 is not in the array. Output: false 3. Approach – Modified Binary Search (with duplicates) This is similar to  LeetCode 33  but now nums may contain  duplicates . Without duplicates: At each step we could tell which half is sorted and then decide which side to search. With duplicates, ...

You need to  reorder  the array into some permutation B such that for every i: ∣ B i - B i+1 ∣≤1 We must decide if such a permutation exists. Key Insight If we  sort  the array to get C (non-decreasing order): In the sorted array, adjacent numbers are as close as possible. Any other permutation can only make  some adjacent differences bigger , never smaller. So: If the  sorted  array already has some adjacent pair with difference > 1, then  no permutation  can satisfy the condition. If the sorted array has  all  adjacent differences ≤ 1, then the sorted array itself is a valid permutation. Therefore, the check is simple: Sort the array. Check all adjacent pairs: If for any i, C[i+1] - C[i] > 1 → print NO. Otherwise → print YES. Algorithm For each test case: Read N and array A. Sort A. For i from 0 to N-2: If A[i+1] - A...

  1. Problem Statement (Simple Explanation) You’re given a  sorted  integer array nums (non-decreasing). You must: Remove extra duplicates  in-place  so that  each unique value appears at most twice . Keep the  relative order  of elements. Put the result in the  first k positions  of nums. Return k (the new length). Anything beyond index k-1 can be ignored. Constraints: Do it in-place,  O(1)  extra memory. nums length up to 3 * 10 4 . 2. Examples Example 1: Input: nums = [1,1,1,2,2,3] Allowed counts: at most 2 of each number. Output: k = 5 nums becomes [1,1,2,2,3,_] (the _ denote “don’t care”). Explanation: 1 appears 3 times → keep 2. 2 appears 2 times → keep 2. 3 appears 1 time → keep 1. Example 2: Input: nums = [0,0,1,1,1,1,2,3,3] Output: k = 7 First 7 elements: [0,0,1,1,2,3,3,_,_] Explanation: 0 → keep [0,0] 1...