2779.maximum-beauty-of-an-array-after-applying-operation.py

#  Tag: Array, Binary Search, Sliding Window, Sorting
#  Time: O(NlogN)
#  Space: O(1)
#  Ref: -
#  Note: -

#  You are given a 0-indexed array nums and a non-negative integer k.
#  In one operation, you can do the following:
#  
#  Choose an index i that hasn't been chosen before from the range [0, nums.length - 1].
#  Replace nums[i] with any integer from the range [nums[i] - k, nums[i] + k].
#  
#  The beauty of the array is the length of the longest subsequence consisting of equal elements.
#  Return the maximum possible beauty of the array nums after applying the operation any number of times.
#  Note that you can apply the operation to each index only once.
#  A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the order of the remaining elements.
#   
#  Example 1:
#  
#  Input: nums = [4,6,1,2], k = 2
#  Output: 3
#  Explanation: In this example, we apply the following operations:
#  - Choose index 1, replace it with 4 (from range [4,8]), nums = [4,4,1,2].
#  - Choose index 3, replace it with 4 (from range [0,4]), nums = [4,4,1,4].
#  After the applied operations, the beauty of the array nums is 3 (subsequence consisting of indices 0, 1, and 3).
#  It can be proven that 3 is the maximum possible length we can achieve.
#  
#  Example 2:
#  
#  Input: nums = [1,1,1,1], k = 10
#  Output: 4
#  Explanation: In this example we don't have to apply any operations.
#  The beauty of the array nums is 4 (whole array).
#  
#   
#  Constraints:
#  
#  1 <= nums.length <= 105
#  0 <= nums[i], k <= 105
#  
#  

class Solution:
    def maximumBeauty(self, nums: List[int], k: int) -> int:
        n = len(nums)
        nums.sort()
        i = 0
        res = 0
        for j in range(n):
            while nums[j] - nums[i] > 2 * k:
                i += 1

            res = max(res, j - i + 1)

        return res
    
class Solution:
    def maximumBeauty(self, nums: List[int], k: int) -> int:
        n = len(nums)
        nums.sort()
        i = 0
        for j in range(n):
            if nums[j] - nums[i] > 2 * k:
                i += 1

        return j - i + 1