What is the time complexity of Maximum Beauty of an Array After Applying Operation?

The optimal solution for Maximum Beauty of an Array After Applying Operation runs in O(n log n) time and uses O(1) space. The sorting step dominates the time complexity, making it O(n log n), while we only use a constant amount of extra space.

What is the brute force solution for Maximum Beauty of an Array After Applying Operation?

The brute force approach for Maximum Beauty of an Array After Applying Operation is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible subsequence to find the longest one that can be made equal after applying the allowed operations. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Beauty of an Array After Applying Operation?

Maximum Beauty of an Array After Applying Operation uses the following concepts: Array, Binary Search, Sliding Window, Sorting. The recommended patterns to study are: Sliding Window, Sorting.

What are the interview tips for Maximum Beauty of an Array After Applying Operation?

Always consider sorting the input if you need to compare ranges or find subsequences. Practice implementing the sliding window technique, as it's common in array problems. Think about edge cases, such as when k is 0 or when all elements are the same.

What are common mistakes when solving Maximum Beauty of an Array After Applying Operation?

Failing to sort the array before applying the two-pointer technique. Not correctly managing the left pointer when the condition is violated.

#2779

Maximum Beauty of an Array After Applying Operation

Medium

ArrayBinary SearchSliding WindowSortingSliding WindowSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

By sorting the array and using a sliding window approach, we can efficiently find the longest subsequence where the difference between the maximum and minimum values is within the allowed range after operations.

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Algorithm

5 steps

1Step 1: Sort the array.
2Step 2: Use two pointers (left and right) to represent the current window of elements.
3Step 3: Expand the right pointer until the condition nums[right] - nums[left] > 2 * k is violated.
4Step 4: Calculate the length of the current valid window and update the maximum length.
5Step 5: Move the left pointer to shrink the window if necessary.

solution.py11 lines

1# Full working Python code
2
3def max_beauty_optimal(nums, k):
4    nums.sort()
5    left = 0
6    max_length = 0
7    for right in range(len(nums)):
8        while nums[right] - nums[left] > 2 * k:
9            left += 1
10        max_length = max(max_length, right - left + 1)
11    return max_length

ℹ

Complexity note: The sorting step dominates the time complexity, making it O(n log n), while we only use a constant amount of extra space.

1Sorting the array allows us to easily check the range of values that can be made equal.
2Using a sliding window helps efficiently find the longest valid subsequence without unnecessary checks.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.