Is Minimum Operations to Make Subarray Elements Equal easy or hard?

Minimum Operations to Make Subarray Elements Equal is considered a Medium difficulty problem. The challenge comes from combining sliding window mechanics with dynamic median maintenance and efficient cost calculation.

Minimum Operations to Make Subarray Elements Equal Python/Java solution

In Python, the solution typically uses two heaps with lazy deletion or a balanced structure like SortedList. In Java and C++, developers often use priority queues or ordered multisets to maintain the two halves of the window and compute costs efficiently.

What is the best approach for Minimum Operations to Make Subarray Elements Equal?

The best approach uses a sliding window of size k combined with median maintenance using two heaps or an ordered multiset. The median minimizes the total absolute difference required to make all elements equal. By maintaining the median while the window slides, you can compute the cost in O(log k) per step, resulting in O(n log k) total time.

Is Minimum Operations to Make Subarray Elements Equal asked at Google/Amazon/Meta?

Problems involving sliding window medians and minimizing absolute differences appear frequently in interviews at companies like Google, Amazon, and Meta. Variants include maintaining a running median or minimizing operations using the median property.

What data structure is used in Minimum Operations to Make Subarray Elements Equal?

The optimal implementation uses two heaps (a max heap and a min heap) or an ordered multiset. These structures allow efficient median tracking and O(log k) insertion and deletion as the sliding window moves.

What is the time complexity of Minimum Operations to Make Subarray Elements Equal?

The optimal solution runs in O(n log k) time and O(k) space. Each sliding window update inserts and removes one element from a balanced structure such as heaps or an ordered set, both of which require O(log k) time.

Description Hints 3 Solution

3422. Minimum Operations to Make Subarray Elements Equal

Q: How to solve Minimum Operations to Make Subarray Elements Equal in O(n log k)?

Maintain a sliding window of length k and keep the median using two heaps (max heap for the lower half and min heap for the upper half). Track the sum of elements in both halves so the cost relative to the median can be computed quickly. When the window moves, insert the new element, remove the outgoing element, rebalance the heaps, and recompute the cost.

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You are given an integer array nums and an integer k. You can perform the following operation any number of times:

Increase or decrease any element of nums by 1.

Return the minimum number of operations required to ensure that at least one subarray of size k in nums has all elements equal.

Example 1:

Input: nums = [4,-3,2,1,-4,6], k = 3

Output: 5

Explanation:

Use 4 operations to add 4 to nums[1]. The resulting array is [4, 1, 2, 1, -4, 6].
Use 1 operation to subtract 1 from nums[2]. The resulting array is [4, 1, 1, 1, -4, 6].
The array now contains a subarray [1, 1, 1] of size k = 3 with all elements equal. Hence, the answer is 5.

Example 2:

Input: nums = [-2,-2,3,1,4], k = 2

Output: 0

Explanation:

The subarray [-2, -2] of size k = 2 already contains all equal elements, so no operations are needed. Hence, the answer is 0.

Constraints:

2 <= nums.length <= 10⁵
-10⁶ <= nums[i] <= 10⁶
2 <= k <= nums.length

Topics

Array Hash Table Heap (Priority Queue)Math Sliding Window

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Hint 1

It can be proven that for each subarray of size k, one optimal common value is the median.

Hint 2

Use 2 multisets to maintain the median dynamically.

Hint 3

Calculate the sums of the 2 multisets dynamically to accelerate the answer calculation.

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3422. Minimum Operations to Make Subarray Elements Equal

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