Minimum Number of Operations to Make Elements in Array Distinct

Minimum Number of Operations to Make Elements in Array Distinct

1. What is this problem about?

The Minimum Number of Operations to Make Elements in Array Distinct coding problem is an "Easy" simulation task. You are given an array and can perform one type of operation: remove the first 3 elements of the array. You need to find the minimum number of such operations required until all remaining elements in the array are distinct (unique).

2. Why is this asked in interviews?

This question is a standard "warm-up" for companies like Microsoft and Meta. It tests if a candidate can handle basic array slicing and frequency checking. It also evaluates if you can identify the "stopping condition" efficiently—specifically, checking for duplicates from the end of the array to find where the "collision" happens.

3. Algorithmic pattern used

The problem falls under the Array, Hash Table interview pattern. A naive approach is to repeatedly remove 3 elements and check the remaining set for duplicates. However, a more efficient way is to iterate from the back of the array to find the first index i that has appeared before. Any element at or before this index must be removed. Since we remove in chunks of 3, the answer is ceil((i + 1) / 3).

4. Example explanation

Array: [1, 2, 3, 4, 2, 5, 6]

1. From back: 6(U), 5(U), 2(U), 4(U), 3(U), 2(Duplicate!)
2. The duplicate '2' is at index 4 (0-indexed).
3. We must remove everything up to index 4.
4. Number of elements to remove = 5.
5. In chunks of 3:
   • Op 1: removes indices 0, 1, 2.
   • Op 2: removes indices 3, 4, 5. Result: 2 operations.

5. Common mistakes candidates make

The most common mistake is not handling the case where the array is already distinct (return 0). Another error is over-complicating the removal process—some might actually modify the array in a loop, which is less efficient than just finding the index of the "leftmost" duplicate.

6. Interview preparation tip

For "Easy" problems involving uniqueness, always think about using a Set or a Hash Table. Also, whenever a problem involves removing from the front, consider if analyzing the array from the back provides a faster way to find the boundary of the required operations.