Minimum Number of Operations to Make Elements in Array Distinct

Problem Description

You are given an integer array nums. You need to ensure that the elements in the array are distinct. To achieve this, you can perform the following operation any number of times:

• Remove 3 elements from the beginning of the array. If the array has fewer than 3 elements, remove all remaining elements.

Note that an empty array is considered to have distinct elements. Return the minimum number of operations needed to make the elements in the array distinct.

Key Insights

• The goal is to remove elements in groups of three until all remaining elements are distinct.
• An empty array is considered distinct, meaning we can stop operations once we reach an empty array or an array with all distinct elements.
• The problem can be approached by checking duplicates in the array and calculating how many operations are required to remove them.

Space and Time Complexity

Time Complexity: O(n) - where n is the length of the array, as we will traverse it to identify duplicates.

Space Complexity: O(n) - in the worst case, we may need additional space to store the counts of elements.

Solution

To solve this problem, we can use a hash table (or dictionary) to count the occurrences of each element in the array. After that, we'll determine how many operations are needed to remove enough elements to ensure that only distinct elements remain. The algorithm follows these steps:

1. Create a dictionary to count the occurrences of each element in nums.
2. For each element in the dictionary, if it appears more than once, count how many additional elements need to be removed.
3. Calculate the number of operations needed based on the total number of elements that need to be removed (removing 3 elements per operation).
4. Return the total number of operations.

Code Solutions