Reduce Array Size to The Half

Problem Description

You are given an integer array arr. You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.

Key Insights

• The goal is to minimize the size of the set of integers chosen for removal.
• To achieve this, we should prioritize removing integers that appear most frequently in the array.
• By sorting the integers based on their frequency, we can efficiently determine the minimum number of unique integers needed to reach the target of removing at least half of the array's size.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the frequency of elements.
Space Complexity: O(n) - for storing the frequency count.

Solution

To solve the problem, we can use the following steps:

1. Count the frequency of each integer in the array using a hash table (or dictionary).
2. Store the frequencies in a list and sort this list in descending order.
3. Initialize a counter for the total removed elements and a counter for the number of unique integers chosen for removal.
4. Iterate through the sorted list of frequencies, adding frequencies to the total removed until at least half of the original array size is removed.
5. Return the count of the unique integers chosen.

Code Solutions