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Maximum Size of a Set After Removals

Difficulty: Medium

Problem Description

You are given two 0-indexed integer arrays nums1 and nums2 of even length n. You must remove n / 2 elements from nums1 and n / 2 elements from nums2. After the removals, you insert the remaining elements of nums1 and nums2 into a set s. Return the maximum possible size of the set s.

Key Insights

  • The main goal is to maximize the number of unique elements in the final set after removing elements from both arrays.
  • Removing duplicates from both arrays can help maximize the size of the resulting set.
  • The constraints require careful consideration of how many elements to remove to ensure the maximum number of unique elements remain.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve this problem, we can use a greedy approach. The idea is to count the frequency of each number in both arrays using a hash table (or dictionary). Then, we determine how many unique elements we can keep after removing half of the elements from each array.

  1. Count the frequency of each number in both arrays.
  2. Calculate the number of unique elements available in both arrays.
  3. Depending on the number of unique elements, decide how many elements can be kept after removals.

This approach ensures that we effectively maximize the size of the set by carefully selecting which elements to remove.

Code Solutions

def maxSize(nums1, nums2):
    from collections import Counter

    count1 = Counter(nums1)
    count2 = Counter(nums2)

    unique1 = len(count1)
    unique2 = len(count2)

    # Total unique elements after removing n/2 from both
    total_unique = unique1 + unique2

    # Number of elements we need to remove from both arrays
    remove_count = len(nums1) // 2

    # The maximum size of the set s we can achieve
    return min(total_unique, len(nums1) + len(nums2) - remove_count)
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