Minimum Number of Operations to Make Arrays Similar

Problem Description

You are given two positive integer arrays nums and target, of the same length. In one operation, you can choose any two distinct indices i and j and set nums[i] = nums[i] + 2 and nums[j] = nums[j] - 2. Two arrays are considered to be similar if the frequency of each element is the same. Return the minimum number of operations required to make nums similar to target.

Key Insights

• The goal is to match the frequency of each element in nums to that in target.
• The operations allow for incrementing one element by 2 while decrementing another by 2, which preserves the sum of the array.
• We can calculate the excess or deficit of each element after sorting both arrays.
• The number of operations is determined by the total excess divided by 2.

Space and Time Complexity

Time Complexity: O(n log n), due to the sorting of the arrays.
Space Complexity: O(n), for storing the differences.

Solution

To solve the problem, we will:

1. Sort both nums and target arrays.
2. Calculate the difference between the two arrays at each index.
3. Count the total surplus and deficit.
4. The number of operations required will be half of the total surplus, as each operation can adjust two units (one from surplus and one from deficit).

Code Solutions