Minimum Number of Operations to Make Arrays Similar - Video Solutions

Problem Overview: You are given two integer arrays nums and target. In one operation, you can choose two indices in nums, add 2 to one element and subtract 2 from the other. The goal is to transform nums so it becomes similar to target, meaning both arrays contain the same multiset of values. The task is to compute the minimum number of operations required.

Approach 1: Greedy Approach with Sorting (O(n log n) time, O(n) space)

The key observation: adding or subtracting 2 never changes the parity of a number. Odd numbers must match with odd numbers, and even numbers must match with even numbers. Split both arrays into two groups based on parity. Sort the odd elements of nums and target, and do the same for the even elements. Then compare corresponding elements and accumulate the positive differences. Each operation effectively shifts 2 units between elements, so the total difference divided appropriately gives the operation count. Sorting ensures the smallest values match first, which minimizes total adjustment. This approach uses classic greedy matching combined with sorting to minimize unnecessary adjustments.

Approach 2: Frequency Matching by Counting and Remainder Groups (O(n log n) or O(n) time depending on map usage, O(n) space)

Another perspective is to track how much adjustment each element requires relative to its matching parity group. Separate elements into odd and even buckets, then sort or frequency-count them. Compute the difference between each pair of corresponding elements. Only positive differences matter because decreases are balanced by increases elsewhere due to the operation structure. Each increase of 2 contributes toward the total operation count. Instead of directly simulating operations, aggregate the total increments needed and divide by 2. Using counting or frequency maps reduces repeated scanning when many values repeat. This approach still relies on the parity constraint but focuses on difference aggregation rather than pairwise greedy matching.

Recommended for interviews: The greedy sorting approach is the expected solution. It clearly shows you recognize the invariant that parity never changes and that matching sorted parity groups minimizes adjustment cost. Interviewers usually want to see the reasoning about parity first, then a clean greedy implementation using arrays or lists. Understanding the parity constraint comes from analyzing the allowed operation on the array, which is the core trick behind this hard problem.