Minimum Operations to Make Array Values Equal to K - Solution & Explanation

Problem Overview: You are given an integer array nums and a target value k. The goal is to determine the minimum number of operations needed so every element becomes exactly k. An operation effectively eliminates a value greater than k by converting all occurrences of that value to k. If any number is already smaller than k, the task becomes impossible because operations only reduce larger values to k.

Approach 1: Hash Set to Track Distinct Values ( O(n) time, O(n) space )

Start by scanning the array once. If you encounter any value smaller than k, immediately return -1 because no valid operation can increase values. For values greater than k, insert them into a set (or hash table). Each distinct value greater than k represents one required operation, since the operation reduces that specific value to k for all its occurrences. After processing the array, the answer equals the number of unique elements stored in the set.

The key insight: multiple occurrences of the same value can be handled in a single operation. Only the number of distinct values above k matters. A hash table or set provides constant‑time insertion and membership checks, making the solution linear.

Implementation is straightforward: iterate through the array, validate values relative to k, and track distinct values larger than k. Languages like Python, Java, and C++ all provide efficient built‑in hash set structures.

Recommended for interviews: The hash‑set approach is the expected solution. Interviewers want to see that you recognize two constraints quickly: values smaller than k make the task impossible, and duplicate values above k should only count once. Explaining this observation shows strong reasoning about hash-based deduplication and linear scans. Brute‑force counting without deduplication leads to incorrect results, so identifying the need for a set demonstrates the key insight.