Minimum Operations to Collect Elements - Video Solutions

Problem Overview: You are given an integer array nums and an integer k. Starting from the end of the array, you remove elements one by one. The goal is to collect every value from 1 to k at least once. The task is to return the minimum number of operations required to achieve this.

Approach 1: Reverse Collection (O(n) time, O(k) space)

The most direct strategy is to scan the array from right to left while collecting values between 1 and k. Maintain a set (or hash structure) that stores which required elements have been seen so far. Each step represents one operation since you are effectively removing an element from the end. When you encounter a value <= k, add it to the set. As soon as the set size becomes k, you have collected all required elements and can return the number of processed elements.

This approach works because removing elements from the end is equivalent to iterating the array in reverse. Hash lookups and insertions are constant time, so the overall complexity remains linear. The method relies on basic array traversal combined with fast membership checks using a hash table.

Approach 2: Decremental Loop Through the Array (O(n) time, O(k) space)

Another implementation tracks how many required elements are still missing instead of storing them all explicitly. Start with a counter remaining = k and a boolean array (or bitmask) to mark which values from 1..k have been collected. Traverse the array from the end and check each value. If the number is within the required range and hasn't been seen before, mark it and decrement remaining.

Once remaining reaches zero, you have collected all elements and can return the number of operations performed. This version replaces a dynamic set with a fixed-size tracking structure, which can also be implemented using bit manipulation for very compact state tracking.

The logic remains the same as the previous approach: iterate backward, track required values, and stop once every number from 1 to k appears. Both solutions run in linear time and scan the array only once.

Recommended for interviews: The reverse traversal with a hash set is the clearest explanation and easiest to implement under time pressure. It demonstrates understanding of array traversal and constant‑time lookups. The decremental tracking version is slightly more optimized and shows stronger control over state management, but interviewers usually accept either once the reverse‑scan insight is explained.