Minimum Operations to Collect Elements

Problem Description

You are given an array nums of positive integers and an integer k. In one operation, you can remove the last element of the array and add it to your collection. Return the minimum number of operations needed to collect elements 1, 2, ..., k.

Key Insights

• You can only collect elements by removing them from the end of the array.
• The goal is to ensure you have all integers from 1 to k in your collection.
• The order of collection matters; you need to track which elements have been collected as you remove elements from the end.

Space and Time Complexity

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

Solution

To solve this problem, we can use a set to keep track of the collected elements. We iterate through the nums array from the end to the beginning, counting the number of operations needed to collect all elements from 1 to k. We stop the iteration once we have collected all required elements.

1. Initialize a set to track collected elements.
2. Start from the last element of nums and remove elements one by one.
3. For each removed element, add it to the set of collected elements.
4. Continue until the set contains all elements from 1 to k.
5. The number of operations is equivalent to the number of elements removed.

Code Solutions