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Minimum Operations to Collect Elements

Number: 3044

Difficulty: Easy

Paid? No

Companies: Deutsche Bank

Problem Description

Given an array of positive integers nums and an integer k, you need to collect the numbers 1, 2, ..., k using a series of operations. In each operation, you remove the last element from the array and add it to your collection. The goal is to determine the minimum number of operations required so that your collection contains all elements from 1 to k.

Key Insights

  • The removal of elements can only be done from the end of the array.
  • You need to collect a specific set of numbers (1 through k).
  • A reverse traversal of the array will allow us to simulate the removal process and count operations until all required numbers are collected.
  • Since the array length is small (up to 50 elements), a simple linear scan is efficient.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the array, since we may need to scan through the entire array. Space Complexity: O(k), for the set used to keep track of the collected required numbers.

Solution

We solve the problem by simulating the removal process from the end of the array towards the beginning. We initialize an empty set to keep track of collected numbers (only the numbers in the range 1 to k are relevant). We iterate backwards through the array while counting the number of removals until the collected set contains all numbers from 1 to k. Once the set's size equals k, we return the count of operations performed.

Code Solutions

# Python solution
def minimumOperations(nums, k):
    # Set to store required collected numbers
    collected = set()
    operations = 0
    # Iterate backwards from the end of the array
    for num in reversed(nums):
        operations += 1  # Simulate an operation (removal)
        # Only add numbers that are required (1 through k)
        if 1 <= num <= k:
            collected.add(num)
        # Check if we have collected all required numbers
        if len(collected) == k:
            return operations
    return operations  # This line is redundant given the problem constraints

# Example usage
print(minimumOperations([3,1,5,4,2], 2))  # Expected output: 4
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