algoadvance

You are given an array nums consisting of distinct positive integers and an integer maxValue. You are also given another integer threshold. You need to perform several operations to collect elements-out. In each operation, you can choose one still remaining element from the array and remove it.

You perform the above operations until there are no elements left in the array, but you can only remove elements in the range [threshold, maxValue].

Return the minimum number of operations required to remove all elements from the array.

Clarifying Questions

1. Range Inclusivity: Are the threshold and maxValue inclusive in the range of values that can be removed?
   • Assumption: Yes. [threshold, maxValue] is inclusive.
2. Distinct Integers: Elements in nums are distinct positive integers. Is this always true?
   • Assumption: Yes, the problem states this explicitly.
3. Range Validity: Can threshold be greater than maxValue and how should it be handled?
   • Assumption: I will assume for now that threshold will not be greater than maxValue.

Strategy

1. Traverse through the nums array and count how many elements fall within the inclusive range [threshold, maxValue].
2. The result will be the count of those elements, because all such elements will need to be removed by operations.

Code

def min_operations(nums, maxValue, threshold):
    count = 0
    for num in nums:
        if threshold <= num <= maxValue:
            count += 1
            
    return count

# Example usage:
nums = [1, 3, 7, 9, 2]
maxValue = 9
threshold = 4
print(min_operations(nums, maxValue, threshold)) # Output: 2

Walkthrough Example

For the input:

• nums = [1, 3, 7, 9, 2]
• maxValue = 9
• threshold = 4

The numbers within the range [4, 9] are 7 and 9, resulting in 2 operations.

Time Complexity

• Time Complexity: O(n), where n is the length of the nums list.
  • We traverse the list once to count the qualifying elements.
• Space Complexity: O(1), we are only using a constant amount of extra space.

This solution is efficient for the given problem constraints.

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