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Minimum Operations to Exceed Threshold Value I

Difficulty: Easy

Problem Description

You are given a 0-indexed integer array nums, and an integer k. In one operation, you can remove one occurrence of the smallest element of nums. Return the minimum number of operations needed so that all elements of the array are greater than or equal to k.

Key Insights

  • The task involves removing the smallest elements from the array until all remaining elements meet or exceed the threshold k.
  • Sorting the array helps to efficiently determine which elements need to be removed.
  • The count of operations corresponds to the number of elements in the sorted array that are less than k.

Space and Time Complexity

Time Complexity: O(n log n) - due to the sorting of the array. Space Complexity: O(1) - as we are using in-place operations on the array.

Solution

To solve this problem, we will:

  1. Sort the given array to easily access the smallest elements.
  2. Traverse the sorted array and count how many elements are less than k.
  3. The count will represent the minimum number of operations needed to ensure all remaining elements are greater than or equal to k.

Code Solutions

def min_operations(nums, k):
    # Sort the array to easily access the smallest elements
    nums.sort()
    
    # Initialize the operation count
    operations = 0
    
    # Count elements less than k
    for num in nums:
        if num < k:
            operations += 1
        else:
            break  # No need to continue once we hit an element >= k
    
    return operations
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