algoadvance

You are given a non-negative integer array nums. In one operation, you must select a positive integer x such that x is less than or equal to the smallest non-zero element of nums, and subtract x from every positive element of nums. Return the minimum number of operations required to make every element in nums equal to 0.

Clarifying Questions

1. Can the input array be empty?
   • For this problem, we might assume the input array is not empty based on typical constraints unless specified otherwise.
2. Can the array contain any 0s initially?
   • Yes, the array can contain 0s as specified in the problem.
3. Is it guaranteed that all elements are non-negative?
   • Yes, the problem specifies that the array contains non-negative integers.

Strategy

1. Understand the Problem:
   • The primary goal is to determine the minimum number of operations required to convert all elements of the array to 0.
2. Insight:
   • Instead of focusing on the subtraction operations, observe that each subtraction operation will effectively reduce the number of distinct positive integers in the array.
   • Thus, each distinct positive integer in the array requires at least one operation to be converted to 0.
3. Steps to Solution:
   • Identify all distinct positive integers in the array.
   • The minimum number of operations is equal to the number of these distinct positive integers.

Code

def minimumOperations(nums):
    # Use a set to find all distinct positive integers
    distinct_positive_numbers = set(num for num in nums if num > 0)
    
    # The number of operations needed is the size of this set
    return len(distinct_positive_numbers)

Time Complexity

• Time Complexity: O(n)
  • Explanation: Constructing the set involves iterating through the array once, which takes O(n) time.
• Space Complexity: O(n)
  • Explanation: The space required for the set can be as large as the input size in the worst case where all elements are distinct and positive.

By using this approach, the problem is simplified to computing the size of a set of positive integers, which is efficient and straightforward.

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