We use cookies (including Google cookies) to personalize ads and analyze traffic. By continuing to use our site, you accept our Privacy Policy.

SimplyLeet
TagsDisclaimersPrivacyTermsContactAbout Us

Make Array Empty

Difficulty: Hard

Problem Description

You are given an integer array nums containing distinct numbers, and you can perform the following operations until the array is empty:

  • If the first element has the smallest value, remove it.
  • Otherwise, put the first element at the end of the array.

Return an integer denoting the number of operations it takes to make nums empty.

Key Insights

  • The smallest element must be removed when it appears at the front of the array.
  • If the smallest element is not at the front, it must be moved to the end of the array until it reaches the front.
  • The number of operations required to make the array empty can be derived from the initial position of the smallest element and the order of elements.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can utilize a greedy approach with a simple traversal of the array. The key steps are:

  1. Identify the smallest element in the array and its index.
  2. Traverse the array to count how many operations are needed to remove each element:
    • Each element before the smallest element must be moved to the end of the array.
    • The smallest element will be removed when it reaches the front.
  3. The total number of operations is the sum of the number of moves and the number of removals.

This approach ensures that we are efficiently calculating the number of operations without needing to simulate the entire process.

Code Solutions

def makeArrayEmpty(nums):
    n = len(nums)
    min_value = min(nums)
    min_index = nums.index(min_value)
    
    # Total operations will be the length of the array plus the index of the minimum value
    return n + min_index

# Example usage
print(makeArrayEmpty([3, 4, -1]))  # Output: 5
print(makeArrayEmpty([1, 2, 4, 3]))  # Output: 5
print(makeArrayEmpty([1, 2, 3]))  # Output: 3
← Back to All Questions