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Number of Distinct Averages

Difficulty: Easy

Problem Description

You are given a 0-indexed integer array nums of even length. As long as nums is not empty, you must repetitively:

  1. Find the minimum number in nums and remove it.
  2. Find the maximum number in nums and remove it.
  3. Calculate the average of the two removed numbers.

Return the number of distinct averages calculated using the above process.

Key Insights

  • The problem requires repeatedly finding the minimum and maximum values, which can be efficiently handled with sorting.
  • Since the values can be removed in any order (due to ties), distinct averages can be tracked using a set.
  • The average of two numbers is straightforward to calculate: (a + b) / 2.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array. Space Complexity: O(n) - if we consider the space used for storing distinct averages in a set.

Solution

To solve the problem, we can follow these steps:

  1. Sort the array nums.
  2. Use a loop to pair the smallest and largest elements, calculate their average, and store it in a set to ensure uniqueness.
  3. Continue this process until all elements in nums are processed.
  4. Finally, the size of the set will give the number of distinct averages.

We utilize sorting to simplify the process of finding minimum and maximum values efficiently, and a set to track distinct averages.

Code Solutions

def distinct_averages(nums):
    nums.sort()  # Sort the array
    distinct_averages_set = set()  # Set to store distinct averages

    # Iterate until we reach the middle of the sorted array
    for i in range(len(nums) // 2):
        avg = (nums[i] + nums[-(i + 1)]) / 2  # Calculate average of min and max
        distinct_averages_set.add(avg)  # Add to the set for uniqueness

    return len(distinct_averages_set)  # Return the count of distinct averages
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