Number of Distinct Averages

You have a list of even-length integers, and you are required to find the minimum and maximum numbers in the list repeatedly, remove them, and then calculate the average of those two numbers. You have to continue this process until the list becomes empty. The task is to count the number of distinct averages you have calculated during this process.

Solution

We can use a set data structure to store the distinct averages, as sets do not allow duplicate values.

Here’s the step-by-step guide to solving this problem:

  1. Sort the List: Sort the list of numbers. This helps in easily finding the minimum and maximum numbers, which will be at the start and end of the sorted list, respectively.

  2. Initialize a Set: Create an empty set to store the distinct averages.

  3. Calculate Averages: Iterate through half the length of the list (since we are removing two numbers at each step) and calculate the averages by taking the smallest and largest numbers from the list. Add each average to the set.

  4. Find Distinct Averages: The number of distinct averages will be equal to the size of the set, as a set only stores unique values.

Code

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class Solution:
    def distinctAverages(self, nums: List[int]) -> int:
        # Step 1: Sort the list
        nums.sort()

        # Step 2: Initialize a set to store distinct averages
        distinct_avg_set = set()

        # Step 3: Iterate through the list and calculate averages
        for i in range(len(nums)//2):
            min_num = nums[i]  # Minimum number
            max_num = nums[-i-1]  # Maximum number
            avg = (min_num + max_num) / 2  # Average of min and max numbers

            # Add the average to the set
            distinct_avg_set.add(avg)

        # Step 4: Return the number of distinct averages
        return len(distinct_avg_set)

Key Takeaways

  • Sorting the list helps us easily access the minimum and maximum numbers.
  • Using a set allows us to keep track of distinct averages efficiently.
  • The final answer is the number of unique values in the set, representing the distinct averages.