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Identify the Largest Outlier in an Array

Difficulty: Medium

Problem Description

You are given an integer array nums. This array contains n elements, where exactly n - 2 elements are special numbers. One of the remaining two elements is the sum of these special numbers, and the other is an outlier. An outlier is defined as a number that is neither one of the original special numbers nor the element representing the sum of those numbers. Return the largest potential outlier in nums.

Key Insights

  • The array contains n - 2 special numbers, one sum of those numbers, and one outlier.
  • The outlier is not among the special numbers or their sum.
  • The task is to find the largest outlier, which may require examining the sum and the special numbers.

Space and Time Complexity

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

Solution

To solve the problem, we can use a hash table (or dictionary) to count the occurrences of each number in the array. We will identify the two largest unique numbers and calculate their potential sum. We then look for the largest number in the array that does not match either the sum or the identified special numbers. This approach allows us to efficiently find the outlier.

Code Solutions

def largest_outlier(nums):
    from collections import Counter
    count = Counter(nums)
    
    # Identify the two largest unique numbers
    unique_nums = sorted(count.keys())
    
    if len(unique_nums) < 3:
        return None  # Not enough unique numbers to find an outlier
    
    # The last two values are the potential special numbers
    special1, special2 = unique_nums[-1], unique_nums[-2]
    potential_sum = special1 + special2
    
    # Find the largest number in nums that is neither the sum nor the special numbers
    outlier = float('-inf')
    for num in nums:
        if num != potential_sum and num != special1 and num != special2:
            outlier = max(outlier, num)
    
    return outlier
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