#3371

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Identify the Largest Outlier in an Array

Identify the largest outlier in an integer array using scanning and hash lookup for efficient detection and validation.

Problem Statement

You are given an integer array nums containing n elements. Exactly n - 2 elements are considered special numbers, one element is the sum of these special numbers, and the remaining element is an outlier. Your task is to determine which element is the largest outlier.

An outlier is defined as a number that is neither a special number nor the sum element. All elements have distinct indices, but values may repeat. Identify the number that breaks the sum pattern and is the largest among any potential outliers.

Examples

Example 1

Input: nums = [2,3,5,10]

Output: 10

The special numbers could be 2 and 3, thus making their sum 5 and the outlier 10.

Example 2

Input: nums = [-2,-1,-3,-6,4]

Output: 4

The special numbers could be -2, -1, and -3, thus making their sum -6 and the outlier 4.

Example 3

Input: nums = [1,1,1,1,1,5,5]

Output: 5

The special numbers could be 1, 1, 1, 1, and 1, thus making their sum 5 and the other 5 as the outlier.

Constraints

3 <= nums.length <= 105
-1000 <= nums[i] <= 1000
The input is generated such that at least one potential outlier exists in nums.

Solution Approach

Scan and Hash

Iterate through nums and maintain a hash table to count occurrences. Use the hash table to quickly check potential sums against other elements, allowing you to detect which number does not fit the sum pattern.

Sum Verification

Compute the total sum of the array and test each candidate as the potential outlier. Subtract each candidate and check if the remaining sum matches any combination of n - 2 elements. This confirms the outlier efficiently.

Return Largest Outlier

If multiple numbers qualify as outliers, select the largest one. This ensures correctness in arrays with repeated values or multiple candidates while adhering to the problem's constraints.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity depends on iterating the array and verifying sums, typically O(n^2) without optimization but can be reduced to O(n) with hash-based lookups. Space complexity is O(n) for storing counts in a hash table.

What Interviewers Usually Probe

They may emphasize the array sum pattern to check your understanding of outlier detection.
Expect questions on optimizing the brute force check using hash maps or counting arrays.
They might hint at arrays with repeated values to test your handling of edge cases.

Common Pitfalls or Variants

Common pitfalls

Assuming all numbers are distinct and ignoring repeated values that affect the sum.
Failing to correctly identify the sum element versus the outlier during verification.
Using inefficient nested loops without leveraging a hash table, causing timeouts for large arrays.

Follow-up variants

Return the smallest outlier instead of the largest in arrays with repeated candidates.
Handle arrays where more than one outlier exists and return all valid outliers.
Given negative numbers, find the largest outlier while ensuring sum calculations handle negatives correctly.

FAQ

What is the main approach to Identify the Largest Outlier in an Array?

Use array scanning with a hash table to track counts and verify sum relationships, allowing fast identification of the outlier.

Can the array contain repeated values?

Yes, repeated values may exist, and the solution must account for duplicates when verifying sums and detecting outliers.

What should I return if multiple numbers qualify as outliers?

Return the largest number among the potential outliers according to the problem requirements.

How does using a hash table help in this problem?

A hash table allows O(1) lookups to check whether the remaining sum matches potential combinations, reducing time complexity.

What edge cases should I watch for?

Watch for negative numbers, repeated values, and arrays where the sum element and outlier have the same value but different indices.

terminal

Solution

Solution 1: Hash Table + Enumeration

We use a hash table $\textit{cnt}$ to record the frequency of each element in the array $\textit{nums}$.

1

2

3

4

5

6

7

8

9

10

11

12

class Solution:
    def getLargestOutlier(self, nums: List[int]) -> int:
        s = sum(nums)
        cnt = Counter(nums)
        ans = -inf
        for x, v in cnt.items():
            t = s - x
            if t % 2 or cnt[t // 2] == 0:
                continue
            if x != t // 2 or v > 1:
                ans = max(ans, x)
        return ans

Continue Practicing

#3267 count almost equal pairs ii #3265 count almost equal pairs i #3044 most frequent prime