Find the Biggest Single Number

Given a list of numbers, identify the largest number that appears only once in the list. This is a common task in data analysis and programming, useful for filtering out noise or identifying unique occurrences within a dataset.

Problem Description

Your task is to write a function that accepts a list of integers and returns the largest integer that appears exactly once in the list. If no number appears exactly once, the function should return a specific indicator (e.g., -1 or null, depending on typical programming language conventions).

Key Requirements:

• Iterate through the input list to count the occurrences of each number.
• Identify numbers that have a count of exactly one.
• From these unique numbers, determine and return the largest one.

Expected Behavior:

• If multiple numbers appear only once, return the maximum among them.
• If no number appears only once, return -1.

Edge Cases to Consider:

• An empty input list.
• A list where all numbers appear more than once.
• A list with only one element.
• A list with negative numbers.

Examples

Example 1:

Input: [5, 7, 3, 9, 4, 9, 5, 1, 3]
Output: 7
Explanation:
- 5 appears 2 times.
- 7 appears 1 time.
- 3 appears 2 times.
- 9 appears 2 times.
- 4 appears 1 time.
- 1 appears 1 time.
The numbers that appear only once are 7, 4, and 1. The largest among them is 7.

Example 2:

Input: [1, 2, 3, 2, 1, 4]
Output: 4
Explanation:
- 1 appears 2 times.
- 2 appears 2 times.
- 3 appears 1 time.
- 4 appears 1 time.
The numbers that appear only once are 3 and 4. The largest among them is 4.

Example 3:

Input: [1, 1, 2, 2, 3, 3]
Output: -1
Explanation: All numbers in the list appear more than once. Therefore, there is no single number, and we return -1.

Constraints

• The input list will contain integers.
• The size of the input list will be between 0 and 10^5.
• The values of the integers in the list will be between -10^9 and 10^9.
• Your solution should aim for an efficient time complexity, ideally O(n) or O(n log n), where n is the number of elements in the input list.

Notes

Consider using a data structure that allows for efficient counting of element occurrences. Think about how to keep track of the maximum unique number found so far as you process the input. The return value of -1 is a convention for when no such number exists; adjust this if your programming environment has a different preferred way to indicate "not found" (e.g., null or an exception).