What is the optimal time complexity of solving Find The Duplicate Number?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Find The Duplicate Number?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Find The Duplicate Number?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Find The Duplicate Number?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Find The Duplicate Number

Learn how to solve the 'Find The Duplicate Number' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.

There is only one repeated number in nums, return this repeated number.

You must solve the problem without modifying the array nums and using only constant extra space.

Implement a function findDuplicate(nums: list) -> int that returns the duplicate number.

Constraints

•1 <= n <= 100000
•nums.length == n + 1
•1 <= nums[i] <= n
•There is only one repeated number in nums, but it could be repeated more than once

Examples

Example 1

Input

[1,3,4,2,2]

Output

Explanation

The duplicate number is 2. It appears twice in the array.

Example 2

Input

[3,1,3,4,2]

Output

Explanation

The duplicate number is 3. It appears twice in the array.

Example 3

Input

[3,3,3,3,3]

Output

Explanation

The duplicate number is 3. It appears five times.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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