Find The Duplicate Number

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Problem

Given an array of n+1 integers where each integer is in the range [1, n] and exactly one value is repeated (possibly more than once), find that duplicate — without modifying the array and using only O(1) extra space.

Examples

Example 1

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

Output:2

Example 2

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

Output:3

Constraints

1 <= n <= 10^5

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How to approach it: the Linked List pattern

A chain of nodes, each pointing to the next. No random access like an array, but insertion and deletion at a known position is O(1), and many classic problems come down to careful pointer rewiring.

Look for this pattern when

The problem explicitly gives you a linked list (reverse it, merge lists, detect a cycle, reorder it).
You need O(1) insertion/deletion without shifting elements, unlike an array.

Read the full Linked List guide →

Video walkthroughs

Original problem on LeetCode ↗