find-the-duplicate-number

Find the Duplicate Number

LeetCode #: 287

Difficulty: Medium

Topics: Array, Two Pointers, Binary Search.

Problem

Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

Example 1:

Input: [1,3,4,2,2]
Output: 2

Example 2:

Input: [3,1,3,4,2]
Output: 3

Note:

• You must not modify the array (assume the array is read only).
• You must use only constant, O(1) extra space.
• Your runtime complexity should be less than O(n^2).
• There is only one duplicate number in the array, but it could be repeated more than once.

Solution Explanation

Reference:

• My easy understood solution with O(n) time and O(1) space without modifying the array. With clear explanation. by echoxiaolee

• https://keithschwarz.com/interesting/code/?dir=find-duplicate

• Cycle Detection on Wikipedia (algorithm by Robert W. Floyd / Donald Knuth)