index.md

287. Find the Duplicate Number

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 uses only constant extra space.

Example 1:

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

Example 2:

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

Example 3:

Input: nums = [3,3,3,3,3] Output: 3

Constraints:

• 1 <= n <= 105
• nums.length == n + 1
• 1 <= nums[i] <= n
• All the integers in nums appear only once except for precisely one integer which appears two or more times.

Follow up:

• How can we prove that at least one duplicate number must exist in nums?
• Can you solve the problem in linear runtime complexity?

Solution

Thoughts

Initially thoought this was a math problem requiring xor, didn;t know we could use the tortoise hare appraoch to this. Got help to solve this problem. Revise this again.

Time Complexity

O(n), where n is the number of elements in the array. The hare moves at most 2n steps, and the tortoise moves at most n steps.

Space Complexity

O(1), as we only use a few integer variables, which use constant space.