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0287-find-the-duplicate-number.adoc

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287. Find the Duplicate Number

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 1:
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, \(O\left(1\right)\) extra space.

  • Your runtime complexity should be less than \(O\left(n^{2}\right)\).

  • There is only one duplicate number in the array, but it could be repeated more than once.

可以使用 142. Linked List Cycle II 中的 Floyd’s Tortoise and Hare (Cycle Detection) 算法来解决。

参考资料

  1. Find the Duplicate Number solution - LeetCode 中 Approach #3 Floyd’s Tortoise and Hare (Cycle Detection) [Accepted] 的好精巧！类似于在链表中发现环。还需要再仔细思考一下这个问题！

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:

  1. You must not modify the array (assume the array is read only).

  2. You must use only constant, O(1) extra space.

  3. Your runtime complexity should be less than O(n2).

  4. There is only one duplicate number in the array, but it could be repeated more than once.

link:{sourcedir}/_0287_FindTheDuplicateNumber.java[role=include]