Skip to content

Latest commit

 

History

History
75 lines (56 loc) · 2.51 KB

0287-find-the-duplicate-number.adoc

File metadata and controls

75 lines (56 loc) · 2.51 KB

287. Find the Duplicate Number

{leetcode}/problems/find-the-duplicate-number/[LeetCode - 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。

思路分析

题目要求“不能修改数组”和“O(1)的空间复杂度”，就比较难办了。可以利用龟兔赛跑找环的方式来解决：

{image_attr}

如果抛开题目要求的“不能修改数组”和“O(1)的空间复杂度”要求，有更多解法：

  1. 不考虑空间复杂度，可以用 Set 来求解

  2. 如果可以修改数组，则原地交换（把 nums[i] 挪到 nums[nums[i]] 上）。

    {image_attr}
一刷
link:{sourcedir}/_0287_FindTheDuplicateNumber.java[role=include]
二刷
link:{sourcedir}/_0287_FindTheDuplicateNumber_2.java[role=include]

参考资料

  1. 287. 寻找重复数 - 官方题解

  2. {leetcode}/problems/find-the-duplicate-number/solution/[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！

  3. 142. 环形链表 II - 快慢指针，清晰严谨的图示推导

  4. 287. 寻找重复数 - 原地交换、龟兔赛跑，清晰图解