What is the pattern used in the 'Find The Original Array of Prefix Xor' problem?

This problem uses the pattern of 'Array plus Bit Manipulation', specifically utilizing the XOR operation to reverse the prefix XOR array.

How do I efficiently solve this problem for large inputs?

The key to solving this problem efficiently is to keep the time complexity to `O(n)` by calculating the elements iteratively with XOR, and ensuring the space complexity is also `O(n)`.

Can this approach be used for other XOR-related problems?

Yes, understanding how to reverse or manipulate XOR sequences is a fundamental technique in many bit manipulation problems, particularly when dealing with cumulative or prefix operations.

What happens if the input prefix array contains zeros?

The solution works even if the prefix array contains zeros, as XOR with zero does not alter the value. The algorithm will correctly handle such cases.

Is there any alternative to the XOR approach?

While the XOR approach is optimal for this problem, alternative methods such as dynamic programming or brute force would likely be less efficient and are not recommended.

#2433

Medium

auto_awesome数组·结合·位运算·操作

LeetCode 题解工作台

找出前缀异或的原始数组

给你一个长度为 n 的整数数组 pref 。找出并返回满足下述条件且长度为 n 的数组 arr ： pref[i] = arr[0] ^ arr[1] ^ ... ^ arr[i] . 注意 ^ 表示按位异或（bitwise-xor）运算。可以证明答案是唯一的。示例 1：输入： p…

数组位运算

题目描述

给你一个长度为 n 的整数数组 pref 。找出并返回满足下述条件且长度为 n 的数组 arr ：

pref[i] = arr[0] ^ arr[1] ^ ... ^ arr[i].

注意 ^ 表示 按位异或（bitwise-xor）运算。

可以证明答案是唯一的。

示例 1：

输入：pref = [5,2,0,3,1]
输出：[5,7,2,3,2]
解释：从数组 [5,7,2,3,2] 可以得到如下结果：
- pref[0] = 5
- pref[1] = 5 ^ 7 = 2
- pref[2] = 5 ^ 7 ^ 2 = 0
- pref[3] = 5 ^ 7 ^ 2 ^ 3 = 3
- pref[4] = 5 ^ 7 ^ 2 ^ 3 ^ 2 = 1

示例 2：

输入：pref = [13]
输出：[13]
解释：pref[0] = arr[0] = 13

提示：

1 <= pref.length <= 10⁵
0 <= pref[i] <= 10⁶

lightbulb

解题思路

方法一：位运算

根据题意，我们有式子一：

pref[i]=arr[0] \oplus arr[1] \oplus \cdots \oplus arr[i]

所以，也就有式子二：

pref[i-1]=arr[0] \oplus arr[1] \oplus \cdots \oplus arr[i-1]

我们将式子一二进行异或运算，得到：

pref[i] \oplus pref[i-1]=arr[i]

即答案数组的每一项都是前缀异或数组的相邻两项进行异或运算得到的。

时间复杂度 $O(n)$ ，其中 $n$ 为前缀异或数组的长度。忽略答案的空间消耗，空间复杂度 $O(1)$ 。

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class Solution:
    def findArray(self, pref: List[int]) -> List[int]:
        return [a ^ b for a, b in pairwise([0] + pref)]

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Can the candidate describe the properties of XOR and how it can be used to reverse the prefix array?
question_mark
Do they understand the iterative nature of the problem and can they apply the XOR operation correctly?
question_mark
Can they optimize the solution to handle large inputs efficiently?

warning

常见陷阱

外企场景

error
Misunderstanding the XOR properties and attempting a more complex solution than necessary.
error
Failing to handle edge cases where the array length is minimal or contains zeros.
error
Overcomplicating the solution by introducing unnecessary operations or data structures.

swap_horiz

进阶变体

外企场景

arrow_right_alt
What if the prefix XOR array is given in reverse order? Can you adjust the approach?
arrow_right_alt
What happens if the array size is much larger? How would you ensure your solution is still efficient?
arrow_right_alt
Could a more complex data structure be used for a different variant of this problem?

help

常见问题

外企场景

继续练习

#2438 二的幂数组中查询范围内的乘积 #2425 所有数对的异或和 #2419 按位与最大的最长子数组