decode-xored-permutation

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Algorithms

There is an integer array <code>perm</code> that is a permutation of the first <code>n</code> positive integers, where <code>n</code> is always odd.

It was encoded into another integer array <code>encoded</code> of length <code>n - 1</code>, such that <code>encoded[i] = perm[i] XOR perm[i + 1]</code>. For example, if <code>perm = [1,3,2]</code>, then <code>encoded = [2,1]</code>.

Given the <code>encoded</code> array, return the original array <code>perm</code>. It is guaranteed that the answer exists and is unique.

&nbsp;
Example 1:

<pre>
Input: encoded = [3,1]
Output: [1,2,3]
Explanation: If perm = [1,2,3], then encoded = [1 XOR 2,2 XOR 3] = [3,1]
</pre>

Example 2:

<pre>
Input: encoded = [6,5,4,6]
Output: [2,4,1,5,3]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>3 &lt;= n &lt;&nbsp;105</code></li>
	<li><code>n</code>&nbsp;is odd.</li>
	<li><code>encoded.length == n - 1</code></li>
</ul>

decode

Decode XORed Permutation

Find Xor-Beauty of Array

find-xor-beauty-of-array

查询数组异或美丽值

Bit Manipulation

Array

给你一个整数数组 <code>perm</code> ，它是前 <code>n</code> 个正整数的排列，且 <code>n</code> 是个 奇数 。

它被加密成另一个长度为 <code>n - 1</code> 的整数数组 <code>encoded</code> ，满足 <code>encoded[i] = perm[i] XOR perm[i + 1]</code> 。比方说，如果 <code>perm = [1,3,2]</code> ，那么 <code>encoded = [2,1]</code> 。

给你 <code>encoded</code> 数组，请你返回原始数组 <code>perm</code> 。题目保证答案存在且唯一。

 

示例 1：

<pre>输入：encoded = [3,1]
输出：[1,2,3]
解释：如果 perm = [1,2,3] ，那么 encoded = [1 XOR 2,2 XOR 3] = [3,1]
</pre>

示例 2：

<pre>输入：encoded = [6,5,4,6]
输出：[2,4,1,5,3]
</pre>

 

提示：

<ul>
	<li><code>3 &lt;= n &lt; 105</code></li>
	<li><code>n</code> 是奇数。</li>
	<li><code>encoded.length == n - 1</code></li>
</ul>