decode-xored-array

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Algorithms

There is a hidden integer array <code>arr</code> that consists of <code>n</code> non-negative integers.

It was encoded into another integer array <code>encoded</code> of length <code>n - 1</code>, such that <code>encoded[i] = arr[i] XOR arr[i + 1]</code>. For example, if <code>arr = [1,0,2,1]</code>, then <code>encoded = [1,2,3]</code>.

You are given the <code>encoded</code> array. You are also given an integer <code>first</code>, that is the first element of <code>arr</code>, i.e. <code>arr[0]</code>.

Return the original array <code>arr</code>. It can be proved that the answer exists and is unique.

&nbsp;
Example 1:

<pre>
Input: encoded = [1,2,3], first = 1
Output: [1,0,2,1]
Explanation: If arr = [1,0,2,1], then first = 1 and encoded = [1 XOR 0, 0 XOR 2, 2 XOR 1] = [1,2,3]
</pre>

Example 2:

<pre>
Input: encoded = [6,2,7,3], first = 4
Output: [4,2,0,7,4]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= n &lt;= 104</code></li>
	<li><code>encoded.length == n - 1</code></li>
	<li><code>0 &lt;= encoded[i] &lt;= 105</code></li>
	<li><code>0 &lt;= first &lt;= 105</code></li>
</ul>

decode

Decode XORed Array

Find The Original Array of Prefix Xor

find-the-original-array-of-prefix-xor

找出前缀异或的原始数组

Bit Manipulation

Array

未知 整数数组 <code>arr</code> 由 <code>n</code> 个非负整数组成。

经编码后变为长度为 <code>n - 1</code> 的另一个整数数组 <code>encoded</code> ，其中 <code>encoded[i] = arr[i] XOR arr[i + 1]</code> 。例如，<code>arr = [1,0,2,1]</code> 经编码后得到 <code>encoded = [1,2,3]</code> 。

给你编码后的数组 <code>encoded</code> 和原数组 <code>arr</code> 的第一个元素 <code>first</code>（<code>arr[0]</code>）。

请解码返回原数组 <code>arr</code> 。可以证明答案存在并且是唯一的。

 

示例 1：

<pre>
输入：encoded = [1,2,3], first = 1
输出：[1,0,2,1]
解释：若 arr = [1,0,2,1] ，那么 first = 1 且 encoded = [1 XOR 0, 0 XOR 2, 2 XOR 1] = [1,2,3]
</pre>

示例 2：

<pre>
输入：encoded = [6,2,7,3], first = 4
输出：[4,2,0,7,4]
</pre>

 

提示：

<ul>
	<li><code>2 <= n <= 104</code></li>
	<li><code>encoded.length == n - 1</code></li>
	<li><code>0 <= encoded[i] <= 105</code></li>
	<li><code>0 <= first <= 105</code></li>
</ul>