# 1720.decode-xored-array

## Statement

``````输入：encoded = [1,2,3], first = 1

``````

``````输入：encoded = [6,2,7,3], first = 4

``````

• `2 <= n <= 104`
• `encoded.length == n - 1`
• `0 <= encoded[i] <= 105`
• `0 <= first <= 105`

• Difficulty: Easy
• Tag: `Bit Manipulation` `Array`

There is a hidden integer array `arr` that consists of `n` non-negative integers.

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

You are given the `encoded` array. You are also given an integer `first`, that is the first element of `arr`, i.e. `arr`.

Return the original array `arr`. It can be proved that the answer exists and is unique.

Example 1:

``````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]
``````

Example 2:

``````Input: encoded = [6,2,7,3], first = 4
Output: [4,2,0,7,4]
``````

Constraints:

• `2 <= n <= 104`
• `encoded.length == n - 1`
• `0 <= encoded[i] <= 105`
• `0 <= first <= 105`

## Solution

``````from typing import List

class Solution:
def decode(self, encoded: List[int], first: int) -> List[int]:
res = [first]
for x in encoded:
res.append(x ^ res[-1])
return res
``````