# 1720. Decode XORed Array

## Description

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[0].

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

## Solutions

XOR.

a = b ^ c => a ^ b = b ^ c ^ b => c = a ^ b.

• class Solution {
public int[] decode(int[] encoded, int first) {
int n = encoded.length;
int[] ans = new int[n + 1];
ans[0] = first;
for (int i = 0; i < n; ++i) {
ans[i + 1] = ans[i] ^ encoded[i];
}
return ans;
}
}

• class Solution {
public:
vector<int> decode(vector<int>& encoded, int first) {
vector<int> ans{ {first} };
for (int i = 0; i < encoded.size(); ++i)
ans.push_back(ans[i] ^ encoded[i]);
return ans;
}
};

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


• func decode(encoded []int, first int) []int {
ans := []int{first}
for i, e := range encoded {
ans = append(ans, ans[i]^e)
}
return ans
}

• function decode(encoded: number[], first: number): number[] {
const ans: number[] = [first];
for (const x of encoded) {
ans.push(ans.at(-1)! ^ x);
}
return ans;
}