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Formatted question description: https://leetcode.ca/all/1720.html

# 1720. Decode XORed Array

Easy

## 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 <= 10^4
• encoded.length == n - 1
• 0 <= encoded[i] <= 10^5
• 0 <= first <= 10^5

## Solution

Create an array arr of length n + 1 and set arr[0] = first. Then use the property of XOR such that if a ^ b == c then there is a ^ c == b and b ^ c == a. Therefore, for each i from 0 to n - 1, there is arr[i + 1] = arr[i] ^ encoded[i]. Finally, return arr.

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

############

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;
}
}

• // OJ: https://leetcode.com/problems/decode-xored-array/
// Time: O(N)
// Space: O(1)
class Solution {
public:
vector<int> decode(vector<int>& A, int first) {
vector<int> ans = {first};
for (int n : A) ans.push_back(n ^ ans.back());
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

############

# 1720. Decode XORed Array
# https://leetcode.com/problems/decode-xored-array/

class Solution:
def decode(self, encoded: List[int], first: int):
res = [first]

for i in range(len(encoded)):
res.append(res[-1] ^ encoded[i])

return res

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