1720. Decode XORed Array

Problem

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 <= 10^5

Problem Summary

The unknown integer array arr consists of n non-negative integers. After being encoded, it becomes another integer array encoded of length n - 1, where encoded[i] = arr[i] XOR arr[i + 1]. For example, arr = [1,0,2,1] is encoded as encoded = [1,2,3]. You are given the encoded array encoded and the first element first of the original array arr (arr[0]). Please decode and return the original array arr. It can be proved that the answer exists and is unique.

Solution Approach

• Simple problem. According to the problem statement, return the original decoded array by sequentially applying the XOR operation to adjacent elements of the encoded array.

Code

package leetcode

func decode(encoded []int, first int) []int {
	arr := make([]int, len(encoded)+1)
	arr[0] = first
	for i, val := range encoded {
		arr[i+1] = arr[i] ^ val
	}
	return arr
}