1720. Decode XORed Array

LeetCode 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 <= 10^4

• encoded.length == n - 1

• 0 <= encoded[i] <= 10^5

• 0 <= first <= 10^5

Tags

Bit Manipulation

Solution

Since encoded[i] = arr[i] XOR arr[i + 1] (i≥-1), then arr[i+1] = encoded[i] XOR arr[i] because XOR is reversible. Thus, we iterate on i from beginning to end, and set arr[i+1] = encoded[i] XOR arr[i].

Complexity

• Time complexity: $O(n)$

• Space complexity: $O(n)$

Code

func decode(encoded []int, first int) []int {
	ans := make([]int, len(encoded)+1)
	ans[0] = first
	for i := 1; i < len(ans); i++ {
		ans[i] = ans[i-1] ^ encoded[i-1]
	}
	return ans
}

Reference

1. https://www.zhihu.com/question/28693672