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

1720. Decode XORed Array

Level

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;
    }
}

All Problems

All Solutions