1734. Decode XORed Permutation

Description

There is an integer array perm that is a permutation of the first n positive integers, where n is always odd.

It was encoded into another integer array encoded of length n - 1, such that encoded[i] = perm[i] XOR perm[i + 1]. For example, if perm = [1,3,2], then encoded = [2,1].

Given the encoded array, return the original array perm. It is guaranteed that the answer exists and is unique.

 

Example 1:

Input: encoded = [3,1]
Output: [1,2,3]
Explanation: If perm = [1,2,3], then encoded = [1 XOR 2,2 XOR 3] = [3,1]

Example 2:

Input: encoded = [6,5,4,6]
Output: [2,4,1,5,3]

 

Constraints:

• 3 <= n < 105
• n is odd.
• encoded.length == n - 1

 

Solutions

Solution: Bit Manipulation

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[]} encoded
 * @return {number[]}
 */
const decode = function (encoded) {
  const size = encoded.length + 1;
  const result = [1];

  for (let n = 2; n <= size; n++) {
    result[0] ^= n;
  }
  for (let index = 1; index < size - 1; index += 2) {
    result[0] ^= encoded[index];
  }
  for (let index = 1; index < size; index++) {
    result[index] = result[index - 1] ^ encoded[index - 1];
  }
  return result;
};