README.md

1734. Decode XORed Permutation

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 (Rust)

1. Solution

impl Solution {
    pub fn decode(encoded: Vec<i32>) -> Vec<i32> {
        let n = encoded.len() + 1;
        let m = n / 2;
        let mut perm = vec![0; n];
        perm[m] = m as i32 + 1;

        for i in 0..m {
            perm[m] ^= ((i + 1) ^ (n - i)) as i32;
            if i % 2 == 0 {
                perm[m] ^= encoded[i] ^ encoded[n - 2 - i];
            }
        }

        for i in 1..=m {
            perm[m - i] = encoded[m - i] ^ perm[m - i + 1];
            perm[m + i] = encoded[m + i - 1] ^ perm[m + i - 1];
        }

        perm
    }
}