Decode XORed Permutation — LeetCode 1734 Python Solution

The problem

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].

Example

Input

encoded = [3,1]

Output

[1,2,3]

Explanation

If perm = [1,2,3], then encoded = [1 XOR 2,2 XOR 3] = [3,1]

Python solution

class Solution:
    def decode(self, encoded: List[int]) -> List[int]:
        n = len(encoded) + 1
        a = b = 0
        for i in range(0, n - 1, 2):
            a ^= encoded[i]
        for i in range(1, n + 1):
            b ^= i
        perm = [0] * n
        perm[-1] = a ^ b
        for i in range(n - 2, -1, -1):
            perm[i] = encoded[i] ^ perm[i + 1]
        return perm

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1734. Decode XORed Permutation is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Bit Manipulation.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

Related problems