Decode XORed Permutation Solution in Python

Problem Description

Ah, the classic “Decode XORed Permutation” problem! It’s like trying to figure out who ate the last slice of pizza at a party. You know someone did, but the evidence is all scrambled up! In this case, you have a list of encoded values that are the result of XOR operations on a permutation of numbers. Your task is to decode this mess and find the original permutation.

Imagine you’re at a party, and everyone is wearing a mask (the numbers in the permutation). The encoded list is like a series of clues that tell you who danced with whom (the XOR results). Your job is to unmask everyone and find out who they really are. Spoiler alert: it’s not as easy as it sounds!

Solution Links

If you’re feeling adventurous and want to explore other languages, check out the solutions below:

Code Solution


class Solution:
    def decode(self, encoded: list[int]) -> list[int]:
        n = len(encoded) + 1
        nXors = functools.reduce(operator.xor, [i for i in range(1, n + 1)])

        xors = 0  # xors(accumulatedEncoded)

        for encode in encoded:
            runningXors ^= encode
            xors ^= runningXors

        ans = [xors ^ nXors]

        for encode in encoded:
            ans.append(ans[-1] ^ encode)

        return ans

Approach Explanation

The approach here is quite clever! The code uses the properties of XOR to decode the original permutation. Here’s a brief breakdown:

Calculate the Total XOR: First, it computes the XOR of all numbers from 1 to n (where n is the length of the original permutation). This gives us a baseline to work with.
Running XOR Calculation: It then iterates through the encoded list, maintaining a running XOR of the encoded values. This helps in figuring out the original values step by step.
Decoding: Finally, it decodes the original permutation by XORing the results appropriately.

Time and Space Complexity

Complexity Type	Complexity
Time Complexity	O(n), where n is the length of the encoded list.
Space Complexity	O(1), as we are using a constant amount of space for variables.

Real-World Example

Let’s say you’re trying to decode a secret message sent by your friend using a series of emojis. Each emoji represents a number, and the encoded message is a series of XORed emojis. By using the same logic as in the problem, you can decode the message and find out what your friend really meant. Spoiler: it’s probably just a cat emoji!