2433. Find The Original Array of Prefix Xor

Problem Link

Description

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You are given an integer array pref of size n. Find and return the array arr of size n that satisfies:

• pref[i] = arr[0] ^ arr[1] ^ ... ^ arr[i].

Note that ^ denotes the bitwise-xor operation.

It can be proven that the answer is unique.

 

Example 1:

Input: pref = [5,2,0,3,1]
Output: [5,7,2,3,2]
Explanation: From the array [5,7,2,3,2] we have the following:
- pref[0] = 5.
- pref[1] = 5 ^ 7 = 2.
- pref[2] = 5 ^ 7 ^ 2 = 0.
- pref[3] = 5 ^ 7 ^ 2 ^ 3 = 3.
- pref[4] = 5 ^ 7 ^ 2 ^ 3 ^ 2 = 1.

Example 2:

Input: pref = [13]
Output: [13]
Explanation: We have pref[0] = arr[0] = 13.

 

Constraints:

• 1 <= pref.length <= 105
• 0 <= pref[i] <= 106

Solution

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Python3

class Solution:
    def findArray(self, pref: List[int]) -> List[int]:
        N = len(pref)
        res = [pref[0]]
 
        # arr[0] = pref[i]
        # arr[i] = pref[i] ^ pref[i - 1]
 
        for i in range(1, N):
            res.append(pref[i] ^ pref[i - 1])
        
        return res