2433

2433. Find The Original Array of Prefix Xor (Medium)

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

Companies: IBM, Morgan Stanley

Related Topics:
Array, Bit Manipulation

Similar Questions:

• Single Number III (Medium)
• Count Triplets That Can Form Two Arrays of Equal XOR (Medium)
• Decode XORed Array (Easy)

Hints:

• Consider the following equation: x ^ a = b. How can you find x?
• Notice that arr[i] ^ pref[i-1] = pref[i]. This is the same as the previous equation.

Solution 1.

// OJ: https://leetcode.com/problems/find-the-original-array-of-prefix-xor
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1) extra space
class Solution {
public:
    vector<int> findArray(vector<int>& A) {
        int N = A.size();
        vector<int> ans = A;
        for (int i = 1; i < A.size(); ++i) ans[i] ^= A[i - 1];
        return ans;
    }
};

Or

// OJ: https://leetcode.com/problems/find-the-original-array-of-prefix-xor
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1) extra space
class Solution {
public:
    vector<int> findArray(vector<int>& A) {
        for (int i = 1, x = A[0]; i < A.size(); ++i) {
            A[i] ^= x;
            x ^= A[i];
        }
        return A;
    }
};