LeetCode 1720. Decode XORed Array Solution in Java, C++, Python & More | Explanation + Code

Description

There is a hidden integer array arr that consists of n non-negative integers.

It was encoded into another integer array encoded of length n - 1, such that encoded[i] = arr[i] XOR arr[i + 1]. For example, if arr = [1,0,2,1], then encoded = [1,2,3].

You are given the encoded array. You are also given an integer first, that is the first element of arr, i.e. arr[0].

Return the original array arr. It can be proved that the answer exists and is unique.

 

Example 1:

Input: encoded = [1,2,3], first = 1
Output: [1,0,2,1]
Explanation: If arr = [1,0,2,1], then first = 1 and encoded = [1 XOR 0, 0 XOR 2, 2 XOR 1] = [1,2,3]

Example 2:

Input: encoded = [6,2,7,3], first = 4
Output: [4,2,0,7,4]

 

Constraints:

• 2 <= n <= 104
• encoded.length == n - 1
• 0 <= encoded[i] <= 105
• 0 <= first <= 105

Solutions

Solution 1: Bit Manipulation

Based on the problem description, we have:

encoded[i] = arr[i] \oplus arr[i + 1]

If we XOR both sides of the equation with arr[i], we get:

arr[i] \oplus arr[i] \oplus arr[i + 1] = arr[i] \oplus encoded[i]

Which simplifies to:

arr[i + 1] = arr[i] \oplus encoded[i]

Following the derivation above, we can start with first and sequentially calculate every element of the array arr.

The time complexity is O(n), and the space complexity is O(n), where n is the length of the array.

PythonJavaC++GoTypeScript

class Solution: def decode(self, encoded: List[int], first: int) -> List[int]: ans = [first] for x in encoded: ans.append(ans[-1] ^ x) return ans(code-box)

class Solution { public int[] decode(int[] encoded, int first) { int n = encoded.length; int[] ans = new int[n + 1]; ans[0] = first; for (int i = 0; i < n; ++i) { ans[i + 1] = ans[i] ^ encoded[i]; } return ans; } }(code-box)

class Solution { public: vector<int> decode(vector<int>& encoded, int first) { vector<int> ans = {{first}}; for (int x : encoded) { ans.push_back(ans.back() ^ x); } return ans; } };(code-box)

func decode(encoded []int, first int) []int { ans := []int{first} for i, x := range encoded { ans = append(ans, ans[i]^x) } return ans }(code-box)

function decode(encoded: number[], first: number): number[] { const ans: number[] = [first]; for (const x of encoded) { ans.push(ans.at(-1)! ^ x); } return ans; }(code-box)