How do you solve Find The Original Array of Prefix Xor on LeetCode?

Find The Original Array of Prefix Xor (LeetCode #2433) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: XOR is reversible, meaning if you know the result of an XOR operation and one of the operands, you can find the other operand.

What algorithm or data structure is used to solve Find The Original Array of Prefix Xor?

Find The Original Array of Prefix Xor uses the following concepts: Array, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Array.

What are the interview tips for Find The Original Array of Prefix Xor?

Always clarify the problem statement and constraints before jumping into coding. Think about the properties of the operations involved, such as XOR in this case. Practice explaining your thought process as you code, as communication is key in interviews.

What are common mistakes when solving Find The Original Array of Prefix Xor?

Confusing the order of operations in XOR, which can lead to incorrect results. Not handling the case for the first element properly, which can lead to index errors.

Find The Original Array of Prefix Xor — LeetCode #2433 (Medium)

Tags: Array, Bit Manipulation

Related patterns: Bit Manipulation, Array

Brute Force approach

Time complexity: O(n²). Space complexity: O(1).

The brute force approach involves calculating the prefix XOR for each element in the original array by iterating through all previous elements. This is straightforward but inefficient for larger arrays.

The time complexity is O(n²) because for each element, we are performing XOR operations which can be considered constant time, but we are iterating through the array multiple times in a nested manner.

Step 1: Initialize an empty array `arr` of the same length as `pref`.
Step 2: For each index `i` from 0 to n-1, calculate `arr[i]` using the formula: `arr[i] = pref[i] ^ pref[i-1]` (with `pref[-1]` treated as 0).
Step 3: Return the constructed array `arr`.

1. Start with pref = [5, 2, 0, 3, 1]. 2. Initialize arr = [0, 0, 0, 0, 0]. 3. arr[0] = pref[0] = 5 → arr = [5, 0, 0, 0, 0]. 4. arr[1] = pref[1] ^ pref[0] = 2 ^ 5 = 7 → arr = [5, 7, 0, 0, 0]. 5. arr[2] = pref[2] ^ pref[1] = 0 ^ 2 = 2 → arr = [5, 7, 2, 0, 0]. 6. arr[3] = pref[3] ^ pref[2] = 3 ^ 0 = 3 → arr = [5, 7, 2, 3, 0]. 7. arr[4] = pref[4] ^ pref[3] = 1 ^ 3 = 2 → arr = [5, 7, 2, 3, 2].

Optimal Solution approach

Time complexity: O(n). Space complexity: O(n).

The optimal approach leverages the properties of XOR to directly compute each element of the original array using the prefix XOR values, leading to a linear time solution.

The time complexity is O(n) because we are iterating through the array once, performing constant time operations for each element. The space complexity is O(n) due to the additional array used to store the result.

Step 1: Initialize an empty array `arr` of the same length as `pref`.
Step 2: Set `arr[0]` to `pref[0]` since it's the first element.
Step 3: For each index `i` from 1 to n-1, compute `arr[i]` using the formula: `arr[i] = pref[i] ^ pref[i - 1]`.
Step 4: Return the constructed array `arr`.

Key Insights

XOR is reversible, meaning if you know the result of an XOR operation and one of the operands, you can find the other operand.
The first element of the original array is always the same as the first element of the prefix array.

Common Mistakes

Confusing the order of operations in XOR, which can lead to incorrect results.
Not handling the case for the first element properly, which can lead to index errors.

Interview Tips

Always clarify the problem statement and constraints before jumping into coding.
Think about the properties of the operations involved, such as XOR in this case.
Practice explaining your thought process as you code, as communication is key in interviews.

#2433

Find The Original Array of Prefix Xor

Medium

Array↗Bit Manipulation↗Bit Manipulation↗Array↗

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal approach leverages the properties of XOR to directly compute each element of the original array using the prefix XOR values, leading to a linear time solution.

⚙️

Algorithm

4 steps

1Step 1: Initialize an empty array `arr` of the same length as `pref`.
2Step 2: Set `arr[0]` to `pref[0]` since it's the first element.
3Step 3: For each index `i` from 1 to n-1, compute `arr[i]` using the formula: `arr[i] = pref[i] ^ pref[i - 1]`.
4Step 4: Return the constructed array `arr`.

solution.py7 lines

1def findOriginalArray(pref):
2    n = len(pref)
3    arr = [0] * n
4    arr[0] = pref[0]
5    for i in range(1, n):
6        arr[i] = pref[i] ^ pref[i - 1]
7    return arr

ℹ

Complexity note: The time complexity is O(n) because we are iterating through the array once, performing constant time operations for each element. The space complexity is O(n) due to the additional array used to store the result.

1XOR is reversible, meaning if you know the result of an XOR operation and one of the operands, you can find the other operand.
2The first element of the original array is always the same as the first element of the prefix array.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.