What is the time complexity of Find The Original Array of Prefix Xor?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Find The Original Array of Prefix Xor?

This problem uses Array, Bit Manipulation. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Find The Original Array of Prefix Xor?

Insight 1: The key insight is understanding the relationship between `pref[i]` and `arr[i]`. We know `pref[i] = arr[0] ^ arr[1] ^ ... ^ arr[i]`. Therefore, `arr[i]` can be obtained by `pref[i] ^ pref[i-1]`. Insight 2: The first element of `arr` is simply the first element of `pref` since `pref[0] = arr[0]`.

Which companies ask LeetCode 2433. Find The Original Array of Prefix Xor in interviews?

This problem is frequently asked at IBM, Morgan Stanley, Nvidia.

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Find The Original Array of Prefix Xor - LeetCode 2433 Solution

Find The Original Array of Prefix Xor - Complete Solution Guide

Find The Original Array of Prefix Xor is LeetCode problem 2433, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

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

Detailed Explanation

The problem asks us to reconstruct the original array `arr` given its prefix XOR array `pref`. The prefix XOR array `pref` is defined such that `pref[i]` is the XOR of all elements from `arr[0]` to `arr[i]`. The goal is to find `arr` from `pref`. For example, if `pref = [5, 2, 0, 3, 1]`, then `arr` should be `[5, 7, 2, 3, 2]` because `5 = 5`, `5 ^ 7 = 2`, `5 ^ 7 ^ 2 = 0`, `5 ^ 7 ^ 2 ^ 3 = 3`, and `5 ^ 7 ^ 2 ^ 3 ^ 2 = 1`. The input is a non-empty array `pref` of integers, and the output is the original array `arr`.

Solution Approach

The solution exploits the properties of the XOR operation. Specifically, if `a ^ b = c`, then `a = c ^ b` and `b = c ^ a`. We can iterate through the `pref` array from the second element onwards (index 1). For each element at index `i`, we replace `pref[i]` with `pref[i] ^ pref[i-1]`. This results in the original array `arr` being stored in the `pref` array itself.

Step-by-Step Algorithm

Step 1: Initialize the first element of the `arr` array as the first element of the `pref` array. In essence, `arr[0] = pref[0]`.
Step 2: Iterate through the `pref` array from index 1 to the end of the array.
Step 3: For each index `i`, calculate `pref[i] = pref[i] ^ pref[i-1]`. This step overwrites the `pref` array with the correct values for the `arr` array.
Step 4: Return the modified `pref` array, which now holds the original `arr` array.

Key Insights

Insight 1: The key insight is understanding the relationship between `pref[i]` and `arr[i]`. We know `pref[i] = arr[0] ^ arr[1] ^ ... ^ arr[i]`. Therefore, `arr[i]` can be obtained by `pref[i] ^ pref[i-1]`.
Insight 2: The first element of `arr` is simply the first element of `pref` since `pref[0] = arr[0]`.
Insight 3: We can perform the XOR operation in-place, modifying the `pref` array directly to store the resulting `arr` values, minimizing space usage.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Bit Manipulation.

Companies

Asked at: IBM, Morgan Stanley, Nvidia.

Find The Original Array of Prefix Xor | LeetCode 2433

Medium

Array Bit Manipulation

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public int[] findArray(int[] pref) {
        for (int i = pref.length - 1; i > 0; i--) {
            pref[i] ^= pref[i - 1];
        }
        return pref;
    }
}

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Problem Info

Description

Problem 2433: Find The Original Array of Prefix Xor - Detailed explanation and solution approaches.

Topics

Array Bit Manipulation

Companies

IBMMorgan StanleyNvidia

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:2433

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

4 steps

1
Step 1: Initialize the first element of the `arr` array as the first element of the `pref` array. In essence, `arr[0] = pref[0]`.
2
Step 2: Iterate through the `pref` array from index 1 to the end of the array.
3
Step 3: For each index `i`, calculate `pref[i] = pref[i] ^ pref[i-1]`. This step overwrites the `pref` array with the correct values for the `arr` array.
4
Step 4: Return the modified `pref` array, which now holds the original `arr` array.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm iterates through the array once, performing a constant-time XOR operation at each element. Thus the time complexity is linear with respect to the size of the input array. The solution modifies the input array in-place, which means that no additional space that scales with the input size is used. Thus, the space complexity is constant.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Using an additional array

Create a new array `arr` of the same size as `pref`. Set `arr[0] = pref[0]`. Iterate from `i = 1` to `n-1` and set `arr[i] = pref[i] ^ pref[i-1]`. Return the new array `arr`.

Time: O(n)Space: O(n)

Trade-offs: This approach uses more space (O(n)) compared to the in-place solution (O(1)). However, it might be easier to understand for some. It avoids modifying the input array directly, which might be preferred in certain scenarios.

✨

Key Insights

1Insight 1: The key insight is understanding the relationship between `pref[i]` and `arr[i]`. We know `pref[i] = arr[0] ^ arr[1] ^ ... ^ arr[i]`. Therefore, `arr[i]` can be obtained by `pref[i] ^ pref[i-1]`.
2Insight 2: The first element of `arr` is simply the first element of `pref` since `pref[0] = arr[0]`.
3Insight 3: We can perform the XOR operation in-place, modifying the `pref` array directly to store the resulting `arr` values, minimizing space usage.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: When the input array `pref` has only one element. In this case, the algorithm correctly returns the input array itself since `arr[0] = pref[0]` and there is nothing else to compute.
Edge case 2: Empty input array (pref.length == 0). The problem constraints specify that 1 <= pref.length <= 10^5, so we do not have to handle this. If the problem allowed an empty input, we would need to add an initial check for pref.length == 0 and return an empty array.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly applying the XOR operation. It's crucial to remember that `arr[i] = pref[i] ^ pref[i-1]`, not `pref[i] = arr[i] ^ arr[i-1]`.

✗Common mistake 2: Not handling the edge case where the input array has only one element. Though the provided constraints handle the empty array case, it's good practice to verify array size at the start.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Data compression. XOR is used in some compression algorithms to represent data more efficiently by finding similarities and differences within data sets.

🏦Real-world scenario 2: Error detection and correction. XOR is used in RAID (Redundant Array of Independent Disks) systems to provide data redundancy and fault tolerance. By XORing data across multiple disks, the system can reconstruct data if one disk fails.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: September 2, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Find The Original Array of Prefix Xor"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether bit manipulation techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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