What is the time complexity of Minimum Number of Operations to Make Array XOR Equal to K?

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

What data structures are used to solve Minimum Number of Operations to Make Array XOR Equal to K?

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

What are the key insights for solving Minimum Number of Operations to Make Array XOR Equal to K?

Insight 1: The bitwise XOR operation is associative and commutative, so the order in which we XOR the elements doesn't matter. Insight 2: Flipping a bit in an element changes the XOR sum by either adding or subtracting a power of 2. The goal is to change the current XOR of the array to the target value 'k'.

Which companies ask LeetCode 2997. Minimum Number of Operations to Make Array XOR Equal to K in interviews?

This problem is frequently asked at American Express.

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Minimum Number of Operations to Make Array XOR Equal to K - LeetCode 2997 Solution

Minimum Number of Operations to Make Array XOR Equal to K - Complete Solution Guide

Minimum Number of Operations to Make Array XOR Equal to K is LeetCode problem 2997, 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 a 0-indexed integer array nums and a positive integer k . You can apply the following operation on the array any number of times: Choose any element of the array and flip a bit in its binary representation. Flipping a bit means changing a 0 to 1 or vice versa. Return the minimum number of operations required to make the bitwise XOR of all elements of the final array equal to k . Note that you can flip leading zero bits in the binary representation of elements. For example, for the

Detailed Explanation

The problem requires finding the minimum number of bit flips needed to make the bitwise XOR of all elements in an array `nums` equal to a given integer `k`. We are allowed to flip any bit (0 to 1 or 1 to 0) in the binary representation of any element in the array an unlimited number of times. The goal is to determine the fewest such flips needed to achieve the desired XOR result.

Solution Approach

The solution calculates the XOR of all elements in the input array `nums`. Then, it calculates the XOR of this result with the target value `k`. The number of set bits (bits equal to 1) in the result of this final XOR operation represents the minimum number of bit flips needed. This works because the XOR operation identifies bits that are different. Each such bit difference signifies a bit that needs to be flipped.

Step-by-Step Algorithm

Step 1: Initialize a variable `current_xor` to 0. This variable will store the XOR of all the elements in the `nums` array.
Step 2: Iterate through the `nums` array. For each element `num` in the array, perform a bitwise XOR operation between `current_xor` and `num`, and store the result back in `current_xor`. After the loop, `current_xor` holds the XOR of all elements in `nums`.
Step 3: Calculate the XOR of `current_xor` and `k`. This value represents the bits that need to be flipped to make the XOR of the array equal to `k`.
Step 4: Count the number of set bits (1s) in the result from step 3. This count represents the minimum number of operations required.
Step 5: Return the count of set bits.

Key Insights

Insight 1: The bitwise XOR operation is associative and commutative, so the order in which we XOR the elements doesn't matter.
Insight 2: Flipping a bit in an element changes the XOR sum by either adding or subtracting a power of 2. The goal is to change the current XOR of the array to the target value 'k'.
Insight 3: The number of bits that differ between the current XOR of the array and 'k' represents the minimum number of flips required. This is because each differing bit needs to be flipped to match 'k'.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Bit Manipulation.

Companies

Asked at: American Express.

Minimum Number of Operations to Make Array XOR Equal to K | LeetCode 2997

Medium

Array Bit Manipulation

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

Solution Code

Available in:

class Solution {
    public int minOperations(int[] nums, int k) {
        int current_xor = 0;
        for (int num : nums) {
            current_xor ^= num;
        }

        int result = current_xor ^ k;
        return Integer.bitCount(result);
    }
}

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Problem Info

Description

Problem 2997: Minimum Number of Operations to Make Array XOR Equal to K - Detailed explanation and solution approaches.

Topics

Array Bit Manipulation

Companies

American Express

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2997

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

5 steps

1
Step 1: Initialize a variable `current_xor` to 0. This variable will store the XOR of all the elements in the `nums` array.
2
Step 2: Iterate through the `nums` array. For each element `num` in the array, perform a bitwise XOR operation between `current_xor` and `num`, and store the result back in `current_xor`. After the loop, `current_xor` holds the XOR of all elements in `nums`.
3
Step 3: Calculate the XOR of `current_xor` and `k`. This value represents the bits that need to be flipped to make the XOR of the array equal to `k`.
4
Step 4: Count the number of set bits (1s) in the result from step 3. This count represents the minimum number of operations required.
5
Step 5: Return the count of set bits.

💡

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 time complexity is dominated by the single loop through the input array, resulting in O(n) complexity. The space complexity is constant because regardless of the input size, only a few integer variables are used.

📖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 built-in bitset (C++)

In C++, you could use a `std::bitset` to represent the XOR result and then use the `count()` method to count the number of set bits.

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

Trade-offs: This approach can be slightly more readable in C++ but doesn't significantly change the performance. The advantage is code clarity; the disadvantage is potentially being less portable to languages without equivalent bitset functionalities.

✨

Key Insights

1Insight 1: The bitwise XOR operation is associative and commutative, so the order in which we XOR the elements doesn't matter.
2Insight 2: Flipping a bit in an element changes the XOR sum by either adding or subtracting a power of 2. The goal is to change the current XOR of the array to the target value 'k'.
3Insight 3: The number of bits that differ between the current XOR of the array and 'k' represents the minimum number of flips required. This is because each differing bit needs to be flipped to match 'k'.

📚

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: The XOR of the initial array is already equal to `k`. In this case, the XOR between `current_xor` and `k` will be 0, and the count of set bits will be 0, correctly indicating that no operations are needed.
Edge case 2: The array is empty. However, the problem statement specifies that `1 <= nums.length <= 10^5`, so we don't need to explicitly handle an empty array. If the array *were* empty, then `current_xor` would remain at its initialized value of 0. The code would then compute 0 XOR k = k, and then count the number of set bits in `k`.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to XOR the current XOR with `k`. Some might think that the count of 1s in current_xor is enough. However, the question asks for the difference between the XOR of all elements and `k`.

✗Common mistake 2: Trying to modify the array directly by flipping bits. This is unnecessary and inefficient, as we only need to determine the *number* of flips required, not the resulting array.

✅

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: Error detection and correction in data transmission. XOR is used to calculate parity bits, which are used to detect single-bit errors. This problem's core logic is similar to understanding how many bits need to be changed to correct an error.

🏦Real-world scenario 2: Cryptography. XOR is used in some simple encryption algorithms to encrypt data. This problem demonstrates basic bit manipulation, which is a fundamental concept in cryptography.

💡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 26, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 13

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

@CodeNinjaJul 6

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

@TechLeadJun 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 "Minimum Number of Operations to Make Array XOR Equal to K"?

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.

🤖 Need help with this problem?