What is the time complexity of Flipping an Image?

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

What data structures are used to solve Flipping an Image?

This problem uses Array, Two Pointers, Bit Manipulation, Matrix, Simulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Flipping an Image?

Insight 1: The flip and invert operations can be performed in place to optimize space complexity. Insight 2: Reversing a row can be done using two pointers, one starting from the left and the other from the right, swapping elements until they meet in the middle.

Which companies ask LeetCode 832. Flipping an Image in interviews?

This problem is frequently asked at IBM.

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Flipping an Image - LeetCode 832 Solution

Flipping an Image - Complete Solution Guide

Flipping an Image is LeetCode problem 832, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given an n x n binary matrix image , flip the image horizontally , then invert it, and return the resulting image . To flip an image horizontally means that each row of the image is reversed. For example, flipping [1,1,0] horizontally results in [0,1,1] . To invert an image means that each 0 is replaced by 1 , and each 1 is replaced by 0 . For example, inverting [0,1,1] results in [1,0,0] . Example 1: Input: image = [[1,1,0],[1,0,1],[0,0,0]] Output: [[1,0,0],[0,1,0],[1,1,1]] Explanation: First r

Detailed Explanation

The problem requires us to take an n x n binary matrix (an array of arrays, where each element is either 0 or 1), perform two operations on it, and return the modified matrix. The two operations are: 1. Flipping the image horizontally, which means reversing each row of the matrix. For example, [1, 1, 0] becomes [0, 1, 1]. 2. Inverting the image, which means replacing each 0 with 1 and each 1 with 0. For example, [0, 1, 1] becomes [1, 0, 0]. The input is the original binary matrix, and the output is the matrix after performing both flip and invert operations.

Solution Approach

The solution iterates through each row of the input matrix. For each row, it first reverses the order of elements (flips the image horizontally). Then, it iterates through the reversed row and inverts each element (0 becomes 1, and 1 becomes 0). This is done in place, modifying the original matrix directly and then returning it. In the Java solution a more optimized approach is implemented by combining the reversing and inverting in one pass, using two pointers to traverse the row from both ends simultaneously, inverting and swapping elements.

Step-by-Step Algorithm

Step 1: Iterate through each row of the input matrix `image`.
Step 2: For each row, reverse the elements within that row. (Python3, CPP solutions.) The Java and C solution do reverse and invert in the same step.
Step 3: Iterate through the reversed row.
Step 4: For each element in the reversed row, invert its value (change 0 to 1 and 1 to 0).
Step 5: Return the modified matrix `image`.

Key Insights

Insight 1: The flip and invert operations can be performed in place to optimize space complexity.
Insight 2: Reversing a row can be done using two pointers, one starting from the left and the other from the right, swapping elements until they meet in the middle.
Insight 3: Inverting a bit (0 or 1) can be efficiently done using the XOR operation with 1 or subtracting from 1: `pixel = 1 - pixel` or `pixel ^= 1`

Complexity Analysis

Time Complexity: O(n*m)

Space Complexity: O(1)

Topics

This problem involves: Array, Two Pointers, Bit Manipulation, Matrix, Simulation.

Companies

Asked at: IBM.

Flipping an Image | LeetCode 832

Easy

Array Two Pointers Bit Manipulation Matrix Simulation

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

Solution Code

Available in:

class Solution {
    public int[][] flipAndInvertImage(int[][] image) {
        int n = image.length;
        for (int i = 0; i < n; i++) {
            int left = 0;
            int right = n - 1;
            while (left <= right) {
                int temp = image[i][left];
                image[i][left] = 1 - image[i][right];
                image[i][right] = 1 - temp;
                left++;
                right--;
            }
        }
        return image;
    }
}

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Problem Info

Description

Problem 832: Flipping an Image - Detailed explanation and solution approaches.

Topics

Array Two Pointers Bit Manipulation Matrix Simulation

Companies

IBM

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:832

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: Iterate through each row of the input matrix `image`.
2
Step 2: For each row, reverse the elements within that row. (Python3, CPP solutions.) The Java and C solution do reverse and invert in the same step.
3
Step 3: Iterate through the reversed row.
4
Step 4: For each element in the reversed row, invert its value (change 0 to 1 and 1 to 0).
5
Step 5: Return the modified matrix `image`.

💡

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*m)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is determined by the number of elements in the matrix, which is n*m. The space complexity is constant because we're not using any extra space that scales with the input size (except C solution).

📖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 extra space for row reversal

Instead of reversing the row in place, you could create a new temporary array to store the reversed row, then invert and copy back to the original matrix.

Time: O(n*m)Space: O(m) - for each row an extra array of size m is created

Trade-offs: This approach is less efficient in terms of space complexity, as it requires extra memory. It may be easier to understand for beginners, but it is not recommended due to the increased memory usage.

✨

Key Insights

1Insight 1: The flip and invert operations can be performed in place to optimize space complexity.
2Insight 2: Reversing a row can be done using two pointers, one starting from the left and the other from the right, swapping elements until they meet in the middle.
3Insight 3: Inverting a bit (0 or 1) can be efficiently done using the XOR operation with 1 or subtracting from 1: `pixel = 1 - pixel` or `pixel ^= 1`

📚

Key Terms Explained

For Students

Array

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

Two Pointers

Using two indices to traverse data from different positions simultaneously.

Edge Cases

Edge case 1: Empty image matrix. The code will still work correctly, as the loops will not execute.
Edge case 2: Image matrix with only one row or one column. The code handles these cases without any special modifications, as the reversing and inverting operations will still execute correctly.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to invert the bits after reversing the row. The problem explicitly requires both operations, so neglecting one leads to incorrect results.

✗Common mistake 2: Incorrectly implementing the in-place reversal, potentially leading to out-of-bounds errors or incorrect swapping. The two-pointer approach, if implemented correctly, avoids such errors.

✅

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: Image processing applications where images need to be manipulated or transformed, such as mirroring an image or applying a simple color inversion.

🏦Real-world scenario 2: Data manipulation in scientific simulations or machine learning tasks, where binary data needs to be flipped and inverted for processing.

💡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

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ 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 21, 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

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

When is the two-pointer technique most effective?

Two pointers work best on sorted arrays or when searching for pairs/triplets that satisfy a condition. Common patterns include: moving pointers inward from both ends (like in two-sum variants), fast/slow pointers for cycle detection, or left/right pointers for partitioning.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Flipping an Image"?

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

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