# Leetcode – Flipping an Image Solution in Python

Handling matrix operations is a key skill in algorithmic problem solving, especially when one starts delving into image processing or two-dimensional data handling. Leetcode’s “Flipping an Image” problem provides a perfect introduction to such operations. This article offers an in-depth walkthrough of the problem and its solution using Python.

1. Problem Statement
2. Unraveling the Problem
3. Solution Strategy
4. Python Implementation
5. Analyzing the Solution
6. Potential Optimizations and Variations
7. Conclusion

### 1. Problem Statement

Given a binary matrix A, we want to flip the image horizontally, and then invert it. 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].

### 2. Unraveling the Problem

To comprehend the task fully, let’s look at a sample:Given matrix:

1 1 0
1 0 1
0 0 0

After flipping horizontally:

0 1 1
1 0 1
0 0 0

After inverting:

1 0 0
0 1 0
1 1 1

### 3. Solution Strategy

The solution can be broken down into two main steps:

1. Horizontal Flip: Iterate over each row in the matrix and reverse its order.
2. Inversion: For each cell in the matrix, change 1 to 0 and 0 to 1.

### 4. Python Implementation

With the strategy in mind, let’s draft a Python solution:

def flipAndInvertImage(A):
# Step 1: Horizontal Flip
for row in A:
row.reverse()

# Step 2: Inversion
for i in range(len(A)):
for j in range(len(A[i])):
A[i][j] = 1 - A[i][j]

return A

### 5. Analyzing the Solution

• The horizontal flipping is straightforward with Python’s built-in .reverse() method for lists.
• For inversion, we iterate through every cell of the matrix. Using the expression 1 - A[i][j] efficiently toggles between 0 and 1 since 1 - 0 is 1 and 1 - 1 is 0.

### 6. Potential Optimizations and Variations

1. Combine Operations: The horizontal flip and inversion can be combined into a single loop, optimizing the iteration process. This can be achieved using list comprehension.
def flipAndInvertImage(A):
return [[1 - x for x in row[::-1]] for row in A]

2. Using Map Function: Python’s map function can be employed for a more functional approach. This can be combined with lambda functions to achieve the desired transformations.

3. Working with Larger Values: While this problem specifically deals with binary values, the concept can be extended to matrices with larger values, introducing more complex flipping and inversion rules.

### 7. Conclusion

The “Flipping an Image” problem is a foundational exercise in matrix operations. It reinforces the importance of understanding two-dimensional data structures and provides essential practice for more advanced image processing or matrix manipulation tasks. Python’s versatile toolkit makes solving such problems efficient, with opportunities for various implementation strategies.