# Zigzag traversal of matrix

When working with matrices in programming, exploring elements in a unique order can be beneficial. Zigzag traversal is a technique where matrix elements are visited in a wave-like pattern, creating an interesting way to process data. In this article, we'll delve into the concept of zigzag traversal, providing a comprehensive explanation, example, approach, algorithm, and Java,C++,Python code. By the end, you'll have a solid grasp of how to perform zigzag traversal on a matrix. ## Problem Statement and Description

Given a matrix of dimensions M x N, the objective is to traverse all its elements in a zigzag pattern and print them in a specific order. Consider the matrix below as an example:

``````1  2  3  4
6  7  8  9
11 12 13 14
16 17 18 19
1  2  3  4``````

Our goal is to traverse this matrix in a zigzag manner and output the elements as follows:

``1  2  6  11  7  3  4  8  12  16  1  17  13  9  14  18  2  3  19  4``

## Idea to Solve the Problem

The zigzag traversal can be divided into two main parts: traversing the top-left triangle (first half) and traversing the bottom-right triangle (second half) of the matrix. For the first half, we move along the diagonals while printing the elements. For the second half, we alternate between two different traversal strategies based on the current iteration.

## Algorithm

1. Initialize variables i, j, and k to keep track of positions within the matrix, and counter to determine traversal strategy.

2. Initialize row and col with the number of rows and columns in the matrix.

3. First Half Zigzag Traversal
• Iterate i from 0 to row-1:
• If counter is even:
• Iterate j from 0 to i and print the element at index matrix[i - j][j].
• If counter is odd:
• Initialize j as i and k as 0.
• Iterate while j is greater than or equal to 0 and k is less than or equal to i:
• Print the element at index matrix[k][j].
• Decrement j and increment k.
• Increment counter.
4. Second Half Zigzag Traversal
• Iterate i from 1 to col-1:
• If counter is even:
• Initialize j as row - 1 and k as i.
• Iterate while j is greater than or equal to 0 and k is less than col:
• Print the element at index matrix[j][k].
• Decrement j and increment k.
• If counter is odd:
• Call the reverse function (explained below) with appropriate arguments to display elements in reverse order.
• Increment counter.
5. Reverse Function
• A recursive function that takes the matrix, i, j, k, and col as arguments.
• If j is greater than or equal to 0 and k is less than col:
• Recursively call reverse with decremented j and incremented k.
• Print the element at index matrix[j][k].

## Time Complexity

The time complexity of this zigzag traversal algorithm is O(M x N), where M is the number of rows and N is the number of columns in the matrix. This is because in the worst case, we visit each element once during traversal.

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