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 wavelike 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 topleft triangle (first half) and traversing the bottomright 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

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

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

First Half Zigzag Traversal
 Iterate i from 0 to row1:
 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.
 If counter is even:
 Iterate i from 0 to row1:

Second Half Zigzag Traversal
 Iterate i from 1 to col1:
 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.
 If counter is even:
 Iterate i from 1 to col1:

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].
Program List

1) Zigzag traversal of matrix in java
2) Zigzag traversal of matrix in c++
3) Zigzag traversal of matrix in c
4) Zigzag traversal of matrix in c#
5) Zigzag traversal of matrix in vb.net
6) Zigzag traversal of matrix in php
7) Zigzag traversal of matrix in node js
8) Zigzag traversal of matrix in typescript
9) Zigzag traversal of matrix in python
10) Zigzag traversal of matrix in ruby
11) Zigzag traversal of matrix in scala
12) Zigzag traversal of matrix in swift
13) Zigzag traversal of matrix in kotlin
14) Zigzag traversal of matrix in golang
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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