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Farthest Distance of a 0 From the Centre of a 2-D Matrix in Java

In the realm of computational mathematics and algorithmic problem-solving, a common task is to manipulate and analyze matrices. One intriguing problem involves finding the farthest distance of a zero (0) from the center of a 2-dimensional matrix. The task not only showcases the elegance of mathematical reasoning but also highlights the importance of efficient algorithms in modern computing.

Given a 2-dimensional matrix filled with numbers, the goal is to determine the maximum distance a zero can be from the center of the matrix. The center, in this context, is defined as the cell at coordinates (m/2, n/2) where m is the number of rows and n is the number of columns in the matrix.

Understanding the Problem

Before diving into the algorithmic approach, it's crucial to grasp the nature of the problem. We're dealing with a grid-like structure, where each cell is indexed by a pair (i, j) representing the row and column numbers respectively.

The distance between two cells (i1, j1) and (i2, j2) can be calculated using the Manhattan distance formula:


Here is a simplified pseudocode representation of the algorithm:


Let's illustrate the algorithm with an example. Consider the following matrix:

In this case, the center of the matrix is at (2, 2). The farthest zero is located at (0, 1), which has a distance of |0 - 2| + |1 - 2| = 3.




Enter the number of rows:
Enter the number of columns:
Enter the elements of the matrix:
1 0 1 1
0 0 0 1
1 0 1 1
1 1 1 1
The farthest distance of a zero from the center is: 3

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