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:

Pseudocode

Here is a simplified pseudocode representation of the algorithm:

function farthestDistance(matrix):
    maxDistance = -1
    centerRow = numberOfRows(matrix) / 2
    centerCol = numberOfColumns(matrix) / 2
    for each cell (i, j) in matrix:
        if matrix[i][j] == 0:
            distance = abs(i - centerRow) + abs(j - centerCol)
            maxDistance = max(maxDistance, distance)
    return maxDistance

Example

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

[1, 0, 1, 1]
[0, 0, 0, 1]
[1, 0, 1, 1]
[1, 1, 1, 1]

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.

Implementation

Filename: FarthestDistance.java

import java.util.Scanner;
public class FarthestDistance {
    public static int farthestDistance(int[][] matrix) {
        int maxDistance = -1;
        int centerRow = matrix.length / 2;
        int centerCol = matrix[0].length / 2;
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (matrix[i][j] == 0) {
                    int distance = Math.abs(i - centerRow) + Math.abs(j - centerCol);
                    maxDistance = Math.max(maxDistance, distance);
                }
            }
        }
        return maxDistance;
    }
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.println("Enter the number of rows:");
        int m = scanner.nextInt();
        System.out.println("Enter the number of columns:");
        int n = scanner.nextInt();
        int[][] matrix = new int[m][n];
        System.out.println("Enter the elements of the matrix:");
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                matrix[i][j] = scanner.nextInt();
            }
        }
        int result = farthestDistance(matrix);
        System.out.println("The farthest distance of a zero from the center is: " + result);
    }
}

Output:

Enter the number of rows:
4
Enter the number of columns:
4
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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