Farthest Distance of a 0 From the Centre of a 2-D Matrix in JavaIn 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 ProblemBefore 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: PseudocodeHere is a simplified pseudocode representation of the algorithm: ExampleLet'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. ImplementationFilename: FarthestDistance.java 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 Next TopicHow to Terminate a Program in Java? |
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