Python - Group Elements in Matrix

Python - Group Elements in Matrix

Let's understand the different aspects of grouping elements in a matrix.

A matrix, represented in Python as a 2D list (or list of lists), may look like:

matrix = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]

Now, depending on how you want to group elements, there are several ways you might approach this:

1. Group by Rows:

This is basically the original matrix. Each row represents a group.

groups = matrix print(groups) # [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

2. Group by Columns:

This transposes the matrix, where each column in the original matrix becomes a group.

transposed = list(zip(*matrix)) print(transposed) # [(1, 4, 7), (2, 5, 8), (3, 6, 9)]

3. Group by Diagonal:

To group by the primary diagonal (from top-left to bottom-right):

diagonal = [matrix[i][i] for i in range(len(matrix))] print(diagonal) # [1, 5, 9]

For the secondary diagonal (from top-right to bottom-left):

diagonal = [matrix[i][len(matrix) - 1 - i] for i in range(len(matrix))] print(diagonal) # [3, 5, 7]

4. Group in Quadrants:

For a 4x4 matrix:

matrix = [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16] ]

We can break it into quadrants:

q1 = [row[:2] for row in matrix[:2]] q2 = [row[2:] for row in matrix[:2]] q3 = [row[:2] for row in matrix[2:]] q4 = [row[2:] for row in matrix[2:]] print(q1) # [[1, 2], [5, 6]] print(q2) # [[3, 4], [7, 8]] print(q3) # [[9, 10], [13, 14]] print(q4) # [[11, 12], [15, 16]]

5. Group by Unique Values:

If you want to group by unique values:

from collections import defaultdict grouped = defaultdict(list) for i, row in enumerate(matrix): for j, val in enumerate(row): grouped[val].append((i, j)) # storing the indices print(dict(grouped))

In this example, each unique number in the matrix is used as a key in the dictionary, and its value is a list of the positions (indices) where that number appears.

Conclusion:

Depending on the problem at hand, there can be several ways to group elements in a matrix. The above methods are just a few common scenarios. The flexibility of Python allows you to craft a solution to match your specific needs.

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