Reshape the matrix problem in C#

General
1

The “Matrix Reshape” problem involves changing the dimensions of a given matrix while preserving its elements. Specifically, if you have a matrix of size r x c and you want to reshape it into a new matrix of size r' x c', the total number of elements must remain the same. If the reshape operation isn’t possible, you should return the original matrix.

Problem Statement

Given a matrix represented by a 2D array and two integers r' and c' representing the desired number of rows and columns, reshape the matrix if possible. Otherwise, return the original matrix.

Approach

  1. Check Dimensions: First, check if the total number of elements in the original matrix equals the total number of elements in the new matrix (r' * c'). If not, return the original matrix.

  2. Flatten the Matrix: If reshaping is possible, flatten the original matrix into a single array.

  3. Build the New Matrix: Use the flattened array to construct the new matrix with the desired dimensions.

C# Implementation

Here’s how you can implement this in C#:

public class MatrixReshape
{
    public int[][] Reshape(int[][] mat, int r, int c)
    {
        int originalRows = mat.Length;
        int originalCols = mat[0].Length;

        // Step 1: Check if reshape is possible
        if (originalRows * originalCols != r * c)
        {
            return mat; // Return the original matrix
        }

        // Step 2: Create the new reshaped matrix
        int[][] reshapedMatrix = new int[r][];
        for (int i = 0; i < r; i++)
        {
            reshapedMatrix[i] = new int[c]; // Initialize each row
        }

        // Step 3: Fill the new matrix
        for (int i = 0; i < originalRows; i++)
        {
            for (int j = 0; j < originalCols; j++)
            {
                // Calculate the index in the new matrix
                int index = i * originalCols + j;
                reshapedMatrix[index / c][index % c] = mat[i][j];
            }
        }

        return reshapedMatrix;
    }
}

Explanation of the Code

  1. Matrix Declaration: The method Reshape takes a jagged array (int[][] mat) representing the original matrix, along with two integers r and c for the desired dimensions.

  2. Check Dimensions: We first calculate the number of rows and columns in the original matrix. If the total number of elements (originalRows * originalCols) does not equal the desired total (r * c), we simply return the original matrix.

  3. Create New Matrix: If reshaping is possible, we create a new jagged array called reshapedMatrix with dimensions r x c. Each row is initialized in a loop.

  4. Fill the New Matrix:

    • We use nested loops to iterate through each element of the original matrix.
    • For each element at (i, j), we calculate the corresponding index in the new matrix using index = i * originalCols + j.
    • We then determine the correct row and column in the new matrix using integer division and modulo operations: index / c gives the row, and index % c gives the column.

  5. Return the Result: Finally, we return the newly reshaped matrix.

Complexity

  • Time Complexity: O(m * n), where m is the number of rows and n is the number of columns in the original matrix, since we traverse the matrix once.
  • Space Complexity: O(r * c) for the new reshaped matrix.

Example

Given the input matrix:

1  2
3  4

If we want to reshape it to 1 x 4, the output will be:

1  2  3  4

If we attempt to reshape it to 2 x 3, since the total number of elements doesn’t match, the output will remain:

1  2
3  4

This implementation effectively handles the reshaping of matrices while ensuring clarity and correctness.