Given a 2D integer array matrix
, return the transpose of matrix
.
The transpose of a matrix is the matrix flipped over its main diagonal, switching the matrix's row and column indices.
For example:
Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output: [[1,4,7],[2,5,8],[3,6,9]]
In this example, the original matrix is a 3x3 matrix. The transpose is created by swapping rows and columns. So, the element at matrix[0][1] which is '2' becomes the element at transposed_matrix[1][0].
Here's another example with a non-square matrix:
Input: matrix = [[1,2,3],[4,5,6]]
Output: [[1,4],[2,5],[3,6]]
In this case, the input is a 2x3 matrix, and the output is a 3x2 matrix. Again, the rows and columns have been swapped.
Your task is to write a function that takes a 2D integer array (a list of lists) as input and returns its transpose.
Consider these constraints:
1 <= m, n <= 1000
where 'm' is the number of rows and 'n' is the number of columns.1 <= m * n <= 10^5
-10^9 <= matrix[i][j] <= 10^9
Can you implement an efficient solution for this problem, considering both time and space complexity?
When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:
The goal is to swap rows and columns in a table. The brute force way to do this is to create a new empty table, then systematically copy elements from the original table into their new, transposed positions in the new table.
Here's how the algorithm would work step-by-step:
def transpose_matrix_brute_force(matrix):
number_of_rows = len(matrix)
number_of_columns = len(matrix[0])
# Initialize the transposed matrix with swapped dimensions
transposed_matrix = [[0 for i in range(number_of_rows)] for j in range(number_of_columns)]
# Iterate through the original matrix
for row_index in range(number_of_rows):
for column_index in range(number_of_columns):
# Swap row and column indices to transpose
transposed_matrix[column_index][row_index] = matrix[row_index][column_index]
return transposed_matrix
The goal is to swap the rows and columns of a table. We can do this efficiently by creating a new table where the original rows become columns and vice versa. A key consideration is handling tables that aren't square, meaning the number of rows and columns are different.
Here's how the algorithm would work step-by-step:
def transpose_matrix(matrix):
number_of_rows = len(matrix)
number_of_columns = len(matrix[0])
# Dimensions are swapped for the transposed matrix.
transposed_number_of_rows = number_of_columns
transposed_number_of_columns = number_of_rows
# Initialize the transposed matrix with swapped dimensions.
transposed_matrix = [([0] * transposed_number_of_columns) for _ in range(transposed_number_of_rows)]
for row_index in range(number_of_rows):
for column_index in range(number_of_columns):
# Copy each element, swapping row and column indices.
transposed_matrix[column_index][row_index] = matrix[row_index][column_index]
return transposed_matrix
Case | How to Handle |
---|---|
Null or undefined matrix input | Return an empty matrix or throw an IllegalArgumentException to signal invalid input. |
Empty matrix (0 rows or 0 columns) | Return an empty matrix or the original matrix if an in-place operation is expected and the input is already empty. |
Non-rectangular matrix (rows with different lengths) | Throw an IllegalArgumentException as a non-rectangular matrix cannot be transposed or pad the shorter rows with a default value. |
1x1 matrix (single element) | Return the original matrix as the transpose will be the same. |
Very large matrix exceeding memory limitations | Consider an out-of-memory error and explore block-wise transposition or external memory algorithms if possible. |
Matrix with integer overflow potential during index calculations | Ensure indices are within acceptable ranges and consider using larger integer types if necessary to prevent overflow during calculations. |
Matrix with negative numbers or extreme values | The transposition algorithm itself is generally not affected by negative numbers or extreme values, but consider potential overflow if these values are used in further calculations after transposition. |
Matrix containing floating point numbers with precision issues | While the transposition itself doesn't cause new precision problems, subsequent operations involving these transposed floats may require consideration for potential precision errors. |