#867

Easy

LeetCode Problem Workspace

Transpose Matrix

Transpose Matrix problem requires flipping a matrix's rows and columns to return the transposed version.

array matrix simulation

Problem Statement

Given a 2D integer array matrix, your task is to return its transpose.

The transpose of a matrix is obtained by flipping it over its main diagonal, switching the row and column indices.

Examples

Example 1

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

Output: [[1,4,7],[2,5,8],[3,6,9]]

Example details omitted.

Example 2

Input: matrix = [[1,2,3],[4,5,6]]

Output: [[1,4],[2,5],[3,6]]

Example details omitted.

Constraints

m == matrix.length
n == matrix[i].length
1 <= m, n <= 1000
1 <= m * n <= 105
-109 <= matrix[i][j] <= 109

Solution Approach

Iterate through the Matrix

Start by iterating over the rows and columns of the matrix. For each element at position matrix[i][j], place it at transpose[j][i]. This method achieves the desired transposition.

Space Efficiency

You can perform this transposition in-place if the matrix is mutable, reducing space complexity. However, if working with immutable matrices, a new array is required to store the result.

Handle Matrix Constraints

Ensure your solution handles matrices with varied row and column sizes, as well as larger input sizes, as matrices can range up to 1000x1000.

Complexity Analysis

Metric	Value
Time	O(R * C)
Space	O(R * C)

The time complexity is O(R * C), where R is the number of rows and C is the number of columns in the matrix. Each element of the matrix is accessed once. The space complexity is also O(R * C), as you need to store the result in a new matrix of the same size.

What Interviewers Usually Probe

Candidate handles basic matrix manipulation problems well.
Candidate uses space efficiently when applicable.
Candidate shows understanding of matrix properties and problem constraints.

Common Pitfalls or Variants

Common pitfalls

Incorrectly swapping rows and columns, leading to a mismatched result.
Overcomplicating the problem by trying to use advanced algorithms.
Failing to account for non-square matrices and assuming the transpose is always symmetric.

Follow-up variants

Transposing a matrix in-place without extra space.
Transposing a matrix where rows and columns have different lengths.
Handling extremely large matrices with efficient time and space complexity.

FAQ

What is the time complexity of the Transpose Matrix problem?

The time complexity is O(R * C), where R is the number of rows and C is the number of columns.

How should I handle large matrices for the Transpose Matrix problem?

Ensure your solution works efficiently for up to 1000x1000 matrices by using space-efficient methods or transposing in-place when possible.

What is the main challenge in the Transpose Matrix problem?

The primary challenge is ensuring that rows are correctly mapped to columns, especially for non-square matrices.

Do I need any advanced algorithms for the Transpose Matrix problem?

No, you only need to understand how rows and columns relate in a matrix and iterate through them.

Can I transpose the matrix in-place?

Yes, if the matrix allows modification, you can transpose it in-place with a carefully designed loop.

terminal

Solution

Solution 1: Simulation

Let $m$ be the number of rows and $n$ be the number of columns in the matrix $\textit{matrix}$. According to the definition of transpose, the transposed matrix $\textit{ans}$ will have $n$ rows and $m$ columns.

1

2

3

class Solution:
    def transpose(self, matrix: List[List[int]]) -> List[List[int]]:
        return list(zip(*matrix))

Continue Practicing

#885 spiral matrix iii #832 flipping an image #749 contain virus