Matrix Transposition

Edit PagePage History

JCSU Unit 5 Problem Set 2 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Easy-Medium
• ⏰ Time to complete: 15 mins
• 🛠️ Topics: Matrix Manipulation, Transposition, Nested Lists

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• What is the goal of the problem?
  • Return the transpose of a given m x n matrix.
• Are there constraints on input?
  • The input may include empty matrices or rectangular matrices (not necessarily square).

HAPPY CASE Input: matrix = [ [1, 2, 3], [4, 5, 6] ] Output: [ [1, 4], [2, 5], [3, 6] ] Explanation: Rows are converted to columns.

EDGE CASE Input: matrix = [] Output: [] Explanation: An empty matrix results in an empty output.

EDGE CASE Input: matrix = [ [1] ] Output: [ [1] ] Explanation: A 1x1 matrix remains the same when transposed.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

For matrix transposition problems, we want to consider the following approaches:

• Using zip(): Use zip(*matrix) to group elements from the rows into columns.
• Nested Loops (Alternative): Build the transpose by iterating through rows and columns manually.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea:
Transpose the matrix by converting rows into columns. Use zip(*matrix) to group elements from the rows and convert the resulting tuples into lists.

Steps:

1. Check if the input matrix is empty. If so, return an empty list.
2. Use zip(*matrix) to group elements from each row into columns.
3. Convert the resulting tuples into lists using a list comprehension.
4. Return the new transposed matrix.

4: I-mplement

Implement the code to solve the algorithm.

def transpose_matrix(matrix):
    # Use zip to group columns of the original matrix together
    # *matrix unpacks rows, and zip() pairs elements from each row into tuples
    transposed = [list(row) for row in zip(*matrix)]
    return transposed  # Return the transposed matrix

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

Example 1:

• Input: matrix = [ [1, 2, 3], [4, 5, 6] ]
• Expected Output: [ [1, 4], [2, 5], [3, 6] ]
• Observed Output: [ [1, 4], [2, 5], [3, 6] ]

Example 2:

• Input: matrix = [ [1, 2], [3, 4], [5, 6] ]
• Expected Output: [ [1, 3, 5], [2, 4, 6] ]
• Observed Output: [ [1, 3, 5], [2, 4, 6] ]

Example 3:

• Input: matrix = []
• Expected Output: []
• Observed Output: []

Example 4:

• Input: matrix = [ [1] ]
• Expected Output: [ [1] ]
• Observed Output: [ [1] ]

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Assume m is the number of rows and n is the number of columns in the matrix.

• Time Complexity: O(m * n) because zip(*matrix) processes each element once.
• Space Complexity: O(m * n) because we create a new matrix to store the transposed result.