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Transpose Matrix

Difficulty: Easy

Problem Description

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.

Key Insights

  • The transpose of a matrix can be obtained by switching the indices of the elements.
  • For an element at position (i, j) in the original matrix, it will be at position (j, i) in the transposed matrix.
  • The resulting matrix will have dimensions of n x m, where n is the number of rows in the original matrix and m is the number of columns.

Space and Time Complexity

Time Complexity: O(m * n)
Space Complexity: O(m * n)

Solution

To transpose the matrix, we can create a new 2D array with the dimensions swapped. We will iterate through each element of the original matrix and place it in the transposed position in the new matrix. We will use a nested loop to facilitate this process.

Code Solutions

def transpose(matrix):
    # Get the number of rows and columns
    m, n = len(matrix), len(matrix[0])
    # Create a new matrix with swapped dimensions
    transposed = [[0] * m for _ in range(n)]
    
    # Fill the transposed matrix
    for i in range(m):
        for j in range(n):
            transposed[j][i] = matrix[i][j]
    
    return transposed
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