Matrices: Transpose a Matrix

You are 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.

Answer

The main idea consists of two steps:

Step 1: Create an empty result matrix of the correct transposed size. We use res = [[0]*rows for i in range(cols)]. This means we create as many rows in the result as there are columns in the original, and each row has as many entries as the original had rows.
Step 2: Fill the result matrix by swapping row and column indices using res[c][r] = matrix[r][c]. A nested for loop is used to visit each $$(r, c)$$ position in the original matrix.

class Solution:
    def transpose(self, matrix: List[List[int]]) -> List[List[int]]:
        rows, cols = len(matrix), len(matrix[0])
        res = [[0]*rows for i in range(cols)]

        for r in range(rows):
            for c in range(cols):
                res[c][r] = matrix[r][c]

        return res

Alternative method (Pythonic one-liner):

transposed = [list(row) for row in zip(*matrix)]

Programming lesson: In zip(*matrix), the symbol * is the unpacking operator. It takes the list of rows [row1, row2, row3, ...] and feeds them into zip as separate arguments:

\texttt{zip(row1, row2, row3, ...)}

This makes zip combine the first elements of each row together, then the second elements, and so on, exactly forming the transpose. This gives a list of tuples hence the need for the list comprehension.