Transpose Matrix

The key idea

The transpose flips the matrix over its main diagonal: the value at row i, column j moves to row j, column i. A matrix with m rows and n columns becomes one with n rows and m columns, so allocate the result with swapped dimensions before copying.

Problem

Given a 2-D 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. In other words, the value at row i, column j of the input becomes the value at row j, column i of the result.

If the input has m rows and n columns, the transpose has n rows and m columns.

Constraints

m == matrix.length
n == matrix[i].length
1 <= m, n <= 1000
1 <= m * n <= 10^5
-10^9 <= matrix[i][j] <= 10^9

Examples

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

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

Complexity

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

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