867. Transpose Matrix
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.
Example 1:
Input: matrix = [[1,2,3],[4,5,6],[7,8,9]] Output: [[1,4,7],[2,5,8],[3,6,9]]
Example 2:
Input: matrix = [[1,2,3],[4,5,6]] Output: [[1,4],[2,5],[3,6]]
Constraints:
m == matrix.length
n == matrix[i].length
1 <= m, n <= 1000
1 <= m * n <= 105
-109 <= matrix[i][j] <= 109
Solutions
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.
For any position $(i, j)$ in $\textit{ans}$, it corresponds to the position $(j, i)$ in the matrix $\textit{matrix}$. Therefore, we traverse each element in the matrix $\textit{matrix}$ and transpose it to the corresponding position in $\textit{ans}$.
After the traversal, we return $\textit{ans}$.
The time complexity is $O(m \times n)$, where $m$ and $n$ are the number of rows and columns in the matrix $\textit{matrix}$, respectively. Ignoring the space consumption of the answer, the space complexity is $O(1)$.
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