Transpose Matrix#

Problem statement#

[1]You are given a 2D integer array matrix, and your objective is to find the transpose of the given matrix.

The transpose of a matrix involves flipping the matrix over its main diagonal, effectively swapping its row and column indices.

\[\begin{equation*} \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \longrightarrow \begin{bmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{bmatrix} \end{equation*}\]

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 <= 10^5.
-10^9 <= matrix[i][j] <= 10^9.

Solution#

Code#

#include <iostream>
#include <vector>
using namespace std;
vector<vector<int>> transpose(const vector<vector<int>>& matrix) {
    // declare the transposed matrix mt of desired size, i.e.
    // mt's number of rows = matrix's number of columns
    // mt's number of columns = matrix's number of rows
    vector<vector<int>> mt(matrix[0].size(), 
                           vector<int>(matrix.size()));
    for (int i = 0; i < mt.size(); i++) {
        for (int j = 0; j < mt[i].size(); j++) {
            mt[i][j] = matrix[j][i];
        }
    }
    return mt;
}
void printResult(const vector<vector<int>>& matrix) {
    cout << "[";
    for (auto& row : matrix) {
        cout << "[";
        for (int m : row) {
            cout << m << ",";
        }
        cout << "]";
    }
    cout << "]\n";
}
int main() {
    vector<vector<int>> matrix = {{1,2,3},{4,5,6},{7,8,9}};
    auto result = transpose(matrix);
    printResult(result);
    matrix = {{1,2,3},{4,5,6}};
    result = transpose(matrix);
    printResult(result);
}

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

Complexity#

Runtime: O(m*n), where m = matrix.length and n = matrix[i].length.
Extra space: O(1).

Implementation note#

Note that the matrix might not be square, you cannot just swap the elements using for example the function std::swap.