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matrix transpose c++

Transpose a Matrix

Given a matrix of N dimensions, and we need to transpose it. One of the standard problem on matrices. Don’t confuse Transpose with Rotation, the rotation is normally performed on the X-Y axis while in a transpose, the matrix is flipped on its diagonal.

Example:

matrix transpose
Matrix Transpose

Solution Approach

This is simple swapping but, its a matrix and the swapping takes place over the diagonal

matrix transposing
Transpose a Matrix
  • Simple swapping
  • Try not to use extra space [constant sapce]
  • Matrix requires minimum of two loops [O(N^2)]

Code to Transpose a Square Matrix

/*Code in C++*/
#include <iostream>
using namespace std;

int main()
{
    int i, j, t, N = 4;
    int A[N][N] = {{1, 2, 3, 4},
                   {5, 5, 5, 5},
                   {6, 7, 8, 9},
                   {10, 10, 10, 10}};

    for (i = 0; i < N; i++)
    {
        for (j = i + 1; j < N; j++)
        {
            t = A[i][j];
            A[i][j] = A[j][i];
            A[j][i] = t;
        }
    }

    for (i = 0; i < N; i++)
    {
        for (j = 0; j < N; j++)
            cout << A[i][j] << " ";
        cout << endl;
    }

    return 0;
}

Output

1 5 6 10
2 5 7 10
3 5 8 10
4 5 9 10

Yes, we did it with Constant Space and only two loops but, this works only for Square matrices where the no.of columns and rows are the same.

Transposing a Rectangular Matrix

Here are a few points to consider,

  • Direct swapping dosen’t work
  • We need to use extra space
  • Dimensions of input and output matrices are different
  • Can do everything within too loops itself.

Pseudocode

  1. Read the input Matrix
  2. Initialize a new Matrix
  3. Exchange each number as we iterate A[i][j] = B[j][i];

We are actually swapping here and the dimensions of the new matrix are reverse of the input matrix i.e if the input matrix has 3 rows and 4 columns the new/transposed matrix will have 4 rows and 3 columns.

Code to Transpose a Rectangular Matrix

/*Code in C++*/
#include <iostream>
using namespace std;

int main()
{
    int M = 3, N = 4, i, j;
    int A[M][N] = {{1, 2, 3, 4},
                   {5, 6, 7, 8},
                   {9, 10, 11, 12}};
    int B[N][M];

    for (i = 0; i < N; i++)
        for (j = 0; j < M; j++)
            B[i][j] = A[j][i];

    for (i = 0; i < N; i++)
    {
        for (j = 0; j < M; j++)
            cout << B[i][j] << " ";
        cout << endl;
    }

    return 0;
}

Conclusion

Unlike a square, the rectangle program works for both square and rectangle. Comparing both Square is more optimized as it doesn’t use any extra space.
Happy Coding!

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