Given a matrix of size N X M, find the transpose of the matrix
Transpose of a matrix is obtained by changing rows to columns and columns to rows. In other words, transpose of A[N][M] is obtained by changing A[i][j] to A[j][i].
Example:
Approach: Follow the given steps to solve the problem:
- Run a nested loop using two integer pointers i and j for 0 <= i < N and 0 <= j < M
- Set B[i][j] equal to A[j][i]
Below is the implementation of the above approach:
C++
// C++ program to find // transpose of a matrix #include <bits/stdc++.h> using namespace std; #define N 4 // This function stores transpose // of A[][] in B[][] void transpose(int A[][N], int B[][N]) { int i, j; for (i = 0; i < N; i++) for (j = 0; j < N; j++) B[i][j] = A[j][i]; } // Driver code int main() { int A[N][N] = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 }, { 4, 4, 4, 4 } }; // Note dimensions of B[][] int B[N][N], i, j; // Function call transpose(A, B); cout << "Result matrix is \n"; for (i = 0; i < N; i++) { for (j = 0; j < N; j++) cout << " " << B[i][j]; cout << "\n"; } return 0; } // This code is contributed by shivanisinghss2110 |
C
// C program to find // transpose of a matrix #include <stdio.h> #define N 4 // This function stores transpose of A[][] in B[][] void transpose(int A[][N], int B[][N]) { int i, j; for (i = 0; i < N; i++) for (j = 0; j < N; j++) B[i][j] = A[j][i]; } // Driver code int main() { int A[N][N] = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 }, { 4, 4, 4, 4 } }; // Note dimensions of B[][] int B[N][N], i, j; // Function call transpose(A, B); printf("Result matrix is \n"); for (i = 0; i < N; i++) { for (j = 0; j < N; j++) printf("%d ", B[i][j]); printf("\n"); } return 0; } |
Java
// Java Program to find // transpose of a matrix class GFG { static final int N = 4; // This function stores transpose // of A[][] in B[][] static void transpose(int A[][], int B[][]) { int i, j; for (i = 0; i < N; i++) for (j = 0; j < N; j++) B[i][j] = A[j][i]; } // Driver code public static void main(String[] args) { int A[][] = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 }, { 4, 4, 4, 4 } }; int B[][] = new int[N][N], i, j; // Function call transpose(A, B); System.out.print("Result matrix is \n"); for (i = 0; i < N; i++) { for (j = 0; j < N; j++) System.out.print(B[i][j] + " "); System.out.print("\n"); } } } // This code is contributed by Anant Agarwal. |
Python3
# Python3 Program to find # transpose of a matrix N = 4 # This function stores # transpose of A[][] in B[][] def transpose(A, B): for i in range(N): for j in range(N): B[i][j] = A[j][i] # Driver code if __name__ == '__main__': A = [[1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4]] # To store result B = [[0 for x in range(N)] for y in range(N)] # Function call transpose(A, B) print("Result matrix is") for i in range(N): for j in range(N): print(B[i][j], " ", end='') print() |
C#
// C# Program to find // transpose of a matrix using System; class GFG { static int N = 4; // This function stores transpose // of A[][] in B[][] static void transpose(int[, ] A, int[, ] B) { int i, j; for (i = 0; i < N; i++) for (j = 0; j < N; j++) B[i, j] = A[j, i]; } // Driver code public static void Main() { int[, ] A = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 }, { 4, 4, 4, 4 } }; int[, ] B = new int[N, N]; // Function call transpose(A, B); Console.WriteLine("Result matrix is \n"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) Console.Write(B[i, j] + " "); Console.Write("\n"); } } } // This code is contributed by nitin mittal |
Javascript
<script> // javascript Program to find // transpose of a matrix var N = 4; // This function stores transpose // of A in B function transpose(A , B) { var i, j; for (i = 0; i < N; i++) for (j = 0; j < N; j++) B[i][j] = A[j][i]; } // Driver code var A = [ [ 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [4, 4, 4, 4]]; var B = Array(N); for(i=0;i<N;i++) B[i] =Array(N).fill(0); transpose(A, B); document.write("Result matrix is <br/>"); for (i = 0; i < N; i++) { for (j = 0; j < N; j++) document.write(B[i][j] + " "); document.write("<br/>"); } // This code contributed by Rajput-Ji </script> |
PHP
<?php // This function stores transpose // of A[][] in B[][] function transpose(&$A, &$B) { $N = 4; for ($i = 0; $i < $N; $i++) for ($j = 0; $j < $N; $j++) $B[$i][$j] = $A[$j][$i]; } // Driver code $A = array(array(1, 1, 1, 1), array(2, 2, 2, 2), array(3, 3, 3, 3), array(4, 4, 4, 4)); $N = 4; // Function call transpose($A, $B); echo "Result matrix is \n"; for ($i = 0; $i < $N; $i++) { for ($j = 0; $j < $N; $j++) { echo $B[$i][$j]; echo " "; } echo "\n"; } // This code is contributed // by Shivi_Aggarwal ?> |
Output
Result matrix is 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Time complexity: O(M x N).
Auxiliary Space: O(M x N), since M x N extra space has been used.
Program to find the transpose of a matrix using constant space:
Note – This approach works only for square matrices (i.e., – where no. of rows are equal to the number of columns). This algorithm is also known as an “in-place” algorithm as it uses no extra space to solve the problem.
Follow the given steps to solve the problem:
- Run a nested loop using two integer pointers i and j for 0 <= i < N and i+1 <= j < N
- Swap A[i][j] with A[j][i]
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h> using namespace std; #define N 4 // Converts A[][] to its transpose void transpose(int A[][N]) { for (int i = 0; i < N; i++) for (int j = i + 1; j < N; j++) swap(A[i][j], A[j][i]); } int main() { int A[N][N] = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 }, { 4, 4, 4, 4 } }; transpose(A); printf("Modified matrix is \n"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) printf("%d ", A[i][j]); printf("\n"); } return 0; } |
Java
// Java Program to find // transpose of a matrix class GFG { static final int N = 4; // Finds transpose of A[][] in-place static void transpose(int A[][]) { for (int i = 0; i < N; i++) for (int j = i + 1; j < N; j++) { int temp = A[i][j]; A[i][j] = A[j][i]; A[j][i] = temp; } } // Driver code public static void main(String[] args) { int A[][] = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 }, { 4, 4, 4, 4 } }; transpose(A); System.out.print("Modified matrix is \n"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) System.out.print(A[i][j] + " "); System.out.print("\n"); } } } |
Python3
# Python3 Program to find # transpose of a matrix N = 4 # Finds transpose of A[][] in-place def transpose(A): for i in range(N): for j in range(i+1, N): A[i][j], A[j][i] = A[j][i], A[i][j] # driver code A = [[1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4]] transpose(A) print("Modified matrix is") for i in range(N): for j in range(N): print(A[i][j], " ", end='') print() # This code is contributed # by Anant Agarwal. |
C#
// C# Program to find transpose of // a matrix using System; class GFG { static int N = 4; // Finds transpose of A[][] in-place static void transpose(int[, ] A) { for (int i = 0; i < N; i++) for (int j = i + 1; j < N; j++) { int temp = A[i, j]; A[i, j] = A[j, i]; A[j, i] = temp; } } // Driver code public static void Main() { int[, ] A = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 }, { 4, 4, 4, 4 } }; transpose(A); Console.WriteLine("Modified matrix is "); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) Console.Write(A[i, j] + " "); Console.WriteLine(); } } } // This code is contributed by anuj_67. |
Javascript
<script> // JavaScript Program to find // transpose of a matrix var N = 4; // Finds transpose of A in-place function transpose(A) { for (i = 0; i < N; i++) for (j = i + 1; j < N; j++) { var temp = A[i][j]; A[i][j] = A[j][i]; A[j][i] = temp; } } // Driver code var A = [ [ 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 4, 4, 4 ] ]; transpose(A); document.write("Modified matrix is <br/>"); for (i = 0; i < N; i++) { for (j = 0; j < N; j++) document.write(A[i][j] + " "); document.write("\<br/>"); } // This code is contributed by aashish1995 </script> |
PHP
<?php // Converts A[][] to its transpose function transpose(&$A) { $N = 4; for ($i = 0; $i < $N; $i++) for ($j = $i + 1; $j < $N; $j++) { $temp = $A[$i][$j]; $A[$i][$j] = $A[$j][$i]; $A[$j][$i] = $temp; } } // Driver Code $N = 4; $A = array(array(1, 1, 1, 1), array(2, 2, 2, 2), array(3, 3, 3, 3), array(4, 4, 4, 4)); transpose($A); echo "Modified matrix is " . "\n"; for ($i = 0; $i < $N; $i++) { for ($j = 0; $j < $N; $j++) echo $A[$i][$j] . " "; echo "\n"; } // This code is contributed // by Akanksha Rai(Abby_akku) ?> |
Output
Modified matrix is 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Time complexity: O(N2).
Auxiliary Space: O(1)
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