The transpose of a matrix can be defined as a new matrix whose rows are the columns of the original matrix and the columns are the rows of the original matrix. If A is a matrix then its transpose is denoted as .
For example:
If a matrix is:
Then the transpose of the matrix is
INPUT: A matrix
OUTPUT: The transpose of the matrix
PROCESS:
Step 1: [taking the input]
Read m, n [the number of rows and columns of the matrix]
For i=0 to m-1 repeat
For j=0 to n-1 repeat
Read a[i][j]
[End of ‘for’ loop]
[End of ‘for’ loop]
Step 2: [The transpose of the matrix]
for i = 0 to m-1 repeat
for j = 0 to n-1 repeat
Set t[j][i]<-a[i][j]
[End of ‘for loop]
[End of ‘for’ loop]
[printing the transpose matrix]
Print "The transpose of the matrix is:"
For i=0 to n-1 repeat
For j=0 to m-1 repeat
Print t[i][j]
If j=m-1 then
Move to the next line
[End of ‘if’]
[End of ‘for’ loop]
[End of ‘for’ loop]
Step 3: Stop.
TIME COMPLEXITY:
for (i = 0; i < m; i++)-------------------- O(m)
for (j = 0; j < n; j++)--------------- O(n)
{ t[j][i]=a[i][j];
}
//printing the transpose matrix
printf("\nThe transpose of the matrix is:\n");
for(i=0;i<n;i++)----------------- O(n)
for(j=0;j<m;j++)------ O(m)
{ printf("%d ",t[i][j]);
if(j==m-1)------- O(c1)
printf("\n");
}
The time complexity is O(m*n). if the number of rows and columns are equal, then the time complexity is O().
APPLICATION:
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