Given a 2-D array of order N x N, print a matrix that is the mirror of the given tree across the diagonal. We need to print the result in a way: swap the values of the triangle above the diagonal with the values of the triangle below it like a mirror image swap. Print the 2-D array obtained in a matrix layout.
Examples:
Input : int mat[][] = {{1 2 4 }
{5 9 0}
{ 3 1 7}}
Output : 1 5 3
2 9 1
4 0 7
Input : mat[][] = {{1 2 3 4 }
{5 6 7 8 }
{9 10 11 12}
{13 14 15 16} }
Output : 1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
A simple solution to this problem involves extra space. We traverse all right diagonal (right-to-left) one by one. During the traversal of the diagonal, first, we push all the elements into the stack and then we traverse it again and replace every element of the diagonal with the stack element.
Below is the implementation of the above idea.
Javascript
<script> // Simple Javascript program to find mirror of matrix across diagonal. let MAX = 100; function imageSwap(mat, n) { // for diagonal which start from at // first row of matrix let row = 0; // traverse all top right diagonal for (let j = 0; j < n; j++) { // here we use stack for reversing // the element of diagonal let s = []; let i = row, k = j; while (i < n && k >= 0) { s.push(mat[i++][k--]); } // push all element back to matrix // in reverse order i = row; k = j; while (i < n && k >= 0) { mat[i++][k--] = s[s.length - 1]; s.pop(); } } // do the same process for all the // diagonal which start from last // column let column = n - 1; for (let j = 1; j < n; j++) { // here we use stack for reversing // the elements of diagonal let s = []; let i = j, k = column; while (i < n && k >= 0) { s.push(mat[i++][k--]); } // push all element back to matrix // in reverse order i = j; k = column; while (i < n && k >= 0) { mat[i++][k--] = s[s.length - 1]; s.pop(); } } } // Utility function to print a matrix function printMatrix(mat, n) { for (let i = 0; i < n; i++) { for (let j = 0; j < n; j++) { document.write(mat[i][j] + " "); } document.write("</br>"); } } let mat = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]; let n = 4; imageSwap(mat, n); printMatrix(mat, n); </script> |
Output:
1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16
Time complexity : O(n*n)
Auxiliary Space: O(1)
An efficient solution to this problem is that if we observe an output matrix, then we notice that we just have to swap (mat[i][j] to mat[j][i]).
Below is the implementation of the above idea.
Javascript
<script> // Efficient Javascript program to find mirror of // matrix across diagonal. let MAX = 100; function imageSwap(mat, n) { // traverse a matrix and swap // mat[i][j] with mat[j][i] for (let i = 0; i < n; i++) for (let j = 0; j <= i; j++) mat[i][j] = mat[i][j] + mat[j][i] - (mat[j][i] = mat[i][j]); } // Utility function to print a matrix function printMatrix(mat, n) { for (let i = 0; i < n; i++) { for (let j = 0; j < n; j++) document.write(mat[i][j] + " "); document.write("</br>"); } } let mat = [ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ], [ 13, 14, 15, 16 ] ]; let n = 4; imageSwap(mat, n); printMatrix(mat, n); </script> |
Output:
1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16
Time complexity : O(n*n)
Auxiliary Space : O(1) because constant space has been used
Please refer complete article on Mirror of matrix across diagonal for more details!
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