# Mirror of matrix across diagonal

Last Updated : 25 Jul, 2022

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.

## C++

 `// Simple CPP program to find mirror of` `// matrix across diagonal.` `#include ` `using` `namespace` `std;`   `const` `int` `MAX = 100;`   `void` `imageSwap(``int` `mat[][MAX], ``int` `n)` `{` `    ``// for diagonal which start from at ` `    ``// first row of matrix` `    ``int` `row = 0;`   `    ``// traverse all top right diagonal` `    ``for` `(``int` `j = 0; j < n; j++) {`   `        ``// here we use stack for reversing` `        ``// the element of diagonal` `        ``stack<``int``> s;` `        ``int` `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.top();` `            ``s.pop();` `        ``}` `    ``}`   `    ``// do the same process for all the` `    ``// diagonal which start from last` `    ``// column` `    ``int` `column = n - 1;` `    ``for` `(``int` `j = 1; j < n; j++) {`   `        ``// here we use stack for reversing ` `        ``// the elements of diagonal` `        ``stack<``int``> s;` `        ``int` `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.top();` `            ``s.pop();` `        ``}` `    ``}` `}`   `// Utility function to print a matrix` `void` `printMatrix(``int` `mat[][MAX], ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``for` `(``int` `j = 0; j < n; j++)` `            ``cout << mat[i][j] << ``" "``;` `        ``cout << endl;` `    ``}` `}`   `// driver program to test above function` `int` `main()` `{` `    ``int` `mat[][MAX] = { { 1, 2, 3, 4 },` `                     ``{ 5, 6, 7, 8 },` `                     ``{ 9, 10, 11, 12 },` `                     ``{ 13, 14, 15, 16 } };` `    ``int` `n = 4;` `    ``imageSwap(mat, n);` `    ``printMatrix(mat, n);` `    ``return` `0;` `}`

## Java

 `// Simple Java program to find mirror of` `// matrix across diagonal.`   `import` `java.util.*;`   `class` `GFG ` `{`   `    ``static` `int` `MAX = ``100``;`   `    ``static` `void` `imageSwap(``int` `mat[][], ``int` `n) ` `    ``{` `        ``// for diagonal which start from at ` `        ``// first row of matrix` `        ``int` `row = ``0``;`   `        ``// traverse all top right diagonal` `        ``for` `(``int` `j = ``0``; j < n; j++) ` `        ``{`   `            ``// here we use stack for reversing` `            ``// the element of diagonal` `            ``Stack s = ``new` `Stack<>();` `            ``int` `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.peek();` `                ``s.pop();` `            ``}` `        ``}`   `        ``// do the same process for all the` `        ``// diagonal which start from last` `        ``// column` `        ``int` `column = n - ``1``;` `        ``for` `(``int` `j = ``1``; j < n; j++)` `        ``{`   `            ``// here we use stack for reversing ` `            ``// the elements of diagonal` `            ``Stack s = ``new` `Stack<>();` `            ``int` `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.peek();` `                ``s.pop();` `            ``}` `        ``}` `    ``}`   `    ``// Utility function to print a matrix` `    ``static` `void` `printMatrix(``int` `mat[][], ``int` `n) ` `    ``{` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``{` `            ``for` `(``int` `j = ``0``; j < n; j++)` `            ``{` `                ``System.out.print(mat[i][j] + ``" "``);` `            ``}` `            ``System.out.println(``""``);` `        ``}` `    ``}`   `    ``// Driver program to test above function` `    ``public` `static` `void` `main(String[] args)` `    ``{`   `        ``int` `mat[][] = {{``1``, ``2``, ``3``, ``4``},` `        ``{``5``, ``6``, ``7``, ``8``},` `        ``{``9``, ``10``, ``11``, ``12``},` `        ``{``13``, ``14``, ``15``, ``16``}};` `        ``int` `n = ``4``;` `        ``imageSwap(mat, n);` `        ``printMatrix(mat, n);` `    ``}` `}`   `// This code contributed by Rajput-Ji`

## Python3

 `# Simple Python3 program to find mirror of` `# matrix across diagonal.` `MAX` `=` `100`   `def` `imageSwap(mat, n):` `    `  `    ``# for diagonal which start from at ` `    ``# first row of matrix` `    ``row ``=` `0` `    `  `    ``# traverse all top right diagonal` `    ``for` `j ``in` `range``(n):` `        `  `        ``# here we use stack for reversing` `        ``# the element of diagonal` `        ``s ``=` `[]` `        ``i ``=` `row` `        ``k ``=` `j` `        ``while` `(i < n ``and` `k >``=` `0``):` `            ``s.append(mat[i][k])` `            ``i ``+``=` `1` `            ``k ``-``=` `1` `            `  `        ``# push all element back to matrix ` `        ``# in reverse order` `        ``i ``=` `row` `        ``k ``=` `j` `        ``while` `(i < n ``and` `k >``=` `0``):` `            ``mat[i][k] ``=` `s[``-``1``]` `            ``k ``-``=` `1` `            ``i ``+``=` `1` `            ``s.pop()` `            `  `    ``# do the same process for all the` `    ``# diagonal which start from last` `    ``# column` `    ``column ``=` `n ``-` `1` `    ``for` `j ``in` `range``(``1``, n): ` `        `  `        ``# here we use stack for reversing ` `        ``# the elements of diagonal` `        ``s ``=` `[]` `        ``i ``=` `j` `        ``k ``=` `column` `        ``while` `(i < n ``and` `k >``=` `0``):` `            ``s.append(mat[i][k])` `            ``i ``+``=` `1` `            ``k ``-``=` `1` `            `  `        ``# push all element back to matrix ` `        ``# in reverse order` `        ``i ``=` `j` `        ``k ``=` `column` `        ``while` `(i < n ``and` `k >``=` `0``):` `            ``mat[i][k] ``=` `s[``-``1``]` `            ``i ``+``=` `1` `            ``k ``-``=` `1` `            ``s.pop()`   `# Utility function to print a matrix` `def` `printMatrix(mat, n):` `    ``for` `i ``in` `range``(n):` `        ``for` `j ``in` `range``(n):` `            ``print``(mat[i][j], end``=``" "``)` `        ``print``()` `        `  `# Driver code` `mat ``=` `[[``1``, ``2``, ``3``, ``4``],[``5``, ``6``, ``7``, ``8``],` `        ``[``9``, ``10``, ``11``, ``12``],[``13``, ``14``, ``15``, ``16``]]` `n ``=` `4` `imageSwap(mat, n)` `printMatrix(mat, n)`   `# This code is contributed by shubhamsingh10`

## C#

 `// Simple C# program to find mirror of` `// matrix across diagonal.` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG ` `{`   `    ``static` `int` `MAX = 100;`   `    ``static` `void` `imageSwap(``int` `[,]mat, ``int` `n) ` `    ``{` `        ``// for diagonal which start from at ` `        ``// first row of matrix` `        ``int` `row = 0;`   `        ``// traverse all top right diagonal` `        ``for` `(``int` `j = 0; j < n; j++) ` `        ``{`   `            ``// here we use stack for reversing` `            ``// the element of diagonal` `            ``Stack<``int``> s = ``new` `Stack<``int``>();` `            ``int` `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.Peek();` `                ``s.Pop();` `            ``}` `        ``}`   `        ``// do the same process for all the` `        ``// diagonal which start from last` `        ``// column` `        ``int` `column = n - 1;` `        ``for` `(``int` `j = 1; j < n; j++)` `        ``{`   `            ``// here we use stack for reversing ` `            ``// the elements of diagonal` `            ``Stack<``int``> s = ``new` `Stack<``int``>();` `            ``int` `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.Peek();` `                ``s.Pop();` `            ``}` `        ``}` `    ``}`   `    ``// Utility function to print a matrix` `    ``static` `void` `printMatrix(``int` `[,]mat, ``int` `n) ` `    ``{` `        ``for` `(``int` `i = 0; i < n; i++) ` `        ``{` `            ``for` `(``int` `j = 0; j < n; j++)` `            ``{` `                ``Console.Write(mat[i,j] + ``" "``);` `            ``}` `            ``Console.WriteLine(``""``);` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args)` `    ``{`   `        ``int` `[,]mat = {{1, 2, 3, 4},` `                    ``{5, 6, 7, 8},` `                    ``{9, 10, 11, 12},` `                    ``{13, 14, 15, 16}};` `        ``int` `n = 4;` `        ``imageSwap(mat, n);` `        ``printMatrix(mat, n);` `    ``}` `}`   `/* This code contributed by PrinciRaj1992 */`

## Javascript

 ``

Output:

```1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16```

Time complexity : O(n2)
Auxiliary Space: O(n), as stack is used

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.

Implementation:

## C++

 `// Efficient CPP program to find mirror of` `// matrix across diagonal.` `#include ` `using` `namespace` `std;`   `const` `int` `MAX = 100;`   `void` `imageSwap(``int` `mat[][MAX], ``int` `n)` `{` `    ``// traverse a matrix and swap ` `    ``// mat[i][j] with mat[j][i]` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``for` `(``int` `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` `void` `printMatrix(``int` `mat[][MAX], ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``for` `(``int` `j = 0; j < n; j++)` `            ``cout << mat[i][j] << ``" "``;` `        ``cout << endl;` `    ``}` `}`   `// driver program to test above function` `int` `main()` `{` `    ``int` `mat[][MAX] = { { 1, 2, 3, 4 },` `                     ``{ 5, 6, 7, 8 },` `                     ``{ 9, 10, 11, 12 },` `                     ``{ 13, 14, 15, 16 } };` `    ``int` `n = 4;` `    ``imageSwap(mat, n);` `    ``printMatrix(mat, n);` `    ``return` `0;` `}`

## Java

 `// Efficient Java program to find mirror of` `// matrix across diagonal.` `import` `java.io.*;`   `class` `GFG {` `    `  `    ``static` `int` `MAX = ``100``;` `    `  `    ``static` `void` `imageSwap(``int` `mat[][], ``int` `n)` `    ``{` `        `  `        ``// traverse a matrix and swap ` `        ``// mat[i][j] with mat[j][i]` `        ``for` `(``int` `i = ``0``; i < n; i++)` `            ``for` `(``int` `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` `    ``static` `void` `printMatrix(``int` `mat[][], ``int` `n)` `    ``{` `        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``for` `(``int` `j = ``0``; j < n; j++)` `                ``System.out.print( mat[i][j] + ``" "``);` `            ``System.out.println();` `        ``}` `    ``}` `    `  `    ``// driver program to test above function` `    ``public` `static` `void` `main (String[] args) ` `    ``{` `        ``int` `mat[][] = { { ``1``, ``2``, ``3``, ``4` `},` `                        ``{ ``5``, ``6``, ``7``, ``8` `},` `                        ``{ ``9``, ``10``, ``11``, ``12` `},` `                        ``{ ``13``, ``14``, ``15``, ``16` `} };` `        ``int` `n = ``4``;` `        ``imageSwap(mat, n);` `        ``printMatrix(mat, n);` `    ``}` `}`   `// This code is contributed by anuj_67.`

## Python3

 `# Efficient Python3 program to find mirror of` `# matrix across diagonal.` `from` `builtins ``import` `range` `MAX` `=` `100``;`   `def` `imageSwap(mat, n):`   `    ``# traverse a matrix and swap` `    ``# mat[i][j] with mat[j][i]` `    ``for` `i ``in` `range``(n):` `        ``for` `j ``in` `range``(i ``+` `1``):` `            ``t ``=` `mat[i][j];` `            ``mat[i][j] ``=` `mat[j][i]` `            ``mat[j][i] ``=` `t`   `# Utility function to print a matrix` `def` `printMatrix(mat, n):` `    ``for` `i ``in` `range``(n):` `        ``for` `j ``in` `range``(n):` `            ``print``(mat[i][j], end``=``" "``);` `        ``print``();`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    ``mat ``=` `[``1``, ``2``, ``3``, ``4``], \` `        ``[``5``, ``6``, ``7``, ``8``], \` `        ``[``9``, ``10``, ``11``, ``12``], \` `        ``[``13``, ``14``, ``15``, ``16``];` `    ``n ``=` `4``;` `    ``imageSwap(mat, n);` `    ``printMatrix(mat, n);`   `# This code is contributed by Rajput-Ji`

## C#

 `// Efficient C# program to find mirror of` `// matrix across diagonal.` `using` `System;` `class` `GFG {` `    `  `    ``//static int MAX = 100;` `    `  `    ``static` `void` `imageSwap(``int` `[,]mat, ``int` `n)` `    ``{` `        `  `        ``// traverse a matrix and swap ` `        ``// mat[i][j] with mat[j][i]` `        ``for` `(``int` `i = 0; i < n; i++)` `            ``for` `(``int` `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` `    ``static` `void` `printMatrix(``int` `[,]mat, ``int` `n)` `    ``{` `        ``for` `(``int` `i = 0; i < n; i++) {` `            ``for` `(``int` `j = 0; j < n; j++)` `                ``Console.Write( mat[i,j] + ``" "``);` `            ``Console.WriteLine();` `        ``}` `    ``}` `    `  `    ``// driver program to test above function` `    ``public` `static` `void` `Main () ` `    ``{` `        ``int` `[,]mat = { { 1, 2, 3, 4 },` `                        ``{ 5, 6, 7, 8 },` `                        ``{ 9, 10, 11, 12 },` `                        ``{ 13, 14, 15, 16 } };` `        ``int` `n = 4;` `        ``imageSwap(mat, n);` `        ``printMatrix(mat, n);` `    ``}` `}`   `// This code is contributed by anuj_67.`

## PHP

 ``

## Javascript

 ``

Output:

```1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16 ```

Time complexity : O(n2)
Auxiliary Space: O(1)

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