Javascript Program for Mirror of matrix across diagonal

Last Updated : 12 Sep, 2024

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 diagonals (right-to-left) one by one. First, we push all the elements into the stack during the traversal of the diagonal. Then we traverse it again and replace every diagonal element with the stack element.

Below is the implementation of the above idea.

JavaScript

// 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++) {
        let output = '';
        for (let j = 0; j < n; j++) {
            output += mat[i][j] + ' ';
        }
        console.log(output);
    }
}

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);

Output

Complexity Analysis:

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

// 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++) {
        let output = "";
        for (let j = 0; j < n; j++)
            output += mat[i][j] + " ";
        console.log(output.trim());
    }
}

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);

Output

Complexity Analysis:

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!

Javascript Program to Inplace rotate square matrix by 90 degrees | Set 1

kartik

Improve

Article Tags :

JavaScript

Javascript Program for Mirror of matrix across diagonal

Complexity Analysis:

Complexity Analysis:

Similar Reads

Thank You!

What kind of Experience do you want to share?