Step by Step solution about How to resolve the algorithm Matrix transposition step by step in the JavaScript programming language

First implementation:

• The Matrix class takes in an array as an argument and initialises its mtx property to the input array.
• It also sets the height and width properties of the matrix based on the input array.
• The toString method returns a string representation of the matrix by joining the rows of the matrix with newlines and the elements of each row with commas.
• The transpose method creates a new matrix by transposing the input matrix, i.e., swapping its rows and columns.

Second implementation:

• The transpose function takes in a list as an argument and returns a new list where each element is a list of the elements in the corresponding column of the input list.
• It uses the map method to create a new list of lists, where each inner list is created by mapping the input list to the element at the corresponding column index.

Third implementation:

• The transpose function takes in a list of lists as an argument and returns a new list of lists where each element is a list of the elements in the corresponding column of the input list.
• It uses the map method to create a new list of lists, where each inner list is created by mapping the input list to the element at the corresponding column index.

Usage:

• The code initialises a matrix object m with a 5x4 matrix of numbers.
• It then prints the original matrix and its transpose.
• The second and third implementations are called with a 4x3 matrix of numbers and their results are printed.

Output:

[1,1,1,1]
[2,4,8,16]
[3,9,27,81]
[4,16,64,256]
[5,25,125,625]

[1,2,3,4,5]
[1,4,9,16,25]
[1,8,27,64,125]
[1,16,81,256,625]

[[1,4,7],[2,5,8],[3,6,9]]

function Matrix(ary) {
    this.mtx = ary
    this.height = ary.length;
    this.width = ary[0].length;
}

Matrix.prototype.toString = function() {
    var s = []
    for (var i = 0; i < this.mtx.length; i++) 
        s.push( this.mtx[i].join(",") );
    return s.join("\n");
}

// returns a new matrix
Matrix.prototype.transpose = function() {
    var transposed = [];
    for (var i = 0; i < this.width; i++) {
        transposed[i] = [];
        for (var j = 0; j < this.height; j++) {
            transposed[i][j] = this.mtx[j][i];
        }
    }
    return new Matrix(transposed);
}

var m = new Matrix([[1,1,1,1],[2,4,8,16],[3,9,27,81],[4,16,64,256],[5,25,125,625]]);
print(m);
print();
print(m.transpose());


(function () {
    'use strict';

    function transpose(lst) {
        return lst[0].map(function (_, iCol) {
            return lst.map(function (row) {
                return row[iCol];
            })
        });
    }
    
    return transpose(
        [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
    );

})();


(() => {
    "use strict";

    // transpose :: [[a]] -> [[a]]
    const transpose = xs =>
        0 < xs.length ? (
            xs[0].map(
                (_, iCol) => xs.map(
                    row => row[iCol]
                )
            )
        ) : [];


    // ---------------------- TEST -----------------------
    const main = () =>
        JSON.stringify(
            transpose([
                [1, 2, 3],
                [4, 5, 6],
                [7, 8, 9]
            ])
        );


    // MAIN ---
    return main();
})();


[[1,4,7],[2,5,8],[3,6,9]]