JavaScript program to generate a matrix whose sum of subdiagonals is equal to a perfect square

We will write a JavaScript program that generates a matrix whose diagonals sum to perfect squares. Our program will use nested loops to iterate over the matrix and calculate the sum of the sub-diagonal elements. We will then use the Math.sqrt() method to find the square root of the sum and check if it is an integer. If so, we would consider the sum to be a perfect square.

method

The method to generate a matrix whose sum of subdiagonals is equal to a perfect square is as follows -

• Create a two-dimensional array of size n x n, where n is the size of the square matrix.

• Fill the matrix with random numbers between 1 and 100.

• Calculate the sum of the subdiagonals of the matrix.

• Check whether the sum is a perfect square. If it is not a perfect square, generate a new matrix and repeat steps 2 to 4.

• Returns a matrix whose subdiagonal sum is equal to a perfect square.

• To check whether a number is a perfect square, you can use the Math.sqrt() function and compare its result with the integer value of the square root.

Example

This is an example of a JavaScript program that generates a matrix such that the sum of its diagonals equals a perfect square -

function generateMatrix(n) {
   let matrix = [];
   for (let i = 0; i < n; i++) {
      matrix[i] = [];
      for (let j = 0; j < n; j++) {
         matrix[i][j] = i * n + j + 1;
      }
   }
   let sum = 0;
   for (let i = 0; i < n; i++) {
      sum += matrix[i][n - i - 1];
   }
   let squareRoot = Math.floor(Math.sqrt(sum));
   if (squareRoot * squareRoot !== sum) {
      return null;
   }
   return matrix;
}

const n = 1;
console.log(generateMatrix(n));

illustrate

• generateMatrixThe function accepts a parameter n, which indicates the size of the matrix to be generated.

• This function initializes an empty 2D array matrix and loops through each row and column to fill the matrix with numbers i * n j 1, where i is the row number, j is the column number.

• This function calculates the sum of the subdiagonals of the matrix by looping through each row and column, adding the values ​​at the index (i, n - i - 1), Where i is the line number.

• This function calculates the square root of the sum and rounds down to the nearest integer. If the square of the integer does not equal the sum, the function returns null, indicating that the sum is not a perfect square.

• If the sum is a perfect square, the function returns the resulting matrix.

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