pascal.hhs

/**
* @author Alan Liang
* @param n - integer, size of final matrix
* @returns - Mat object matrix
*
* a symmetric Pascal matrix contains the binomial coefficients as its elements.
*
*/

function pascal(n)
{
  // wrong argument number
  if (arguments.length === 0) {
    throw new Error('Exception occurred in pascal - no argument given');
  }
  else if (arguments.length > 1) {
    throw new Error('Exception occurred in pascal - wrong argument number');
  }
  // the input shoule be an integer
  if(!Number.isInteger(n)) {
    throw new Error("Exception occurred in pascal - the parameter must be an integer.");
  }

  let pascalSquare = Array(n).fill(0).map(x => Array(n).fill(0));

  // Fill the first row with 1s
  pascalSquare[0] = Array(n).fill(1);

  // Fill the first column with 1s
  for (let row = 0; row < n; row++) {
    pascalSquare[row][0] = 1;
  }

  // Use the definition of pascal matrix
  for (let row = 1; row < n; row++) {
    for (let col = 1; col < n; col++) {
      pascalSquare[row][col] = pascalSquare[row-1][col] + pascalSquare[row][col-1];
    }
  }
return pascalSquare;
}