Step by Step solution about How to resolve the algorithm Pascal's triangle step by step in the PHP programming language

1. Pascal's Triangle Function:

• function pascalsTriangle($num): This function calculates and returns Pascal's triangle up to the specified row number $num.

Implementation:

• It initializes a variable $c to 1 and an array $triangle to store the triangle.
• It iterates over the rows from 0 to $num.
• For each row, it initializes an array to store the coefficients.
• If the previous row doesn't exist, the first coefficient is set to 1.
• Otherwise, it calculates each coefficient by combining the values from the previous row.
• The calculated triangle is returned.

2. tre Function:

• function tre($n): This function calculates and prints the nth row of Pascal's triangle.

Implementation:

• It initializes $ck to 1, $kn to $n + 1, and a flag $i to 0.
• If $kn is even, it divides $kn by 2 and sets $i to 0. Otherwise, it increments $kn and sets $i to 1.
• It then calculates the coefficients in a loop:
  • It divides $ck by $k times the value ($n-$k+1).
  • It stores the coefficient in an array $arr and prints it on the console.
• If $kn is greater than 1, it prints the first coefficient of the row and reverses the array $arr.
• It then iterates over the reversed array and prints the coefficients.

3. Usage:

• The tre function is used in a loop to print the first 20 rows of Pascal's triangle.
• The pascalsTriangle function is used to calculate and print the first 8 rows of the triangle.

Overall, this code generates and displays Pascal's triangle using two different methods, each with its own implementation.

<?php
 //Author Ivan Gavryshin @dcc0
function tre($n) {
  $ck=1;
  $kn=$n+1;
    
 if($kn%2==0) {
 $kn=$kn/2;
 $i=0;
  }
 else
  {

  $kn+=1;
  $kn=$kn/2;
  $i= 1;
}

 for ($k = 1; $k <= $kn-1; $k++) { 
   $ck = $ck/$k*($n-$k+1);
   $arr[] = $ck;
   echo  "+" . $ck ;
 
  }
 

if ($kn>1) {
  echo $arr[i];
  $arr=array_reverse($arr);
 for ($i; $i<= $kn-1; $i++) {
 echo  "+" . $arr[$i]  ;
     }
 
   }
 
 }
 //set amount of strings here
 while ($n<=20) {
 ++$n;
 echo tre($n);
 echo "<br/>";
}
 
 
?>

function pascalsTriangle($num){
	$c = 1;
	$triangle = Array();
	for($i=0;$i<=$num;$i++){
		$triangle[$i] = Array();
		if(!isset($triangle[$i-1])){
			$triangle[$i][] = $c;
		}else{
			for($j=0;$j<count($triangle[$i-1])+1;$j++){
				$triangle[$i][] = (isset($triangle[$i-1][$j-1]) && isset($triangle[$i-1][$j])) ? $triangle[$i-1][$j-1] + $triangle[$i-1][$j] : $c;
			}
		}
	}
	return $triangle;
}

$tria = pascalsTriangle(8);
foreach($tria as $val){
	foreach($val as $value){
		echo $value . ' ';
	}
	echo '<br>';
}