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  1. <?php
  2.  
  3. class BCN implements Iterator {
  4.   private static $table = [];
  5.   private $n, $k;
  6.  
  7.   public function __construct ($n) { $this->n=$n; }
  8.  
  9.   public function rewind() { $this->k=0; }
  10.  
  11.   public function current() { return $this->get($this->k); }
  12.  
  13.   public function key() { return $this->k; }
  14.  
  15.   public function next() { ++$this->k; }
  16.  
  17.   public function valid() { return $this->k <= $this->n; }  
  18.  
  19.   public function get ($k) {
  20.     if ($this->n==0 || $k==0 || $this->n==$k) return 1;
  21.  
  22.     if ($k > $this->n / 2)
  23.        $k = $this->n-$k;
  24.  
  25.     if (!isset (self::$table[$this->n][$k])) {
  26.       $bcn = new BCN ($this->n-1);
  27.       self::$table[$this->n][$k] = $bcn->get($k-1)+$bcn->get($k);
  28.     }
  29.  
  30.     return self::$table[$this->n][$k];
  31.   }
  32. }
  33.  
  34.  
  35. function check_binom ($a, $b, $n) {
  36.  
  37.   echo "($a+$b)^$n=", pow($a+$b, $n), '=';
  38.  
  39.   $sum=0;
  40.   $x = $a+$b-1;
  41.   $xk = 1;
  42.   foreach (new BCN($n) as $k=>$bc) {
  43.      if ($k) echo '+';
  44.      echo $bc,'*',$xk;
  45.      $sum += $bc*$xk;
  46.      $xk *= $x;
  47.   }
  48.  
  49.   echo '=', $sum;
  50. }
  51.  
  52.  
  53. $a=4;
  54. $b=5;
  55. $n=6;
  56. check_binom ($a, $b, $n);
Success #stdin #stdout 0.01s 20568KB
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(4+5)^6=531441=1*1+6*8+15*64+20*512+15*4096+6*32768+1*262144=531441
https://ideone.com/gk9GkM
language:
PHP (php 7.3.5)
created:
9 years ago
visibility:
public

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