Простой бинарный поиск

index.php

function binary_search($list, $item) {
	$min = 0;
	$max = count($list)-1;
  
	while($min <= $max) {
		$middle = round(($min+$max)/2);
		$guess = $list[$middle];
		if($guess === $item) {
			return 'index - ' .$middle . ', value -' . $item;
		} elseif ($guess > $item) {
			$max = $middle - 1;
		} elseif($guess < $item) {
			$min = $middle + 1;
		}
	}
	return null;
}
var_dump(binary_search(array(1, 3, 5, 6, 8, 9, 10, 90), 5));