用PHP实现二分法查找之递归和迭代

关于递归和迭代分别的时间复杂度，递归的时间复杂度是O(N)，而迭代的时间复杂度是O(logN),由y=N 和Y＝logN两条曲线我们知道，一定是O(logN)更优一些。

以下是两段代码，和傻瓜式测效率的代码。

function dichotomyIterationSearch($arr, $n, $v)
{
    $left   = 0;
    $right  = $n - 1;
    while ($left <= $right) {
        $middle  = bcdiv(bcadd($right, $left), 2);
        if ($arr[$middle] > $v) {
            $right = $middle - 1;
        } elseif ($arr[$middle] < $v) {
            $left  = $middle + 1;
        } else {
            return $middle;
        }
    }
    return -1;
}


$arr = [];
for ($i=0;$i<300000;$i++){
    $arr[] = $i;
}
list($first) = explode(" ",microtime());
echo dichotomyIterationSearch($arr,count($arr),35387);echo '';
list($second) = explode(" ",microtime());
echo round($second - $first,5)*1000000;


function dichotomyRecursionSearch($arr, $low, $high, $v)
{
    $middle = bcdiv(bcadd($low, $high), 2);

    if ($low < $high) {
        if ($arr[$middle] > $v) {
            $high = $middle - 1;
            return dichotomyRecursionSearch($arr, $low, $high, $v);
        } elseif ($arr[$middle] < $v) {
            $low = $middle + 1;
            return dichotomyRecursionSearch($arr, $low, $high, $v);
        } else {
            return $middle;
        }
    } elseif ($high == $low) {
        if ($arr[$middle] == $v) {
            return $middle;
        } else {
            return -1;
        }
    }
    return -1;
}


$arr = [];
for ($i=0;$i<300000;$i++){
    $arr[] = $i;
}
echo "";
list($first) = explode(" ",microtime());
echo dichotomyRecursionSearch($arr,0, count($arr),35387);echo '';
list($second) = explode(" ",microtime());
echo round($second - $first, 5)*1000000;