Detecting if two number ranges clash

Question

This is hopefully a very simple maths question. If I have two number ranges, what is the simplest and most efficient way to check if they clash, eg:

10-20 and 11-14 // clash as B is contained in A
11-15 and 20-22 // don't clash
24-26 and 20-30 // clash as A is contained in B
15-25 and 20-30 // clash as they overlap at each end

I currently have this mess, but there must be a much simpler way to do this check:

$clash = ($b1 >= $a1 && $b1 <= $a2)
    || ($b2 >= $a1 && $b2 <= $a2)
    || ($a1 >= $b1 && $a1 <= $b2)
    || ($a2 >= $b1 && $a2 <= $b2);

Answer 1

The ranges DO NOT clash if and only if $a2 <= $b1 or $a1 >= $b2 (assuming that ranges are given as ordered pairs). Now negate the condition.

Answer 2

Well, first make sure you have well-ordered pairs (probably a good idea anyway, depending on what you plan to do with them):

if($a1 > $a2) {
    // swap $a1 and $a2
    $temp = $a1;
    $a1 = $a2;
    $a2 = $temp;
}
if($b1 > $b2) {
    // swap $b1 and $b2
    $temp = $b1;
    $b1 = $b2;
    $b2 = $temp;
}

Then you should be able to simplify to:

$clash = ($a2 <= $b1) || ($a1 >= $b2);

Edit: Whoops, got that test backwards! Try:

$clash = !(($a2 <= $b1) || ($a1 >= $b2));

Answer 3

I think it should be as simple as this:

clash = A_LOW <= B_HIGH AND A_HIGH >= B_LOW

Answer 4

What you're looking for is the intersection of the arrays. http://us3.php.net/array_intersect

Basically,

$intersect = array_intersect($arr1, $arr2);
$clash = (count($intersect) > 0);

If any elements are in both $arr1 and $arr2, then $intersect will list those values. The count() call returns 1 (or more), so doing > 0 gives you if $arr1 and $arr2 have any similar elements.