Test if a range intersects another range of numbers

Question

I have 2 range of numbers:

• $startTime to $endTime
• $offerStartTime to $offerEndTime

Each of the above variables are integers.

I want to see if the range offerStartTime to offerEndTime falls in the range startTime and endTime.

For example, if the startTime and endTime range was: 10 to 20, then the following example ranges would return true:

• offerStartTime: 5, offerEndTime: 11
• offerStartTime: 5, offerEndTime: 100
• offerStartTime: 10, offerEndTime: 15
• offerStartTime: 10, offerEndTime: 100
• offerStartTime: 12, offerEndTime: 15
• offerStartTime: 19, offerEndTime: 100

The following would return false:

• offerStartTime: 1, offerEndTime: 3
• offerStartTime: 90, offerEndTime: 100
• offerStartTime: 1, offerEndTime: 10
• offerStartTime: 20, offerEndTime: 100

How can I do this? Would ideally like answers in PHP, but pseudo code would be fine.

Answer 1

If you are just checking whether any part of the offer overlaps any part of the range, it's simple.

if ($offerStartTime < $endTime && $offerEndTime > $startTime)  {
    echo 'The ranges overlap';
}

Here's a picture representing all the possibilities of overlap and non-overlap to visualize why this works.

Based on your inputs and expected false outputs, I used < and >. If you wanted to also include ranges that intersected at a point, you would need to use <= and >= instead.

Answer 2

//$startTime to $endTime
//$offerStartTime to $offerEndTime
//you can compare php times by using normal comparators so this is just a logic problem. here's the solution.


//ok let's start by making sure that neither offered time is within the range because if it is we KNOW it's already good so

if(($offerStartTime < $endTime && offerStartTime > $startTime) || ($offerEndTime < $endTime && offerEndTime > $startTime)){
      return true;
 }
 //so it's not easily already within the range so we have to test if the lower one is under the starting one but the other is above. ie.
elseif(($offerStartTime < $startTime) && ($offerEndTime > $startTime)){
     return true; 
}
//so the only other acceptable possibility is that the offered start time is lower than the endtime and the offered end time is higher ie
elseif(($offerStartTime < $endTime) && ($offerEndTime > $endTime)){
      return true;
}
//so we've exhausted all other valid possibilities it must be false
else{
      return false;
}

Answer 3

You can use range and array_intersect, i.e.:

function time_intersect($startTime, $endTime, $offerStartTime, $offerEndTime)
{
    $start_to_end = range($startTime, $endTime, 1);
    $offer_start_end = range($offerStartTime, $offerEndTime, 1);
    if (!empty(array_intersect($start_to_end, $offer_start_end)))
    {
      # time overlaps
      return true;
    }
}

---

Explanation:

With range we create 2 arrays containing numbers based on the 4 variables (start, end), then we use array_intersect to check if the 2 arrays have numbers in common, if the output is not empty, we know the numbers (time) overlap.