Algorithm for finding overlapping events/times

Question

While working on custom calendar, I can't figure out how to find time slots that overlaps any other time slot.

Time slots start from 0 to 720 (9am to 9pm with each pixel representing a minute).

var events = [
 {id : 1, start : 0, end : 40},  // an event from 9:00am to 9:40am
 {id : 2, start : 30, end : 150},  // an event from 9:30am to 11:30am
 {id : 3, start : 20, end : 180},  // an event from 9:20am to 12:00am
 {id : 4, start : 200, end : 230},  // an event from 12:20pm to 12:30pm
 {id : 5, start : 540, end : 600}, // an event from 6pm to 7pm
 {id : 6, start : 560, end : 620} // an event from 6:20pm to 7:20pm
];

Each time slots is of one hour, for example 9 to 10, 10 to 11, 11 to 12 and so on.

In the above example, three events (id: 1,2,3) are overlapping for the 9-10 start time: 9:00, 9:30 and 9:20. And other events overlapping are int time slot of 6 to 7 (id: 5, 6) with 6 and 6:20 start times. The event with id 4 doesn't have any overlapping events in the time slot of 12 to 1.

I am looking for a way to get all overlapping event ids as well as number of events in a particular time slot, this is expected output:

[
 {id:1, eventCount: 3},
 {id:2, eventCount: 3},
 {id:3, eventCount: 3},
 {id:5, eventCount: 2},
 {id:6, eventCount: 2}
]

For ids (1 to 3), there are 3 events for time slot 9 to 10 and 2 events for time slot 6 to 7.

I have created this formula to convert time number to actual time:

var start_time = new Date(0, 0, 0, Math.abs(events[i].start / 60) + 9, Math.abs(events[i].start % 60)).toLocaleTimeString(),
var end_time = new Date(0, 0, 0, Math.abs(events[i].end / 60) + 9, Math.abs(events[i].end % 60)).toLocaleTimeString();

This is what I have so far:

function getOverlaps(events) {
   // sort events
   events.sort(function(a,b){return a.start - b.start;});

   for (var i = 0, l = events.length; i < l; i++) {
      // cant figure out what should be next
   }
}

DEMO if you need.

Answer 1

from my jquery-week-calendar commit, this is how i do it:

    _groupOverlappingEventElements: function($weekDay) {
        var $events = $weekDay.find('.wc-cal-event:visible');
        var complexEvents = jQuery.map($events, function (element, index) {
            var $event = $(element);
            var position = $event.position();
            var height = $event.height();
            var calEvent = $event.data('calEvent');
            var complexEvent = {
                'event': $event,
                'calEvent': calEvent,
                'top': position.top,
                'bottom': position.top + height
            };
            return complexEvent;
        }).sort(function (a, b) {
            var result = a.top - b.top;
            if (result) {
                return result;
            }
            return a.bottom - b.bottom;
        });
        var groups = new Array();
        var currentGroup;
        var lastBottom = -1;
        jQuery.each(complexEvents, function (index, element) {
            var complexEvent = element;
            var $event = complexEvent.event;
            var top = complexEvent.top;
            var bottom = complexEvent.bottom;
            if (!currentGroup || lastBottom < top) {
                currentGroup = new Array();
                groups.push(currentGroup);
            }
            currentGroup.push($event);
            lastBottom = Math.max(lastBottom, bottom);
        });
        return groups;
    }

there's a bit of component-specific noise around, but you'll get the logic:

• sort the events by their starting ascending
• sort the events by their ending ascending
• iterate over the sorted events and check the starting/ending of the previous event (done rather by position, than by the event properties themself - just because the design might overlap, but the events not ... eg: making a border 2px, events with not overlapping start/end-times might overlap or "touch")
• each overlapping-group (currentGroup) is a new array inside the groups-array

soo ... your code might look sth alike this (btw, no need to work with the real date-instances)

events.sort(function (a, b) {
    var result = a.start - b.start;
    if (result) {
        return result;
    }
    return a.end - b.end;
});
var groups = new Array();
var currentGroup;
var lastEnd = -1;
jQuery.each(events, function (index, element) {
    var event = element;
    var start = event.start;
    var end = event.end;
    if (!currentGroup || lastEnd < start) {
        currentGroup = new Array();
        groups.push(currentGroup);
    }
    currentGroup.push(event);
    lastEnd = Math.max(lastEnd, end);
});
return groups;

soo ... you are not willed to push some own energy into your problem ... well

var output = new Array();
jQuery.each(groups, function (index, element) {
    var group = element;
    if (group.length <= 1) {
        return;
    }
    jQuery.each(group, function (index, element) {
        var event = element;
        var foo = {
            'id': event.id,
            'eventCount': group.length
        };
        output.push(foo);
    });
});

Answer 2

To me it is easier to use timestamps for each start and end event, that way you can work with them directly or change them to date objects. To get the value, create a date object for each start and end, then:

var a.start = startDate.getTime();
var a.end = endDate.getTime();

For overlap:

if (a.start <= b.start && a.end > b.start ||
    a.start < b.end && a.end >= b.end) {
    // a overlaps b
}

You can leave them as date objects if you like, the above will work just as well.

Edit

Ok here's a working example:

Assuming a nominal date of 2012-05-15, then the events array looks like:

// Use iso8601 like datestring to make a local date object
function getDateObj(s) {
  var bits = s.split(/[- :]/);
  var date = new Date(bits[0], bits[1] - 1, bits[2]);
  date.setHours(bits[3], bits[4], 0);
  return date;
}

var events = [
  {id: 1, start: getDateObj('2012-05-15 09:00'), end: getDateObj('2012-05-15 09:30')}, 
  {id: 2, start: getDateObj('2012-05-15 09:30'), end: getDateObj('2012-05-15 11:30')}, 
  {id: 3, start: getDateObj('2012-05-15 09:20'), end: getDateObj('2012-05-15 12:00')}, 
  {id: 4, start: getDateObj('2012-05-15 12:20'), end: getDateObj('2012-05-15 12:30')}, 
  {id: 5, start: getDateObj('2012-05-15 18:00'), end: getDateObj('2012-05-15 19:00')}, 
  {id: 6, start: getDateObj('2012-05-15 18:20'), end: getDateObj('2012-05-15 19:20')}
];

function getOverlappingEvents(eventArray) {
  var result = [];
  var a, b;

  // Sort the event array on start time
  eventArray.sort(function(a, b) {
      return a.start - b.start;
    });

  // Get overlapping events
  for (var i=0, iLen=eventArray.length - 1; i<iLen; i++) {
    a = eventArray[i];
    b = eventArray[i + 1];

    if ((a.start <= b.start && a.end > b.start) ||
        (a.start < b.end && a.end >= b.end) ) {
       result.push([a.id, b.id]);
    }
  }
  return result;
}

// Run it    
alert(getOverlappingEvents(events).join('\n')); // 1,3 2,3 5,6

Answer 3

Here's code that will do what you want. As others have mentioned you'd probably be better served by storing date objects, but that's a different issue.

function getOverlaps(events) {
    // sort events
    events.sort(function (a, b) {
        return a.start - b.start;
    });

    var results = [];
    for (var i = 0, l = events.length; i < l; i++) {
        var oEvent = events[i];
        var nOverlaps = 0;
        for (var j = 0; j < l; j++) {
            var oCompareEvent = events[j];
            if (oCompareEvent.start <= oEvent.end && oCompareEvent.end > oEvent.start || oCompareEvent.end <= oEvent.start && oCompareEvent.start > oEvent.end) {
                nOverlaps++;
            }
        }
        if (nOverlaps > 1) {
            results.push({
                id: oEvent.id,
                eventCount: nOverlaps,
                toString: function () {
                    return "[id:" + this.id + ", events:" + this.eventCount + "]"
                }
            });
        }

    }
    return results;
}