Count maximum number of overlapping dates within array of objects

Question

If I have the following array of objects with start and end dates, how can I best calculate the maximum number of ranges that overlap each other? I just want the count for the highest number of overlapping ranges. eg my example below the highest number of overlapping ranges would be 3.

[
  { start_date: '2021-01-01 10:00:00', end_date: '2021-01-01 11:00:00'},
  { start_date: '2021-01-01 08:00:00', end_date: '2021-01-01 11:00:00'},
  { start_date: '2021-01-01 12:00:00', end_date: '2021-01-01 14:00:00'},
  { start_date: '2021-01-01 12:30:00', end_date: '2021-01-01 14:30:00'},
  { start_date: '2021-01-01 14:00:00', end_date: '2021-01-01 17:30:00'},
]

Answer 1

Two elements of the list overlap if Math.max(start_1, start_2) < Math.min(end_1, end_2) .

I'm unsure of your counting requirement for the number of overlapping time segments, but this should get you on the right path.

const list = [
  { start_date: '2021-01-01 10:00:00', end_date: '2021-01-01 11:00:00'},
  { start_date: '2021-01-01 08:00:00', end_date: '2021-01-01 11:00:00'},
  { start_date: '2021-01-01 12:00:00', end_date: '2021-01-01 14:00:00'},
  { start_date: '2021-01-01 12:30:00', end_date: '2021-01-01 14:30:00'},
  { start_date: '2021-01-01 14:00:00', end_date: '2021-01-01 17:30:00'},
];

// Step 1 : Convert to Date objects
const dt_list = list.map((currItem) => {
  return [new Date(currItem.start_date), new Date(currItem.end_date)];
});

// Map over arrays of Date values
const result = dt_list.map((item, index) => {
  let count = 0;
  // Count overlaps with remainder of list
  for (let i=(index + 1); i < dt_list.length; i++) {
    if (Math.max(item[0], dt_list[i][0]) < Math.min(item[1], dt_list[i][1]))
      count += 1;
  }
  return count;
}).reduce((sum, current) => {
  return sum + current;
}, 0);

console.log(result); // 3

Answer 2

Assuming your date format is always YYYY-MM-DD hh:mm:ss , you can use string comparisons for comparing the date/times. If other formats are possible as well, I would suggest using some library like Moment.js .

You could loop over the ranges and check for each range whether it overlaps another one, like:

 const ranges = [ { start_date: '2021-01-01 10:00:00', end_date: '2021-01-01 11:00:00'}, { start_date: '2021-01-01 08:00:00', end_date: '2021-01-01 11:00:00'}, { start_date: '2021-01-01 12:00:00', end_date: '2021-01-01 14:00:00'}, { start_date: '2021-01-01 12:30:00', end_date: '2021-01-01 14:30:00'}, { start_date: '2021-01-01 14:00:00', end_date: '2021-01-01 17:30:00'}, ]; let overlaps = 0; for (let i = 0; i < ranges.length; i++) { const range1 = ranges[i]; for (let j = i + 1; j < ranges.length; j++) { const range2 = ranges[j]; if (!(range1.start_date >= range2.end_date || range2.end_date <= range1.start_date || range2.start_date >= range1.end_date || range1.end_date <= range2.start_date)) { console.log(JSON.stringify(ranges[i]) + ' overlaps ' + JSON.stringify(ranges[j])); overlaps++; } } } console.log('Overlaps: ' + overlaps); // Overlaps: 3

Answer 3

You could convert all the dates to timeStamps ( seconds since 1970/01/01 ) for better comparison. Then push all of them into a new array converted_dates[] to use them inside a double loop where a conditional statement its implemented to see if there is an overlap between any of the ranges.

This code should work with any date and any time, keeping in mind, that to do so, it should maintain the date format of the original range array.

Try the following snippet

 const ranges = [ { start_date: '2021-01-01 10:00:00', end_date: '2021-01-01 11:00:00'}, { start_date: '2021-01-01 08:00:00', end_date: '2021-01-01 11:00:00'}, { start_date: '2021-01-01 12:00:00', end_date: '2021-01-01 14:00:00'}, { start_date: '2021-01-01 12:30:00', end_date: '2021-01-01 14:30:00'}, { start_date: '2021-01-01 14:00:00', end_date: '2021-01-01 17:30:00'}, ]; const converted_dates = []; for(let range of ranges){ var start_sliced_date = range.start_date.slice(0,10); var start_sliced_hour = range.start_date.slice(11,19); var end_sliced_date = range.end_date.slice(0,10); var end_sliced_hour = range.end_date.slice(11,19); // Create a date object to use getTime() method let newDate = new Date(start_sliced_date + "T" + start_sliced_hour); let start_timeStamp = newDate.getTime()/1000; newDate = new Date(end_sliced_date + "T" + end_sliced_hour); let end_timeStamp = newDate.getTime()/1000; // Create a new array with the dates converted to timeStamps converted_dates.push({ "start": start_timeStamp, "end": end_timeStamp }); } var count = 0; for(var i = 0; i < converted_dates.length; i++){ let end = converted_dates[i].end; for(var pos = i + 1; pos < converted_dates.length; pos++){ let otherStart = converted_dates[pos].start; // Is there an overlap? if(end>otherStart){ count++, console.log('Overlap of range ' + (i + 1) + ' with ' + (pos + 1)); } } } console.log('Total number of overalped ranges: ' + count);

Answer 4

If you want to find the max number of overlaps:

1. You can insert all dates to one big dict or map (In our case size will be 10). Key represents the the date itself (no matter if it's start or end) and value is either 's' for start_date or 'e' for end_date.
2. Sort the array in increasing order by date.
3. Hold a var named count. While linear looping through the dict, increase the count by 1 when you meet a starting point and decrease by 1 when you meet a ending point. (Key doesn't matter in this case, just value)

Notice. you have to keep in mind the maximum point count had reached. There's your max overlaps!

Time complexity O(N log(N)). Space complexity O(N).

I hope this answer was helpful.

Thank you!