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19. Insert Interval

mediumAsked at Booking

Insert a new booking window into a sorted list of non-overlapping reservations and merge any conflicts — exactly the operation Booking runs when a new reservation arrives on a partially-booked property calendar.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

You are given an array of non-overlapping intervals sorted by start time and a new interval. Insert the new interval, merging overlapping intervals as needed, and return the resulting array of non-overlapping intervals sorted by start.

Constraints

  • 0 <= intervals.length <= 10^4
  • intervals[i].length == 2
  • 0 <= start_i <= end_i <= 10^5
  • intervals is sorted in ascending order by start_i
  • newInterval.length == 2

Examples

Example 1

Input
intervals = [[1,3],[6,9]], newInterval = [2,5]
Output
[[1,5],[6,9]]

Explanation: [1,3] and [2,5] overlap and merge into [1,5].

Example 2

Input
intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]
Output
[[1,2],[3,10],[12,16]]

Approaches

1. Rebuild with merge pass

Collect all non-overlapping intervals before and after the new interval, then merge the middle group.

Time
O(n)
Space
O(n)
function insert(intervals, newInterval) {
  const result = [];
  let i = 0;
  const n = intervals.length;

  // Add all intervals that end before newInterval starts
  while (i < n && intervals[i][1] < newInterval[0]) {
    result.push(intervals[i++]);
  }

  // Merge all overlapping intervals with newInterval
  while (i < n && intervals[i][0] <= newInterval[1]) {
    newInterval[0] = Math.min(newInterval[0], intervals[i][0]);
    newInterval[1] = Math.max(newInterval[1], intervals[i][1]);
    i++;
  }
  result.push(newInterval);

  // Add remaining intervals
  while (i < n) {
    result.push(intervals[i++]);
  }

  return result;
}

Tradeoff:

Booking-specific tips

Booking looks for disciplined boundary conditions: 'ends before' vs 'starts after'. Candidates who conflate strict vs non-strict inequality introduce silent overbooking bugs — make both checks explicit.

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Output

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