# Insert Interval

Given a set of non-overlapping intervals, insert a new interval into the intervals (merge if necessary).

You may assume that the intervals were initially sorted according to their start times.

Example 1:

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

Example 2:

```Input: intervals = `[[1,2],[3,5],[6,7],[8,10],[12,16]]`, newInterval = `[4,8]`
Output: [[1,2],[3,10],[12,16]]
Explanation: Because the new interval `[4,8]` overlaps with `[3,5],[6,7],[8,10]`.```

## Solution

```public List<Interval> insert(List<Interval> intervals, Interval newInterval) {
int i = 0;
// add all the intervals ending before newInterval starts
while (i < intervals.size() && intervals.get(i).end < newInterval.start)
// merge all overlapping intervals to one considering newInterval
while (i < intervals.size() && intervals.get(i).start <= newInterval.end) {
newInterval = new Interval( // we could mutate newInterval here also
Math.min(newInterval.start, intervals.get(i).start),
Math.max(newInterval.end, intervals.get(i).end));
i++;
}