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:
Given intervals [1,3],[6,9], insert and merge [2,5] in as [1,5],[6,9].

Example 2:
Given [1,2],[3,5],[6,7],[8,10],[12,16], insert and merge [4,9] in as [1,2],[3,10],[12,16].

This is because the new interval [4,9] overlaps with [3,5],[6,7],[8,10].

One pass merge as go solution

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/**
 * Definition for an interval.
 * public class Interval {
 *     int start;
 *     int end;
 *     Interval() { start = 0; end = 0; }
 *     Interval(int s, int e) { start = s; end = e; }
 * }
 */
public class Solution {
    public List<Interval> insert(List<Interval> intervals, Interval newInterval) {
        if (intervals == null || intervals.size() < 1) return Arrays.asList(newInterval);
        int index = 0;
        while (index < intervals.size() && intervals.get(index).end < newInterval.start) index++;
        while (index < intervals.size() && intervals.get(index).start <= newInterval.end){
            newInterval = new Interval(
                Math.min(intervals.get(index).start, newInterval.start),
                Math.max(intervals.get(index).end, newInterval.end)
            );
            intervals.remove(index);
        }
        intervals.add(index, newInterval);
        return intervals;
    }
}

my insert first then merge solution

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/**
 * Definition for an interval.
 * public class Interval {
 *     int start;
 *     int end;
 *     Interval() { start = 0; end = 0; }
 *     Interval(int s, int e) { start = s; end = e; }
 * }
 */
public class Solution {
    public List<Interval> insert(List<Interval> intervals, Interval newInterval) {
        if (intervals == null || intervals.size() == 0) return Arrays.asList(newInterval);
        
        int start = -1, end = intervals.size(), middle = (start + end) / 2;
        while (start < end) {
            if (start == middle || end == middle) break;
            Interval middleInterval = intervals.get(middle);
            if (middleInterval.start < newInterval.start) {
                start = middle;
            } else {
                end = middle;
            }
            middle = (start + end) / 2;
        }
        if (start == middle) {
            intervals.add(start + 1, newInterval);
        } else {
            end = end - 1 < 0 ? 0 : end - 1;
            intervals.add(end, newInterval);
        }
        
        List<Interval> result = new LinkedList<Interval>();
        Interval prev = null;
        
        for (Interval interval : intervals) {
            if (prev == null || prev.end < interval.start) {
                result.add(interval);
                prev = interval;
            } else {
                prev.end = Math.max(prev.end, interval.end);
            }
        }
        return result;
    }
}