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:
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].

/**
 * Definition for an interval.
 * struct Interval {
 *     int start;
 *     int end;
 *     Interval() : start(0), end(0) {}
 *     Interval(int s, int e) : start(s), end(e) {}
 * };
 */
class Solution {
public:
    vector<Interval> insert(vector<Interval> &intervals, Interval newInterval) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        vector<Interval> result;
        bool processed = false;
        for (int i = 0; i < intervals.size(); ++i) {
            if (intervals[i].end < newInterval.start) {
                result.push_back(intervals[i]);
            }
            if (intervals[i].start <= newInterval.start && intervals[i].end > newInterval.end) {
                processed = true;
                result.push_back(intervals[i]);
                continue;
            }
            if (newInterval.end >= intervals[i].start && newInterval.end < intervals[i].end) {
                Interval in;
                in.start = newInterval.start;
                in.end = intervals[i].end;
                processed = true;
                result.push_back(in);
                continue;
            }
            if (intervals[i].start <= newInterval.start && intervals[i].end >= newInterval.start) {
                Interval in;
                in.start = intervals[i].start;
                ++i;
                while (intervals[i].start <= newInterval.end && i < intervals.size()) { 
                    ++i;
                }
                in.end = newInterval.end > intervals[i-1].end ? newInterval.end : intervals[i-1].end;
                processed = true;
                result.push_back(in);
                if (i >= intervals.size()) {
                    break;
                }
            }
            if (intervals[i].start > newInterval.end) {
                if (!processed) {
                    processed = true;
                    result.push_back(newInterval);
                }
                result.push_back(intervals[i]);
            }
        }
        
        if (!processed) {
             result.push_back(newInterval);
        }
        return result;
    }
};