[LeetCode] Insert Interval

Problem Statement (link):

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].

Analysis:
We need to keep checking overlaps between the new interval and each intervals in the given vector. Given that the original vector is sorted on the start value, we have following three cases to deal with. See code below for specifics.

Code:

/**
 * 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) {
        vector<Interval> res;
        if (intervals.size()==0) {
            res.push_back(newInterval);
            return res;
        }
       
        for (int i=0; i<intervals.size(); i++) {
            if (newInterval.start>intervals[i].end)
                res.push_back(intervals[i]);
            else if (newInterval.end<intervals[i].start) {
                res.push_back(newInterval);
                newInterval=intervals[i];
            }
            else {
                newInterval.start=min(newInterval.start, intervals[i].start);
                newInterval.end=max(newInterval.end, intervals[i].end);
            }
        }
        res.push_back(newInterval);
        return res;
    }
};