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].

思路：

对于有n个区间的vector，分成了2*n+1个部分。根据这个性质，对于一个新的interval，先判断它的左右点都在哪一部分，然后将被覆盖的部分删除即可。

下面代码中findIndex负责找到某个int值所在的区域。

代码：

    int findIndex(vector<Interval> &intervals, int val){
        int n = intervals.size();
        if(val < intervals[0].start) 
            return 0;
        if(val > intervals[n-1].end)
            return 2*n;
        for(int i = 0; i < n; i++){
            if(val >= intervals[i].start && val <= intervals[i].end)
                return 2*i+1;
            if(i < n-1 && val > intervals[i].end && val < intervals[i+1].start)
                return 2*i+2;
            if(i > 0 && val > intervals[i-1].end && val < intervals[i].start)
                return 2*i;
        }
    }
    vector<Interval> insert(vector<Interval> &intervals, Interval newInterval) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        if(intervals.size() == 0){
            intervals.push_back(newInterval);
            return intervals;
        }
        int size = intervals.size();
        int s = findIndex(intervals, newInterval.start), e = findIndex(intervals, newInterval.end);
        cout<<s<<"-"<<e<<endl;
        if(s%2 == 1){
            newInterval.start = intervals[s/2].start;
        }
        if(e%2 == 1){
            newInterval.end = intervals[e/2].end;
        }
        if(s == e){
            if(s%2 != 1)
                intervals.insert(intervals.begin()+s/2, newInterval);
        }
        else{
            s /= 2;
            if(e%2 == 0)
                e /= 2;
            else
                e = e/2+1;
            if(e > size)
                e = size;
            cout<<s<<"-"<<e<<endl;
            intervals.erase(intervals.begin()+s, intervals.begin()+e);
            intervals.insert(intervals.begin()+s, newInterval);
        }
        return intervals;
    }