[LeetCode] 57. Insert Interval 解决思路

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].

问题：给定一个区间数组，插入一个新的区间元素。区间数组已经按照 区间开始值升序排序。

思路：

1. 找到左边第一个 intervals[i].end >= newInterval.start 的元素。

2. 若 intervals[i].start > newInterval.end，则在 i 位置插入 newInterval ，程序结束。否则，将后续所有 intervals[j].start <= newInterval.end (i <= j)的元素合并到 i 位置，intervals[i].start 取涉及合并的最小值， intervals[i].end 取涉及合并的最大值。

3. 将 i 后面没有涉及合并的元素往前移动，移动至紧跟 i 元素。

这道题的思路不难也比较直观，时间效率为 O(n)，只是需要处理的边界情况比较多。例如有首部插入区间数组、尾部插入区间数组、以及完全覆盖的区间数组情况。

vector<Interval> insert(vector<Interval>& intervals, Interval newInterval) {
    
    if (intervals.size() == 0) {
        intervals.push_back(newInterval);
        return intervals;
    }
    
    if (newInterval.end < intervals[0].start) {
        intervals.insert(intervals.begin(), newInterval);
        return intervals;
    }
    
    if (newInterval.start > intervals[intervals.size()-1].end) {
        intervals.push_back(newInterval);
        return intervals;
    }
    
    if (newInterval.start <= intervals[0].start && intervals[intervals.size()-1].end <= newInterval.end) {
        intervals.clear();
        intervals.push_back(newInterval);
        return intervals;
    }
    
    
    int len = (int)intervals.size();
    int i = 0;
    for ( ; i < intervals.size(); i++) {
        if (intervals[i].end >= newInterval.start) {
            break;
        }
    }
    int theIdx = i;
    
    if (intervals[theIdx].start > newInterval.end) {
        vector<Interval>::iterator nth = intervals.begin() + theIdx;
        intervals.insert(nth, newInterval);
        return intervals;
    }else{
        intervals[theIdx].start = min( intervals[theIdx].start, newInterval.start);

    }

    while (i < intervals.size() && intervals[i].start <= newInterval.end) {
        intervals[theIdx].end = max(intervals[i].end, newInterval.end);
        i++;
    }
        
    int j = theIdx + 1;
    
    while (i < intervals.size()) {
        intervals[j] = intervals[i];
        i++;
        j++;
    }
    
    while (j < len) {
        intervals.pop_back();
        j++;
    }
    
    return intervals;
}