Problem:

A Range Module is a module that tracks ranges of numbers. Your task is to design and implement the following interfaces in an efficient manner.

• addRange(int left, int right) Adds the half-open interval [left, right), tracking every real number in that interval. Adding an interval that partially overlaps with currently tracked numbers should add any numbers in the interval [left, right)
  that are not already tracked.
• queryRange(int left, int right) Returns true if and only if every real number in the interval [left, right) is currently being tracked.
• removeRange(int left, int right) Stops tracking every real number currently being tracked in the interval [left, right).

Example 1:

addRange(10, 20): null
removeRange(14, 16): null
queryRange(10, 14): true (Every number in [10, 14) is being tracked)
queryRange(13, 15): false (Numbers like 14, 14.03, 14.17 in [13, 15) are not being tracked)
queryRange(16, 17): true (The number 16 in [16, 17) is still being tracked, despite the remove operation)

Note:

• A half open interval [left, right) denotes all real numbers left <= x < right.
• 0 < left < right < 10^9 in all calls to addRange, queryRange, removeRange.
• The total number of calls to addRange in a single test case is at most 1000.
• The total number of calls to queryRange in a single test case is at most 5000.
• The total number of calls to removeRange in a single test case is at most 1000.

Solution:

　　Leetcode 57. Insert Interval的升級版，addRange函式一樣，removeRange函式如果segments[i]和要刪除的部分沒有重疊，則新增到結果集中，如果有重疊則分為兩種情況：

　　1. ---------  segments[i]

　　        ---------

　　left如果大於segments[i]的first，則新增（segments[i].first，left）

　　2.      ---------  segments[i]

　　    ---------

　　right如果小於segments[i]的second，則新增（right，segments[i].second）

　　對於queryRange函式，簡單的二分查詢即可

Code:

 1 class RangeModule {
 2 public:
 3     RangeModule() {
 4         
 5     }
 6     
 7     void addRange(int left, int right) {
 8         auto iter = segments.begin();
 9         while(iter != segments.end() && (*iter).first < left)
10             iter++;
11         segments.insert(iter,make_pair(left,right));
12         vector<pair<int,int>> result;
13         for(int i = 0;i != segments.size();++i){
14             if(result.empty() || segments[i].first > result.back().second)
15                 result.push_back(segments[i]);
16             else{
17                 result.back().second = max(result.back().second,segments[i].second);
18             }
19         }
20         segments = result;
21     }
22     
23     bool queryRange(int left, int right) {
24         if(segments.size() == 0 || left < segments[0].first){
25             return false;
26         }
27         int start = 0;
28         int end = segments.size()-1;
29         while(start < end){
30             int pivot = start+(end-start+1)/2;
31             if(segments[pivot].first > left)
32                 end = pivot-1;
33             else
34                 start = pivot;
35         }
36         return segments[start].second >= right;
37     }
38     
39     void removeRange(int left, int right) {
40         vector<pair<int,int>> result;
41         for(int i = 0;i != segments.size();++i){
42             if(segments[i].second <= left || segments[i].first >= right)
43                 result.push_back(segments[i]);
44             else {
45                 if(segments[i].first < left)
46                     result.push_back(make_pair(segments[i].first,left));
47                 if(segments[i].second > right)
48                     result.push_back(make_pair(right,segments[i].second));
49             }
50         }
51         segments = result;
52     }
53 private:
54     vector<pair<int,int>> segments;
55 };
56 
57 /**
58  * Your RangeModule object will be instantiated and called as such:
59  * RangeModule obj = new RangeModule();
60  * obj.addRange(left,right);
61  * bool param_2 = obj.queryRange(left,right);
62  * obj.removeRange(left,right);
63  */