cpp-flashcards/org/study_deck_02/dsa/intervals/1851-minimum-interval-to-include-each-query.org

#+ANKI_DECK: study_deck_02
* TODO 1851. Minimum Interval to Include Each Query :hard:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*1851. Minimum Interval to Include Each Query][1851. Minimum Interval to Include Each Query]]
:END:

You are given a 2D integer array ~intervals~, where ~intervals[i] = [left_{i}, right_{i}]~ describes the ~i^{th}~ interval starting at ~left_{i}~ and ending at ~right_{i}~ *(inclusive)*. The *size* of an interval is defined as the number of integers it contains, or more formally ~right_{i} - left_{i} + 1~.

You are also given an integer array ~queries~. The answer to the ~j^{th}~ query is the *size of the smallest interval* ~i~ such that ~left_{i} <= queries[j] <= right_{i}~. If no such interval exists, the answer is ~-1~.

Return /an array containing the answers to the queries/.

*Example 1:*


#+begin_src
Input: intervals = [[1,4],[2,4],[3,6],[4,4]], queries = [2,3,4,5]
Output: [3,3,1,4]
Explanation: The queries are processed as follows:
- Query = 2: The interval [2,4] is the smallest interval containing 2. The answer is 4 - 2 + 1 = 3.
- Query = 3: The interval [2,4] is the smallest interval containing 3. The answer is 4 - 2 + 1 = 3.
- Query = 4: The interval [4,4] is the smallest interval containing 4. The answer is 4 - 4 + 1 = 1.
- Query = 5: The interval [3,6] is the smallest interval containing 5. The answer is 6 - 3 + 1 = 4.
#+end_src


*Example 2:*


#+begin_src
Input: intervals = [[2,3],[2,5],[1,8],[20,25]], queries = [2,19,5,22]
Output: [2,-1,4,6]
Explanation: The queries are processed as follows:
- Query = 2: The interval [2,3] is the smallest interval containing 2. The answer is 3 - 2 + 1 = 2.
- Query = 19: None of the intervals contain 19. The answer is -1.
- Query = 5: The interval [2,5] is the smallest interval containing 5. The answer is 5 - 2 + 1 = 4.
- Query = 22: The interval [20,25] is the smallest interval containing 22. The answer is 25 - 20 + 1 = 6.
#+end_src


*Constraints:*

 - ~1 <= intervals.length <= 10^{5}~

 - ~1 <= queries.length <= 10^{5}~

 - ~intervals[i].length == 2~

 - ~1 <= left_{i} <= right_{i} <= 10^{7}~

 - ~1 <= queries[j] <= 10^{7}~

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python :lc-problem 1851 :lc-lang python3
class Solution:
    def minInterval(self, intervals: List[List[int]], queries: List[int]) -> List[int]:
#+end_src

** TODO C++
#+begin_src cpp :lc-problem 1851
class Solution {
public:
    vector<int> minInterval(vector<vector<int>>& intervals, vector<int>& queries) {
        
    }
};
#+end_src