# 759.Employee-Free-Time

## 759. Employee Free Time

## 题目地址

<https://leetcode.com/problems/employee-free-time/>

## 题目描述

```
We are given a list schedule of employees, which represents the working time for each employee.

Each employee has a list of non-overlapping Intervals, and these intervals are in sorted order.

Return the list of finite intervals representing common, positive-length free time for all employees, also in sorted order.

(Even though we are representing Intervals in the form [x, y], the objects inside are Intervals, not lists or arrays. For example, schedule[0][0].start = 1, schedule[0][0].end = 2, and schedule[0][0][0] is not defined).  Also, we wouldn't include intervals like [5, 5] in our answer, as they have zero length.



Example 1:

Input: schedule = [[[1,2],[5,6]],[[1,3]],[[4,10]]]
Output: [[3,4]]
Explanation: There are a total of three employees, and all common
free time intervals would be [-inf, 1], [3, 4], [10, inf].
We discard any intervals that contain inf as they aren't finite.
Example 2:

Input: schedule = [[[1,3],[6,7]],[[2,4]],[[2,5],[9,12]]]
Output: [[5,6],[7,9]]


Constraints:

1 <= schedule.length , schedule[i].length <= 50
0 <= schedule[i].start < schedule[i].end <= 10^8
```

## 代码

Approach 1: Events (Line Sweep)

**Complexity Analysis**

* Time Complexity: O\_(\_C\_log\_C), where C is the number of intervals across all employees.
* Space Complexity: O\_(\_C).

```java
/*
// Definition for an Interval.
class Interval {
    public int start;
    public int end;

    public Interval() {}

    public Interval(int _start, int _end) {
        start = _start;
        end = _end;
    }
};
*/
class Solution {
  public List<Interval> employeeFreeTime(List<List<Interval>> schedule) {
        int OPEN = 0, CLOSE = 1;

    List<int[]> events = new ArrayList();
    for (List<Interval> employee : schedule) {
      for (Interval iv : employee) {
        events.add(new int[] {iv.start, OPEN});
        events.add(new int[] {iv.end, CLOSE});
      }
    }

    Collections.sort(events, (a, b) -> a[0] != b[0] ? a[0] - b[0] : a[1] - b[1]);
    List<Interval> ans = new ArrayList();

    int prev = -1, bal = 0;
    for (int[] event : events) {
      if (bal == 0 && prev >= 0) {
        ans.add(new Interval(prev, event[0]));
      }
      bal += (event[1] == OPEN ? 1 : -1);
      prev = event[0];
    }

    return ans;
  }
}
```

Approach #2 Priority Queue

**Complexity Analysis**

* Time Complexity: &#x4F;*(\_C\_log\_N*), where N *is the number of employees, and \_C* is the number of jobs across all employees. The maximum size of the heap is *N*, so each push and pop operation is &#x4F;*(log\_N*), and there are &#x4F;*(\_C*) such operations.
* Space Complexity: O\_(\_N) in additional space complexity.

```java
class Solution {
    public List<Interval> employeeFreeTime(List<List<Interval>> avails) {
        List<Interval> ans = new ArrayList();
        PriorityQueue<Job> pq = new PriorityQueue<Job>((a, b) ->
            avails.get(a.eid).get(a.index).start -
            avails.get(b.eid).get(b.index).start);
        int ei = 0, anchor = Integer.MAX_VALUE;

        for (List<Interval> employee: avails) {
            pq.offer(new Job(ei++, 0));
            anchor = Math.min(anchor, employee.get(0).start);
        }

        while (!pq.isEmpty()) {
            Job job = pq.poll();
            Interval iv = avails.get(job.eid).get(job.index);
            if (anchor < iv.start)
                ans.add(new Interval(anchor, iv.start));
            anchor = Math.max(anchor, iv.end);
            if (++job.index < avails.get(job.eid).size())
                pq.offer(job);
        }

        return ans;
    }
}

class Job {
    int eid, index;
    Job(int e, int i) {
        eid = e;
        index = i;
    }
}
```
