## Problem

Problem ID: 759

Title: Employee Free Time

Difficulty: Hard

Description: 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.

## Thoughts

For this problem, I utilised a technique used for Hackerrank’s Sprint Training question. The technique of storing the delta of intervals is very useful when you want to compute the number of overlapped intervals.

## Solution

General Idea: For each time (start/end) we will store the change in number of employees that will become busy. This will let us easily simulate moving through time and detecting any time intervals when none of the employees are busy (same as all employees free).

Data Structure: map<int, int> busy_times stores the time: delta in number of busy employee. We use ordered map so that we can iterate through the busy times in ascending order.

Algorithm:

• Populating busy_times
• As each interval is disjoint, this means that at Interval.start an employee becomes busy (busy_times[Interval.start]++) and at Interval.end an employee becomes free (busy_times[Interval.end]--).
• Getting free intervals:
• We will store the prev_time that stores the previous processed time and busy_count that tracks the number of busy employee
• Iterate through busy_times
• if the previous busy_count=0, it signifies that it is the end of a all employee free interval.
• Update the prev_time with the current time and busy_count with the current delta.

### Implementation

class Solution {
public:
vector<Interval> employeeFreeTime(vector<vector<Interval>> schedule) {
map<int, int> busy_times;
int n = schedule.size();
for (const auto& emp_sch : schedule) {
for (const auto& interval : emp_sch) {
busy_times[interval.start]++;
busy_times[interval.end]--;
}
}

vector<Interval> ret;
int prev_time = -1;
int busy_count = -1;
for (const auto& [time, busy_delta] : busy_times) {
if (prev_time == -1) {
prev_time = time;
busy_count = busy_delta;
continue;
}
if (busy_count == 0) {
ret.emplace_back(prev_time, time);
}
busy_count += busy_delta;
prev_time = time;
}
return ret;
}
};