2432. The Employee That Worked on the Longest Task
Description
There are n
employees, each with a unique id from 0
to n  1
.
You are given a 2D integer array logs
where logs[i] = [id_{i}, leaveTime_{i}]
where:
id_{i}
is the id of the employee that worked on thei^{th}
task, andleaveTime_{i}
is the time at which the employee finished thei^{th}
task. All the valuesleaveTime_{i}
are unique.
Note that the i^{th}
task starts the moment right after the (i  1)^{th}
task ends, and the 0^{th}
task starts at time 0
.
Return the id of the employee that worked the task with the longest time. If there is a tie between two or more employees, return the smallest id among them.
Example 1:
Input: n = 10, logs = [[0,3],[2,5],[0,9],[1,15]] Output: 1 Explanation: Task 0 started at 0 and ended at 3 with 3 units of times. Task 1 started at 3 and ended at 5 with 2 units of times. Task 2 started at 5 and ended at 9 with 4 units of times. Task 3 started at 9 and ended at 15 with 6 units of times. The task with the longest time is task 3 and the employee with id 1 is the one that worked on it, so we return 1.
Example 2:
Input: n = 26, logs = [[1,1],[3,7],[2,12],[7,17]] Output: 3 Explanation: Task 0 started at 0 and ended at 1 with 1 unit of times. Task 1 started at 1 and ended at 7 with 6 units of times. Task 2 started at 7 and ended at 12 with 5 units of times. Task 3 started at 12 and ended at 17 with 5 units of times. The tasks with the longest time is task 1. The employee that worked on it is 3, so we return 3.
Example 3:
Input: n = 2, logs = [[0,10],[1,20]] Output: 0 Explanation: Task 0 started at 0 and ended at 10 with 10 units of times. Task 1 started at 10 and ended at 20 with 10 units of times. The tasks with the longest time are tasks 0 and 1. The employees that worked on them are 0 and 1, so we return the smallest id 0.
Constraints:
2 <= n <= 500
1 <= logs.length <= 500
logs[i].length == 2
0 <= id_{i} <= n  1
1 <= leaveTime_{i} <= 500
id_{i} != id_{i+1}
leaveTime_{i}
are sorted in a strictly increasing order.
Solutions
Solution 1: Direct Traversal
We use a variable $last$ to record the end time of the last task, a variable $mx$ to record the longest working time, and a variable $ans$ to record the employee with the longest working time and the smallest $id$. Initially, all three variables are $0$.
Next, we traverse the array $logs$. For each employee, we subtract the end time of the last task from the time the employee completes the task to get the working time $t$ of this employee. If $mx$ is less than $t$, or $mx$ equals $t$ and the $id$ of this employee is less than $ans$, then we update $mx$ and $ans$. Then we update $last$ to be the end time of the last task plus $t$. Continue to traverse until the entire array is traversed.
Finally, return the answer $ans$.
The time complexity is $O(n)$, where $n$ is the length of the array $logs$. The space complexity is $O(1)$.














Solution 2

