<p>There is a computer that can run an unlimited number of tasks <strong>at the same time</strong>. You are given a 2D integer array <code>tasks</code> where <code>tasks[i] = [start<sub>i</sub>, end<sub>i</sub>, duration<sub>i</sub>]</code> indicates that the <code>i<sup>th</sup></code> task should run for a total of <code>duration<sub>i</sub></code> seconds (not necessarily continuous) within the <strong>inclusive</strong> time range <code>[start<sub>i</sub>, end<sub>i</sub>]</code>.</p>

<p>You may turn on the computer only when it needs to run a task. You can also turn it off if it is idle.</p>

<p>Return <em>the minimum time during which the computer should be turned on to complete all tasks</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> tasks = [[2,3,1],[4,5,1],[1,5,2]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
- The first task can be run in the inclusive time range [2, 2].
- The second task can be run in the inclusive time range [5, 5].
- The third task can be run in the two inclusive time ranges [2, 2] and [5, 5].
The computer will be on for a total of 2 seconds.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> tasks = [[1,3,2],[2,5,3],[5,6,2]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> 
- The first task can be run in the inclusive time range [2, 3].
- The second task can be run in the inclusive time ranges [2, 3] and [5, 5].
- The third task can be run in the two inclusive time range [5, 6].
The computer will be on for a total of 4 seconds.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= tasks.length &lt;= 2000</code></li>
	<li><code>tasks[i].length == 3</code></li>
	<li><code>1 &lt;= start<sub>i</sub>, end<sub>i</sub> &lt;= 2000</code></li>
	<li><code>1 &lt;= duration<sub>i</sub> &lt;= end<sub>i</sub> - start<sub>i</sub> + 1 </code></li>
</ul>

class Solution:
    def findMinimumTime(self, tasks: List[List[int]]) -> int:
        # sort using the finish time
        # we turn on the computer on each task's finish time
        # after doing so, we go through the rest of the tasks to see if turning on at this point would help reduce the need to turn on computer in this task
        tasks = sorted(tasks, key = lambda x: (x[1],x[0]))
        res = 0
        ran = collections.defaultdict(int)
        for i, (start, end, duration) in enumerate(tasks):
            cur_time = duration
            for j in range(start, end+1):
                cur_time-=int(bool(ran[j]))
            if cur_time>0:
                j=end
                for _ in range(cur_time):
                    while ran[j]:
                        j-=1
                    ran[j]=1

                res+=cur_time

        return res


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