<p>You are given an array <code>tasks</code> where <code>tasks[i] = [actual<sub>i</sub>, minimum<sub>i</sub>]</code>:</p>

<ul>
	<li><code>actual<sub>i</sub></code> is the actual amount of energy you <strong>spend to finish</strong> the <code>i<sup>th</sup></code> task.</li>
	<li><code>minimum<sub>i</sub></code> is the minimum amount of energy you <strong>require to begin</strong> the <code>i<sup>th</sup></code> task.</li>
</ul>

<p>For example, if the task is <code>[10, 12]</code> and your current energy is <code>11</code>, you cannot start this task. However, if your current energy is <code>13</code>, you can complete this task, and your energy will be <code>3</code> after finishing it.</p>

<p>You can finish the tasks in <strong>any order</strong> you like.</p>

<p>Return <em>the <strong>minimum</strong> initial amount of energy you will need</em> <em>to finish all the tasks</em>.</p>

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

<pre>
<strong>Input:</strong> tasks = [[1,2],[2,4],[4,8]]
<strong>Output:</strong> 8
<strong>Explanation:</strong>
Starting with 8 energy, we finish the tasks in the following order:
    - 3rd task. Now energy = 8 - 4 = 4.
    - 2nd task. Now energy = 4 - 2 = 2.
    - 1st task. Now energy = 2 - 1 = 1.
Notice that even though we have leftover energy, starting with 7 energy does not work because we cannot do the 3rd task.</pre>

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

<pre>
<strong>Input:</strong> tasks = [[1,3],[2,4],[10,11],[10,12],[8,9]]
<strong>Output:</strong> 32
<strong>Explanation:</strong>
Starting with 32 energy, we finish the tasks in the following order:
    - 1st task. Now energy = 32 - 1 = 31.
    - 2nd task. Now energy = 31 - 2 = 29.
    - 3rd task. Now energy = 29 - 10 = 19.
    - 4th task. Now energy = 19 - 10 = 9.
    - 5th task. Now energy = 9 - 8 = 1.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> tasks = [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
<strong>Output:</strong> 27
<strong>Explanation:</strong>
Starting with 27 energy, we finish the tasks in the following order:
    - 5th task. Now energy = 27 - 5 = 22.
    - 2nd task. Now energy = 22 - 2 = 20.
    - 3rd task. Now energy = 20 - 3 = 17.
    - 1st task. Now energy = 17 - 1 = 16.
    - 4th task. Now energy = 16 - 4 = 12.
    - 6th task. Now energy = 12 - 6 = 6.
</pre>

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

<ul>
	<li><code>1 &lt;= tasks.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= actual<sub>​i</sub>&nbsp;&lt;= minimum<sub>i</sub>&nbsp;&lt;= 10<sup>4</sup></code></li>
</ul>

import bisect
class Solution:
    def minimumEffort(self, tasks: List[List[int]]) -> int:
        tasks.sort(key=lambda x: x[0] - x[1])
        
        def canFinish(energy):
            for actual, minimum in tasks:
                if energy < minimum:
                    return False
                energy -= actual

            return True

        res = 0
        l = sum(x[0] for x in tasks)
        r = sum(x[1] for x in tasks)

        while l <= r:
            mid = (l + r) // 2
            if canFinish(mid):
                res = mid
                r = mid - 1
            else:
                l = mid + 1

        return res

    
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