<p>You have <code>n</code> tasks and <code>m</code> workers. Each task has a strength requirement stored in a <strong>0-indexed</strong> integer array <code>tasks</code>, with the <code>i<sup>th</sup></code> task requiring <code>tasks[i]</code> strength to complete. The strength of each worker is stored in a <strong>0-indexed</strong> integer array <code>workers</code>, with the <code>j<sup>th</sup></code> worker having <code>workers[j]</code> strength. Each worker can only be assigned to a <strong>single</strong> task and must have a strength <strong>greater than or equal</strong> to the task&#39;s strength requirement (i.e., <code>workers[j] &gt;= tasks[i]</code>).</p>

<p>Additionally, you have <code>pills</code> magical pills that will <strong>increase a worker&#39;s strength</strong> by <code>strength</code>. You can decide which workers receive the magical pills, however, you may only give each worker <strong>at most one</strong> magical pill.</p>

<p>Given the <strong>0-indexed </strong>integer arrays <code>tasks</code> and <code>workers</code> and the integers <code>pills</code> and <code>strength</code>, return <em>the <strong>maximum</strong> number of tasks that can be completed.</em></p>

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

<pre>
<strong>Input:</strong> tasks = [<u><strong>3</strong></u>,<u><strong>2</strong></u>,<u><strong>1</strong></u>], workers = [<u><strong>0</strong></u>,<u><strong>3</strong></u>,<u><strong>3</strong></u>], pills = 1, strength = 1
<strong>Output:</strong> 3
<strong>Explanation:</strong>
We can assign the magical pill and tasks as follows:
- Give the magical pill to worker 0.
- Assign worker 0 to task 2 (0 + 1 &gt;= 1)
- Assign worker 1 to task 1 (3 &gt;= 2)
- Assign worker 2 to task 0 (3 &gt;= 3)
</pre>

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

<pre>
<strong>Input:</strong> tasks = [<u><strong>5</strong></u>,4], workers = [<u><strong>0</strong></u>,0,0], pills = 1, strength = 5
<strong>Output:</strong> 1
<strong>Explanation:</strong>
We can assign the magical pill and tasks as follows:
- Give the magical pill to worker 0.
- Assign worker 0 to task 0 (0 + 5 &gt;= 5)
</pre>

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

<pre>
<strong>Input:</strong> tasks = [<u><strong>10</strong></u>,<u><strong>15</strong></u>,30], workers = [<u><strong>0</strong></u>,<u><strong>10</strong></u>,10,10,10], pills = 3, strength = 10
<strong>Output:</strong> 2
<strong>Explanation:</strong>
We can assign the magical pills and tasks as follows:
- Give the magical pill to worker 0 and worker 1.
- Assign worker 0 to task 0 (0 + 10 &gt;= 10)
- Assign worker 1 to task 1 (10 + 10 &gt;= 15)
The last pill is not given because it will not make any worker strong enough for the last task.
</pre>

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

<ul>
	<li><code>n == tasks.length</code></li>
	<li><code>m == workers.length</code></li>
	<li><code>1 &lt;= n, m &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= pills &lt;= m</code></li>
	<li><code>0 &lt;= tasks[i], workers[j], strength &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def maxTaskAssign(self, tasks: List[int], workers: List[int], pills: int, strength: int) -> int:
        n, m = len(workers), len(tasks)
        workers.sort(reverse=True)
        tasks.sort()

        def check(md):
            p = pills
            
            theap = []
            wheap = []
            for i in range(md):
                heappush(wheap, (workers[i], 1))
                heappush(theap, tasks[i])
            one, two = True, False
            trash = []
            while wheap and theap:
                if theap[0] <= wheap[0][0]:
                    heappop(theap)
                    x, y = heappop(wheap)
                    if y:
                        heappush(trash, x)

                elif p and wheap[0][1] == 1:
                    two = True
                    p -= 1
                    heappush(wheap, (heappop(wheap)[0] + strength, 0))
                elif p:
                    x, y = heappop(wheap)
                    while trash and trash[0] + strength < theap[0]:
                        heappop(trash)
                    if not trash:
                        return False
                    
                    heappop(theap)
                    heappop(trash)
                    p -= 1
                        
                else:
                    return False
            
            return True
        
        l = 0
        h = min(m, n)

        while l <= h:
            md = (l + h)//2

            if check(md):
                l = md + 1
            else:
                h = md - 1
        
        return h
        
        
        
        
        
1939