<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:
        tasks.sort()
        workers.sort()

        
        def canAssign(tasks, workers, n, pills, strength):
            _tasks = tasks[:n]
            _workers = workers[-n:]
            _pills = pills
            taskIndex = 0
            workerIndex = 0
            res = 0
            
            for i in range(n):
                worker = _workers[workerIndex]
                task = _tasks[taskIndex]

                if worker >= task:
                    workerIndex += 1
                    taskIndex += 1
                    continue
                newWorker = worker + strength
                if _pills > 0 and task <= newWorker:
                    pos = bisect.bisect_right(_tasks, newWorker)
                    _tasks.pop(pos - 1)
                    workerIndex += 1
                    _pills -= 1
                    continue
                return False
            return True
        
        start, end = 0, min(len(tasks), len(workers))

        while start + 1 < end:
            mid = (start + end) // 2
            if canAssign(tasks, workers, mid, pills, strength):
                start = mid
            else:
                end = mid
        
        if canAssign(tasks, workers, end, pills, strength):
            return end
        return start







# 5 5 8 9 9
# 1 2 4 6 6


#  def maxTaskAssign(self, tasks: List[int], workers: List[int], pills: int, strength: int) -> int:
#         if min(tasks) > max(workers) + (strength if pills > 0 else 0):
#             return 0

#         tasks.sort()
#         workers.sort()

#         def can_finish_n_tasks(n, pills):
#             new_workers = workers[-n:] # most powerful n workers
#             new_tasks = tasks[:n] # easiest n tasks
#             task_idx = worker_idx = 0

#             for _ in range(n):
#                 if new_tasks[task_idx] <= new_workers[worker_idx]:
#                     worker_idx += 1
#                     task_idx += 1
#                     continue
#                 new_strength = new_workers[worker_idx]+strength
#                 if pills > 0 and new_tasks[task_idx] <= new_strength:
#                     idx = bisect.bisect_right(new_tasks, new_strength)
#                     new_tasks.pop(idx-1)
#                     worker_idx += 1
#                     pills -= 1
#                     continue
#                 return False
#             return True

#         lo = 0
#         hi = min(len(tasks), len(workers))
#         while lo + 1 < hi:
#             n = (lo+hi) // 2
#             if can_finish_n_tasks(n, pills):
#                 lo = n
#             else:
#                 hi = n
#         if can_finish_n_tasks(hi, pills):
#             return hi
#         return lo
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