2071. Maximum Number of Tasks You Can Assign

Problem Link

Description

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You have n tasks and m workers. Each task has a strength requirement stored in a 0-indexed integer array tasks, with the ith task requiring tasks[i] strength to complete. The strength of each worker is stored in a 0-indexed integer array workers, with the jth worker having workers[j] strength. Each worker can only be assigned to a single task and must have a strength greater than or equal to the task's strength requirement (i.e., workers[j] >= tasks[i]).

Additionally, you have pills magical pills that will increase a worker's strength by strength. You can decide which workers receive the magical pills, however, you may only give each worker at most one magical pill.

Given the 0-indexed integer arrays tasks and workers and the integers pills and strength, return the maximum number of tasks that can be completed.

 

Example 1:

Input: tasks = [3,2,1], workers = [0,3,3], pills = 1, strength = 1
Output: 3
Explanation:
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 >= 1)
- Assign worker 1 to task 1 (3 >= 2)
- Assign worker 2 to task 0 (3 >= 3)

Example 2:

Input: tasks = [5,4], workers = [0,0,0], pills = 1, strength = 5
Output: 1
Explanation:
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 >= 5)

Example 3:

Input: tasks = [10,15,30], workers = [0,10,10,10,10], pills = 3, strength = 10
Output: 2
Explanation:
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 >= 10)
- Assign worker 1 to task 1 (10 + 10 >= 15)
The last pill is not given because it will not make any worker strong enough for the last task.

 

Constraints:

• n == tasks.length
• m == workers.length
• 1 <= n, m <= 5 * 104
• 0 <= pills <= m
• 0 <= tasks[i], workers[j], strength <= 109

Solution

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Python3

class Solution:
    def maxTaskAssign(self, tasks: List[int], workers: List[int], pills: int, strength: int) -> int:
        tasks.sort()
        workers.sort()
        left, right = 0, min(len(tasks), len(workers))
 
        while left < right:
            mid = (left + right + 1)//2
            usedPills = 0
            avail = workers[-mid:]            
            canAssign = True
 
            for t in reversed(tasks[:mid]):
                if avail[-1] >= t:
                    avail.pop()
                else:
                    idx = bisect.bisect_left(avail, t - strength)
                    if idx == len(avail) or usedPills == pills:
                        canAssign = False
                        break
                    usedPills += 1
                    avail.pop(idx)
 
            if canAssign:
                left = mid
            else:
                right = mid - 1
 
        return left