Maximum Number of Tasks You Can Assign

Problem Description

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.

Key Insights

• Workers can be enhanced by using magical pills, which can help them meet task strength requirements.
• A greedy approach can be applied to maximize task assignments, ensuring that stronger workers are assigned to more challenging tasks.
• Sorting both tasks and workers can facilitate efficient matching using binary search or two-pointer techniques.

Space and Time Complexity

Time Complexity: O(n log n + m log m) due to sorting both tasks and workers. Space Complexity: O(1) for in-place sorting, O(n + m) for additional arrays if needed.

Solution

To solve the problem, we can follow these steps:

1. Sort the tasks and workers arrays.
2. For each task, check if there are any workers available who can complete it without a pill.
3. If no worker can complete the task without a pill, check if we can use a pill on a worker to make them strong enough for the task.
4. Use a two-pointer technique to efficiently assign tasks to workers, considering both direct assignments and assignments after administering pills.

Code Solutions