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Maximum Number of Tasks You Can Assign

Hard

You have n tasks and m workers. Each task has a strength requirement stored in a 0-indexed integer array tasks , with the i th task requiring tasks[i] strength to complete. The strength of each worker is stored in a 0-indexed integer array workers , with the j th worker having workers[j] strength. Each worker can only be assigned to a single task and has to 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.

Provided the 0-indexed integer arrays tasks and workers and the integers pills and strength , produce the maximum count of tasks that can be completed.

Example 1

Input: tasks = [ 3, 2, 1], workers = [ 0, 3, 3], pills = 1, strength = 1

Output: 3

Explanation: In this case, 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: In this case, 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: In this case, 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 * 10^4
  • 0 <= pills <= m
  • 0 <= tasks[i], workers[j], strength <= 10^9

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