Posts tagged as “hard”

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)

Example 4:

Input: tasks = [5,9,8,5,9], workers = [1,6,4,2,6], pills = 1, strength = 5
Output: 3
Explanation:
We can assign the magical pill and tasks as follows:
- Give the magical pill to worker 2.
- Assign worker 1 to task 0 (6 >= 5)
- Assign worker 2 to task 2 (4 + 5 >= 8)
- Assign worker 4 to task 3 (6 >= 5)

Constraints:

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

Solution: Greedy + Binary Search in Binary Search.

Find the smallest k, s.t. we are NOT able to assign. Then answer is k- 1.

The key is to verify whether we can assign k tasks or not.

Greedy: We want k smallest tasks and k strongest workers.

Start with the hardest tasks among (smallest) k:
1. assign task[i] to the weakest worker without a pill (if he can handle the hardest work so far, then the stronger workers can handle any simpler tasks left)
2. If 1) is not possible, we find a weakest worker + pill that can handle task[i] (otherwise we are wasting workers)
3. If 2) is not possible, impossible to finish k tasks.

Let k = min(n, m)
Time complexity: O((logk)² * k)
Space complexity: O(k)