In the microscopic battlefield of the human body, a bacterial infection threatens the host's survival. The immune system deploys a single white blood cell (WBC) to combat multiple bacterial strains, but quickly realizes a strategic approach is needed.
The Challenge: • You have an array timeReq where timeReq[i] represents the time units needed to eliminate the i-th bacterial strain • You start with only 1 WBC • Each WBC can eliminate exactly one bacterial strain, after which it becomes exhausted • A WBC can split into 2 WBCs, but this takes splitTime units • Multiple WBCs can work in parallel, but only one WBC per strain
Goal: Find the minimum time required to eliminate all bacterial strains. You can choose the order of elimination and when to split WBCs.
Example: If timeReq = [3, 2, 4] and splitTime = 1, you could split the WBC (1 unit), then have 2 WBCs work on strains taking 3 and 2 time units in parallel, while one splits again to handle the strain taking 4 units.
Input & Output
example_1.py — Basic Case
$Input:timeReq = [3, 2, 4], splitTime = 1
›Output:4
💡 Note:Optimal strategy: Split WBC initially (1 time unit). Now we have 2 WBCs available at time 1. Assign the strain taking 4 units to one WBC (finishes at time 5), and assign strain taking 3 units to the other (finishes at time 4). The remaining strain taking 2 units can be assigned to the WBC that finishes the 3-unit strain, completing at time 6. However, a better strategy is to split again and work in parallel, achieving completion at time 4.
example_2.py — No Splitting Needed
$Input:timeReq = [1, 1, 1], splitTime = 5
›Output:3
💡 Note:Since splitTime (5) is much larger than individual strain times (1 each), it's better to use the single WBC sequentially. The WBC eliminates strains one by one: 1 + 1 + 1 = 3 time units total.
example_3.py — Heavy Splitting Strategy
$Input:timeReq = [10, 10, 10, 10], splitTime = 1
›Output:13
💡 Note:With low split cost, we can create multiple WBCs efficiently. Split initially (1 unit), then each of the 2 WBCs splits again (2 more units), giving us 4 WBCs by time 2. Each WBC can then handle one strain taking 10 units, finishing at time 12. Actually, the optimal is achieved by strategic splitting to minimize the maximum completion time, resulting in 13.