Find Time Required to Eliminate Bacterial Strains - Solution & Explanation

Q: Is Find Time Required to Eliminate Bacterial Strains easy or hard?

Find Time Required to Eliminate Bacterial Strains is classified as a Hard problem. While the core idea relies on a greedy strategy, recognizing the need for a priority queue and correctly modeling the elimination timing makes the implementation more challenging.

Q: Find Time Required to Eliminate Bacterial Strains Python/Java solution

Python implementations typically use heapq for the priority queue, while Java uses PriorityQueue. The algorithm pushes each strain into the heap, repeatedly pops the smallest element, updates the cumulative time, and processes all strains in O(n log n) time.

Q: How to solve Find Time Required to Eliminate Bacterial Strains in O(n)?

A strict O(n) solution generally isn't feasible because the problem requires repeatedly selecting the next optimal strain to eliminate. Maintaining this order efficiently requires a heap or balanced structure, which leads to O(n log n) complexity. Attempts to simulate the process without a heap typically degrade to O(n^2).

Q: What is the best approach for Find Time Required to Eliminate Bacterial Strains?

The most efficient solution uses a greedy strategy combined with a min-heap (priority queue). Each strain is inserted into the heap based on the effective time needed to eliminate it. Repeatedly removing the smallest element ensures the optimal elimination order. This approach runs in O(n log n) time and uses O(n) extra space.

Q: Is Find Time Required to Eliminate Bacterial Strains asked at Google/Amazon/Meta?

Problems involving greedy ordering with heaps frequently appear in interviews at companies like Google, Amazon, and Meta. Variants of scheduling, resource allocation, or task prioritization often use the same priority queue pattern seen in this problem.

Q: What data structure is used in Find Time Required to Eliminate Bacterial Strains?

The core data structure is a min-heap (priority queue). It allows efficient retrieval of the strain with the smallest effective elimination time. Arrays store the input, while the heap maintains the greedy processing order.

Q: What is the time complexity of Find Time Required to Eliminate Bacterial Strains?

The optimal approach runs in O(n log n) time because each strain is inserted into and removed from a priority queue once. Heap push and pop operations take O(log n). The space complexity is O(n) due to the heap storing all strains.

HardPremiumFree on FleetCodeArray Math Greedy Heap (Priority Queue)12 min read

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Problem Statement

You are given an integer array timeReq and an integer splitTime.

In the microscopic world of the human body, the immune system faces an extraordinary challenge: combatting a rapidly multiplying bacterial colony that threatens the body's survival.

Initially, only one white blood cell (WBC) is deployed to eliminate the bacteria. However, the lone WBC quickly realizes it cannot keep up with the bacterial growth rate.

The WBC devises a clever strategy to fight the bacteria:

The i^th bacterial strain takes timeReq[i] units of time to be eliminated.
A single WBC can eliminate only one bacterial strain. Afterwards, the WBC is exhausted and cannot perform any other tasks.
A WBC can split itself into two WBCs, but this requires splitTime units of time. Once split, the two WBCs can work in parallel on eliminating the bacteria.
Only one WBC can work on a single bacterial strain. Multiple WBCs cannot attack one strain in parallel.

You must determine the minimum time required to eliminate all the bacterial strains.

Note that the bacterial strains can be eliminated in any order.

Example 1:

Input: timeReq = [10,4,5], splitTime = 2

Output: 12

Explanation:

The elimination process goes as follows:

Initially, there is a single WBC. The WBC splits into 2 WBCs after 2 units of time.
One of the WBCs eliminates strain 0 at a time t = 2 + 10 = 12. The other WBC splits again, using 2 units of time.
The 2 new WBCs eliminate the bacteria at times t = 2 + 2 + 4 and t = 2 + 2 + 5.

Example 2:

Input: timeReq = [10,4], splitTime = 5

Output:15

Explanation:

The elimination process goes as follows:

Initially, there is a single WBC. The WBC splits into 2 WBCs after 5 units of time.
The 2 new WBCs eliminate the bacteria at times t = 5 + 10 and t = 5 + 4.

Constraints:

2 <= timeReq.length <= 10⁵
1 <= timeReq[i] <= 10⁹
1 <= splitTime <= 10⁹

Approach Overview

Problem Overview: You are given multiple bacterial strains represented in an array. Each strain takes time to eliminate, and the elimination order affects the total time required. The goal is to determine the minimum total time needed to remove all strains while accounting for how remaining strains evolve as time progresses.

Approach 1: Simulation with Repeated Scanning (Brute Force) (Time: O(n^2), Space: O(1))

The most direct idea is to simulate the elimination process step by step. At every step, iterate through the entire array to find the strain that should be removed next according to the greedy rule (usually the smallest effective cost or earliest completion time). After eliminating it, update the remaining strains to reflect the time that has passed. This approach works conceptually but becomes inefficient because every elimination requires scanning the full array again.

Approach 2: Greedy + Min Heap (Priority Queue) (Time: O(n log n), Space: O(n))

A better strategy keeps track of the next strain to eliminate using a min-heap. Each heap entry represents the effective time or cost associated with removing that strain. Push all strains into the priority queue, ordered by the earliest elimination time. Repeatedly pop the smallest element, update the global time, and adjust any derived values for remaining strains using simple math calculations rather than rescanning the array.

The key insight: elimination order should always prioritize the strain that becomes optimal to remove earliest. A priority queue maintains this ordering efficiently. Each push/pop operation costs O(log n), so processing all strains results in O(n log n) time. This pattern appears frequently in scheduling and resource allocation problems.

Implementation relies on a heap structure from the language standard library. Push initial states derived from the input array, repeatedly pop the smallest element, update cumulative time, and continue until the heap is empty.

Recommended for interviews: Interviewers expect the greedy strategy with a priority queue. The brute-force simulation shows you understand the elimination order, but the heap (priority queue) optimization demonstrates practical algorithm design. The final implementation combines greedy decision making with efficient ordering using a heap and some lightweight math to update the effective time after each step.

Solution

First, consider the case where there is only one type of bacteria. In this case, there is no need to split the white blood cell (WBC); it can directly eliminate the bacteria, and the time cost is timeSeq[0].

If there are two types of bacteria, the WBC needs to split into two, and each WBC eliminates one type of bacteria. The time cost is splitTime + max(timeSeq[0], timeSeq[1]).

If there are more than two types of bacteria, at each step, we need to consider splitting the WBCs into multiple cells, which is difficult to handle with a forward-thinking approach.

Instead, we can adopt a reverse-thinking approach: instead of splitting the WBCs, we merge the bacteria. We select any two types of bacteria i and j to merge into a new type of bacteria. The time cost for this merge is splitTime + max(timeSeq[i], timeSeq[j]).

To minimize the involvement of bacteria with long elimination times in the merging process, we can greedily select the two bacteria with the smallest elimination times for merging at each step. Therefore, we can maintain a min-heap, repeatedly extracting the two bacteria with the smallest elimination times and merging them until only one type of bacteria remains. The elimination time of this final bacteria is the answer.

The time complexity is O(n times log n), and the space complexity is O(n), where n is the number of bacteria.

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Detailed Complexity Analysis

Approach	Time	Space	When to Use
Brute Force Simulation	O(n^2)	O(1)	Useful for understanding the elimination process or when input size is very small
Greedy + Min Heap (Priority Queue)	O(n log n)	O(n)	Best general solution when elimination order must always pick the smallest effective time

Frequently Asked Questions

Is Find Time Required to Eliminate Bacterial Strains easy or hard?

Find Time Required to Eliminate Bacterial Strains is classified as a Hard problem. While the core idea relies on a greedy strategy, recognizing the need for a priority queue and correctly modeling the elimination timing makes the implementation more challenging.

Find Time Required to Eliminate Bacterial Strains Python/Java solution

Python implementations typically use heapq for the priority queue, while Java uses PriorityQueue. The algorithm pushes each strain into the heap, repeatedly pops the smallest element, updates the cumulative time, and processes all strains in O(n log n) time.

How to solve Find Time Required to Eliminate Bacterial Strains in O(n)?

A strict O(n) solution generally isn't feasible because the problem requires repeatedly selecting the next optimal strain to eliminate. Maintaining this order efficiently requires a heap or balanced structure, which leads to O(n log n) complexity. Attempts to simulate the process without a heap typically degrade to O(n^2).

What is the best approach for Find Time Required to Eliminate Bacterial Strains?

The most efficient solution uses a greedy strategy combined with a min-heap (priority queue). Each strain is inserted into the heap based on the effective time needed to eliminate it. Repeatedly removing the smallest element ensures the optimal elimination order. This approach runs in O(n log n) time and uses O(n) extra space.

Is Find Time Required to Eliminate Bacterial Strains asked at Google/Amazon/Meta?

Problems involving greedy ordering with heaps frequently appear in interviews at companies like Google, Amazon, and Meta. Variants of scheduling, resource allocation, or task prioritization often use the same priority queue pattern seen in this problem.

What data structure is used in Find Time Required to Eliminate Bacterial Strains?

The core data structure is a min-heap (priority queue). It allows efficient retrieval of the strain with the smallest effective elimination time. Arrays store the input, while the heap maintains the greedy processing order.

What is the time complexity of Find Time Required to Eliminate Bacterial Strains?

The optimal approach runs in O(n log n) time because each strain is inserted into and removed from a priority queue once. Heap push and pop operations take O(log n). The space complexity is O(n) due to the heap storing all strains.

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Problem Info

DifficultyHard

Acceptance62.6%

Approaches1

Reading time12 min