Is Minimum Amount of Damage Dealt to Bob easy or hard?

Minimum Amount of Damage Dealt to Bob is classified as a Hard problem because the key step is recognizing the scheduling optimization hidden in the statement. Once you translate the objective to minimizing sum(weight × completion time), the greedy ordering rule becomes clear.

Minimum Amount of Damage Dealt to Bob Python/Java solution

Implementations in Python, Java, C++, and other languages follow the same pattern: compute hits needed for each enemy, sort enemies by damage divided by hits, then iterate to accumulate total damage based on completion time. The logic is language independent and relies on built-in sorting functions.

How to solve Minimum Amount of Damage Dealt to Bob in O(n)?

An O(n) solution is generally not feasible because the optimal strategy requires ordering enemies by a ratio metric. Determining this order requires sorting, which takes O(n log n) time in comparison-based algorithms. The rest of the computation after sorting is linear.

What is the best approach for Minimum Amount of Damage Dealt to Bob?

The optimal solution uses a greedy scheduling strategy. Compute the number of hits needed for each enemy and sort enemies by the ratio damage / hits in descending order. This ensures enemies that contribute the most damage per unit time are eliminated first. The approach runs in O(n log n) time due to sorting.

Is Minimum Amount of Damage Dealt to Bob asked at Google/Amazon/Meta?

Problems based on greedy scheduling and minimizing weighted completion time frequently appear in interviews at companies like Google, Amazon, and Meta. Variants often involve ordering tasks to minimize penalties or accumulated costs. This problem is a practical example of that pattern.

What data structure is used in Minimum Amount of Damage Dealt to Bob?

The solution primarily uses arrays or lists to store enemy attributes such as damage and required hits. A sorting step orders these elements based on a computed ratio like damage per hit. No advanced data structures beyond sorting and iteration are required.

What is the time complexity of Minimum Amount of Damage Dealt to Bob?

The optimal solution runs in O(n log n) time because enemies must be sorted by a greedy priority metric such as damage per hit. After sorting, a single linear pass computes the accumulated damage. Space complexity is O(n) for storing enemy attributes and hit counts.

Description Hints 2 Solution Video 15:27

3273. Minimum Amount of Damage Dealt to Bob

Hard39.6% acceptance1 company

You are given an integer power and two integer arrays damage and health, both having length n.

Bob has n enemies, where enemy i will deal Bob damage[i] points of damage per second while they are alive (i.e. health[i] > 0).

Every second, after the enemies deal damage to Bob, he chooses one of the enemies that is still alive and deals power points of damage to them.

Determine the minimum total amount of damage points that will be dealt to Bob before all n enemies are dead.

Example 1:

Input: power = 4, damage = [1,2,3,4], health = [4,5,6,8]

Output: 39

Explanation:

Attack enemy 3 in the first two seconds, after which enemy 3 will go down, the number of damage points dealt to Bob is 10 + 10 = 20 points.
Attack enemy 2 in the next two seconds, after which enemy 2 will go down, the number of damage points dealt to Bob is 6 + 6 = 12 points.
Attack enemy 0 in the next second, after which enemy 0 will go down, the number of damage points dealt to Bob is 3 points.
Attack enemy 1 in the next two seconds, after which enemy 1 will go down, the number of damage points dealt to Bob is 2 + 2 = 4 points.

Example 2:

Input: power = 1, damage = [1,1,1,1], health = [1,2,3,4]

Output: 20

Explanation:

Attack enemy 0 in the first second, after which enemy 0 will go down, the number of damage points dealt to Bob is 4 points.
Attack enemy 1 in the next two seconds, after which enemy 1 will go down, the number of damage points dealt to Bob is 3 + 3 = 6 points.
Attack enemy 2 in the next three seconds, after which enemy 2 will go down, the number of damage points dealt to Bob is 2 + 2 + 2 = 6 points.
Attack enemy 3 in the next four seconds, after which enemy 3 will go down, the number of damage points dealt to Bob is 1 + 1 + 1 + 1 = 4 points.

Example 3:

Input: power = 8, damage = [40], health = [59]

Output: 320

Constraints:

1 <= power <= 10⁴
1 <= n == damage.length == health.length <= 10⁵
1 <= damage[i], health[i] <= 10⁴

Asked at 1 company

Amazon

Topics

Hints open one at a time

Hint 1

Can we use sorting here along with a custom comparator?

Hint 2

For any two enemies i and j with damages damage[i] and damage[j], and time to take each of them down t_i and t_j, when is it better to choose enemy i over enemy j first?

15:27

Still stuck?Read 2 approaches, or watch a walkthrough.

Open solution