How do you solve Minimum Amount of Damage Dealt to Bob on LeetCode?

Minimum Amount of Damage Dealt to Bob (LeetCode #3273) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Prioritize attacking enemies based on their damage output and health to minimize total damage.

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

The optimal solution for Minimum Amount of Damage Dealt to Bob runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to sorting the enemies, and the space complexity is O(n) for storing the enemy data.

What is the brute force solution for Minimum Amount of Damage Dealt to Bob?

The brute force approach for Minimum Amount of Damage Dealt to Bob is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves simulating each second of the battle, choosing an enemy to attack without any strategy. This will lead to a straightforward but inefficient solution. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Amount of Damage Dealt to Bob?

Minimum Amount of Damage Dealt to Bob uses the following concepts: Array, Greedy, Sorting. The recommended patterns to study are: Greedy Algorithms, Sorting.

What are the interview tips for Minimum Amount of Damage Dealt to Bob?

Always clarify the problem statement and constraints before diving into coding. Discuss your thought process and reasoning for each step of your solution. Be prepared to analyze the time and space complexity of your solution.

What are common mistakes when solving Minimum Amount of Damage Dealt to Bob?

Not considering the damage output of enemies when deciding the order of attacks. Failing to account for the time it takes to defeat each enemy.

#3273

Minimum Amount of Damage Dealt to Bob

Hard

ArrayGreedySortingGreedy AlgorithmsSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

The optimal approach uses a greedy strategy: prioritize attacking enemies based on their damage output and health. By sorting enemies, we can minimize the damage dealt to Bob.

⚙️

Algorithm

3 steps

1Step 1: Create a list of enemies with their damage and health.
2Step 2: Sort the enemies based on the ratio of damage to health (damage[i] / (health[i] / power)).
3Step 3: Simulate the battle by attacking the sorted enemies in order until all are defeated, calculating the total damage to Bob.

solution.py9 lines

1def min_damage_optimal(power, damage, health):
2    enemies = sorted(zip(damage, health), key=lambda x: x[0] / (x[1] / power))
3    total_damage = 0
4    time = 0
5    for d, h in enemies:
6        time_to_kill = (h + power - 1) // power
7        total_damage += time_to_kill * d
8        time += time_to_kill
9    return total_damage

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the enemies, and the space complexity is O(n) for storing the enemy data.

1Prioritize attacking enemies based on their damage output and health to minimize total damage.
2Sorting enemies helps in making optimal decisions on which enemy to attack first.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.