Leetcode #2214: Minimum Health to Beat Game
In this guide, we solve Leetcode #2214 Minimum Health to Beat Game in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are playing a game that has n levels numbered from 0 to n - 1. You are given a 0-indexed integer array damage where damage[i] is the amount of health you will lose to complete the ith level.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Greedy, Array
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: damage = [2,7,4,3], armor = 4
Output: 13
Explanation: One optimal way to beat the game starting at 13 health is:
On round 1, take 2 damage. You have 13 - 2 = 11 health.
On round 2, take 7 damage. You have 11 - 7 = 4 health.
On round 3, use your armor to protect you from 4 damage. You have 4 - 0 = 4 health.
On round 4, take 3 damage. You have 4 - 3 = 1 health.
Note that 13 is the minimum health you need to start with to beat the game.
Python Solution
class Solution:
def minimumHealth(self, damage: List[int], armor: int) -> int:
return sum(damage) - min(max(damage), armor) + 1
Complexity
The time complexity is , where is the length of the array . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.