# Minimum Health to Beat Game

Published: Sep 9, 2022

Medium Arrays Greedy

## Introduction

The point here would be to understand the problem correctly. If we could, this is not a difficult problem. We can use the armor at most once, so this goes to the max value in the array.

## Problem Description

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. You are also given an integer `armor`. You may use your armor ability at most once during the game on any level which will protect you from at most armor damage.

You must complete the levels in order and your health must be greater than 0 at all times to beat the game.

Return the minimum health you need to start with to beat the game.

Constraints:

• `n == damage.length`
• `1 <= n <= 10**5`
• `0 <= damage[i] <= 10**5`
• `0 <= armor <= 10**5`

https://leetcode.com/problems/minimum-health-to-beat-game/

## Examples

``````Example 1:
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.
``````
``````Example 2:
Input: damage = [2,5,3,4], armor = 7
Output: 10
Explanation: One optimal way to beat the game starting at 10 health is:
On round 1, take 2 damage. You have 10 - 2 = 8 health.
On round 2, use your armor to protect you from 5 damage. You have 8 - 0 = 8 health.
On round 3, take 3 damage. You have 8 - 3 = 5 health.
On round 4, take 4 damage. You have 5 - 4 = 1 health.
Note that 10 is the minimum health you need to start with to beat the game.
``````
``````Example 3:
Input: damage = [3,3,3], armor = 0
Output: 10
Explanation: One optimal way to beat the game starting at 10 health is:
On round 1, take 3 damage. You have 10 - 3 = 7 health.
On round 2, take 3 damage. You have 7 - 3 = 4 health.
On round 3, take 3 damage. You have 4 - 3 = 1 health.
Note that you did not use your armor ability.
``````

## Analysis

In any case, at least 1 should be retained. Also, the armor value reduction goes to the max value. So, start from taking a sum of all values, plus one for minimum level, minus max value or armor. This is the answer.

## Solution

``````class MinimumHealthToBeatGame:
def minimumHealth(self, damage: List[int], armor: int) -> int:
return sum(damage) + 1 - min(max(damage), armor)
``````

## Complexities

• Time: `O(n)`
• Space: `O(1)`