Minimum Health to Beat Game

class Solution {
public:
    long long minimumHealth(vector<int>& damage, int armor) {
        int highestDamage = 0;
        long long sumDamage = 0;
        
        for (int dmg : damage) {
            sumDamage += dmg;
            highestDamage = max(highestDamage, dmg);
        }

        return sumDamage - min(armor, highestDamage) + 1;
    }
};

The provided C++ solution computes the minimum health necessary to beat a game where damage is taken at various points. The function minimumHealth accepts two parameters: damage, a vector of integers representing the damage taken at each encounter, and armor, an integer representing the maximum amount of damage that can be reduced in a single encounter.

Here's how the code accomplishes the task:

1. Initialize two variables: highestDamage to track the most severe single damage encounter, and sumDamage to store the cumulative damage across all encounters.
2. Iterate over the damage vector, updating sumDamage with each encounter's damage and updating highestDamage if a current damage value exceeds the previously found values.
3. Calculate the needed minimum health by reducing the cumulative damage, sumDamage, by the lesser of highestDamage or armor. Add 1 to account for surviving at least with 1 health point after all damage is taken.

The final result is the precise calculation of minimum health required which factors in optimal usage of the available armor against the most significant single damage instance. This method ensures efficiency by traversing the damage list only once and performing minimal comparisons and calculations, thus operating optimally for scenarios with large lists of damage instances.

class Solution {
    public long calculateMinimumHealth(int[] hits, int shield) {
        int peakDamage = 0;
        long sumDamage = 0;

        for (int hit : hits) {
            sumDamage += hit;
            peakDamage = Math.max(peakDamage, hit);
        }

        return sumDamage - Math.min(shield, peakDamage) + 1;
    }
}

In this solution for the "Minimum Health to Beat Game" problem using Java, the goal is to determine the minimum health required to sustain through a series of damaging hits even when a shield is utilized for maximum single-hit damage mitigation.

Assume you have an array named hits which contains integers denoting the amount of damage dealt by each consecutive hit in a game. Additionally, an integer shield signifies the maximum amount of damage a shield can absorb from a single hit.

• First, initialize two variables:

  • peakDamage to store the maximum damage dealt in a single hit.
  • sumDamage to accumulate the total damage from all hits.

• Iterate through the hits array:

  • Increment sumDamage with the damage of the current hit.
  • Update peakDamage to reflect the highest damage dealt in a single hit using the Math.max function.

• After calculating the sum of damages and identifying the peak damage, compute the minimum health required to survive all hits:

  • Subtract the smallest value between the shield's capacity and the peak damage from the total sum of damages. This represents utilizing the shield optimally against the most damaging single hit to minimize overall health loss.
  • Add 1 to the result to ensure that the player survives with at least 1 health point.

Given this implementation, return the computed sumDamage adjusted for optimal shield usage plus one, to determine the minimum health necessary to beat the game. This approach efficiently aggregates total potential damage and applies the most effective mitigation using the available shield against the most extreme single hit, providing a clear understanding of the minimum threshold of health required.