Maximum Points After Enemy Battles

Maximum Points After Enemy Battles

1. What is this problem about?

The Maximum Points After Enemy Battles interview question is a strategic greedy problem that asks you to manage a resource (current energy) to gain points. You are given an array of enemy energies and an initial energy amount. You can perform two types of actions:

1. If you have at least as much energy as enemy i's energy, you can "battle" them: decrease your energy by enemies[i] and gain 1 point. You can do this to an enemy you haven't "marked" yet.
2. If you have at least 1 point, you can "absorb" an enemy: increase your energy by enemies[i] and mark the enemy as defeated. You don't gain points from this, but you can only do it once per enemy.

The goal is to find the maximum points you can achieve.

2. Why is this asked in interviews?

This Maximum Points After Enemy Battles coding problem is a great test of greedy logic and observation. Companies like Rubrik use it to see if a candidate can find the most efficient way to use resources. It's not about complex data structures but about finding the "optimal move" at each step. It tests if you can recognize that to maximize points, you should always battle the weakest enemy and absorb the strongest enemies to get the most energy back.

3. Algorithmic pattern used

The Array, Greedy interview pattern is the heart of this problem. The optimal strategy is:

1. Find the enemy with the minimum energy. If your initial energy is less than this minimum, you can't even get your first point, so you get 0 points.
2. Once you have at least 1 point (obtained by battling the weakest enemy or having enough starting energy), you should absorb all other enemies to maximize your energy.
3. Finally, use all that accumulated energy to "battle" the weakest enemy as many times as possible to get the maximum points.

4. Example explanation

Initial energy: 10. Enemies: [5, 10, 15, 20].

1. Weakest enemy is 5.
2. Battle 5: Energy 10 - 5 = 5. Points = 1.
3. Now we have a point, so we can absorb the others.
4. Absorb 10, 15, 20: Energy = 5 + 10 + 15 + 20 = 50.
5. Use this energy to battle the weakest (5) repeatedly: Points = 1 + floor(50 / 5) = 1 + 10 = 11. Max points: 11.

Note: You can't absorb the 5 if you used it to get your first point unless you have another enemy to start with. But actually, the rule says you can battle an unmarked enemy. If you battle the weakest, you can still use others to gain energy.

5. Common mistakes candidates make

In the Maximum Points After Enemy Battles coding problem, a common error is trying to simulate the process step-by-step with a complex loop, which is unnecessary. Some might try to use a heap to always pick the "best" enemy, but the greedy observation simplifies it much more. Another mistake is forgetting the requirement of having at least 1 point before you can absorb energy. If you can't defeat the smallest enemy with your starting energy, you can never gain any points or absorb any energy.

6. Interview preparation tip

For greedy problems, always look for the "extremes." What is the cheapest way to get what I want? What is the most expensive resource I can trade? In this case, the cheapest point comes from the weakest enemy, and the most energy comes from the strongest enemies. Practice identifying these "bottleneck" conditions where a single observation can turn a complex simulation into a simple mathematical formula.