Asked in: Amazon
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All Testcases Passed ✔
Solution
def helper(n):
if n<=0:
return 0
return n*helper(n-2)
// ... rest of solution available after purchaseExplanation
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To approach the problem of determining the minimum starting health a player needs to pass all game rounds, begin by understanding the rules and constraints carefully. The player must pass through n rounds, and in each round, they lose a certain amount of health specified by an array called power. The player is allowed to use a special defense mechanism, called armor, exactly once during the game, in any one round. This armor reduces the damage taken in that round by up to its value — specifically, by min(armor, power[i]) for the chosen round i.
The most critical constraint is that the player’s health must remain strictly greater than zero at all times. That means after each round, the player's health must be more than zero. If at any point the health becomes zero or negative, the player loses. Your goal is to compute the smallest possible starting health such that the player can successfully complete all the rounds under these conditions.
To begin solving this, the core idea is to simulate the total damage a player would take if they went through all the rounds without any armor, and then subtract the maximum benefit they could get by using the armor in the most effective way. This requires evaluating the damage across all rounds and determining which round would benefit the most from armor usage.
First, think about what happens if armor is not used at all. The total damage the player would take is simply the sum of all values in the power array. However, since the player can use armor exactly once, the actual total damage can be reduced by the most the armor can help in any single round. So you need to figure out which round, when armor is applied, reduces the damage by the greatest amount. This is determined by min(armor, power[i]) for each round. The round that yields the highest such reduction is the optimal round to use the armor.
Once you identify this optimal armor usage, the total effective damage the player will take becomes the total sum of the power array minus this maximum reduction. Since the player’s health must remain above zero at all times, and they can’t end with zero health, the minimum starting health is the effective total damage plus 1. The extra 1 ensures that after all rounds are complete, the player still has more than zero health left.
Let’s walk through the logic step-by-step:
1. Initialize a variable to store the total damage, which is the sum of all elements in the power array.
2. For each round, calculate the potential damage reduction if armor were applied to that round, using min(armor, power[i]).
3. Keep track of the maximum reduction possible among all rounds.
4. Subtract this maximum reduction from the total damage to get the effective damage the player will experience when armor is used optimally.
5. Add 1 to this effective damage to ensure that health remains above zero at the end of the last round.
This logic ensures that the starting health is minimized while guaranteeing survival through all rounds.
An important part of your thought process should involve edge cases. For example, what happens when the armor value is zero? In that case, the player gets no benefit from using armor, so the total damage is simply the sum of the power array, and you must start with health equal to that sum plus 1. Similarly, if the armor value is very large compared to all power values, its effect is capped by the largest power[i] value, since the armor can’t block more damage than is dealt in any single round.
Another consideration is that since you can only use armor once, you must choose carefully. Using it too early on a small damage round could result in higher net damage later when bigger rounds occur. This is why the strategy must be to always find the single round where using armor yields the most benefit and subtract that from the total.
This approach has the advantage of being simple, efficient, and easy to verify since it processes each round only once and finds the maximum damage reduction in a straightforward loop. By focusing on minimizing the total damage the player actually experiences, while adhering to the strict “health must stay greater than zero” rule, this strategy guarantees the correct minimum starting health needed to survive all rounds successfully.
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