0972MediumArrayGreedy

Least Charge to Get Through the Rounds

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Trains the technique from

LeetCode 2214Minimum Health to Beat Game

This is an original problem, written from a brief that listed the technique, the difficulty, the topics, the function shape and the input bounds — none of that problem's wording, examples, hints or editorials. The link is there so you can map your practice onto the standard set.

Same function shape, different story and different numbers.

A machine runs through rounds in order, and round i drains damage[i] charge.

The machine carries one shield of strength armor, which may be used on at most one round. Used on a round, it absorbs that round's drain up to its own strength, so the drain becomes whatever is left over.

The machine must keep strictly more than zero charge at every moment. Return the least charge it can start with and still get through every round.

Examples

Example 1

Input: damage = [14, 3, 27, 9], armor = 12
Output: 42

The rounds drain 53 in total. The shield is worth most on the round draining 27, where it absorbs all 12 of its strength, leaving 41 to be paid for and one charge to be kept.

Example 2

Input: damage = [1], armor = 5
Output: 1

The shield is stronger than the only round, so it absorbs the whole drain and the machine needs only the one charge it must keep.

Example 3

Input: damage = [0, 0, 0], armor = 10
Output: 1

Nothing drains at all, so the machine needs only the charge it must keep.

Constraints

1 <= damage.length <= 10^5
0 <= damage[i] <= 10^5
0 <= armor <= 10^5

The signature

The editor is preloaded with this. It matches the parent problem's shape, so a solution that works here transfers to a judge unchanged.

Python

def minimum_health(damage: list[int], armor: int) -> int:

Java

public long minimumHealth(int[] damage, int armor)

The intended approach

Time O(n) for n rounds, one pass.Space O(1).

Order never comes into it: the machine gets through exactly when its starting charge is more than the total drain less whatever the shield absorbs, so the only question is which round to use the shield on. The shield absorbs the smaller of its own strength and the round's drain, so it saves the most on the heaviest round, and there is no reason to save it for later. So the answer is the total drain, less the smaller of the shield's strength and the heaviest single drain, plus one for the charge that must remain. One pass finds both the total and the heaviest.

Pythonentry point: minimum_health

def minimum_health(damage, armor):
    total = 0
    heaviest = 0
    for v in damage:
        total += v
        if v > heaviest:
            heaviest = v
    saved = armor if armor < heaviest else heaviest
    return total - saved + 1

The obvious version

Try using the shield on each round in turn, and for each choice walk the rounds working out the drain that lands, keeping the smallest starting charge that gets through. Quadratic in the round count and it makes no argument about which round to shield.

This is not filler. It was written independently of the fast solution and the two were run against thousands of random inputs to confirm they agree — which is how the answer above is known to be right. Read it when the intended approach feels like a rabbit pulled out of a hat.

Python

def bf_minimum_health(damage, armor):
    n = len(damage)
    best = None
    for shielded in range(-1, n):
        total = 0
        for i in range(n):
            hit = damage[i]
            if i == shielded:
                hit -= armor if armor < hit else hit
            total += hit
        need = total + 1
        if best is None or need < best:
            best = need
    return best

How this problem was checked

Reference solution executed against 11 test cases — 11 passed
3 worked examples confirmed by running the code
0 eight-word sequences shared with the parent problem's text
Agrees with an independent brute-force implementation on random inputs
Test set proven to catch deliberately broken solutions
Reviewed by a separate quality pass
Function arity matches the parent problem's

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