Crafter

This is an interactive problem.

Note: This problem statement, theme, and framing have been substantially paraphrased, and the problems have been merged and extended.

Implement the class CraftingEngine, which simulates a crafting system on the MMORPG server Wynncraft. In this game, players craft weapons by imbuing crafting materials into a base weapon. Each material contributes some damage to the weapon, but at the cost of consuming some of the weapon's durability.

You will receive a stream of crafting materials, each described by a durability cost and a damage contribution. Your engine must support querying the maximum damage achievable given a durability budget, as well as tracking potentially unstable crafting sequences.

A material is considered poor if its durability cost exceeds its damage contribution. A crafting sequence becomes unstable when it contains threshold or more consecutive poor materials — at which point the weapon must be replaced. Your engine should be able to count how many such replacements have occurred across all materials added so far.

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Methods

CraftingEngine(base_durability)

• base_durability is a positive integer representing the weapon's starting durability before any materials are applied.

add(cost, damage)

• Adds a new crafting material with durability cost and damage contribution to the engine's internal list.
• cost and damage are both non-negative integers.

countReplacements(threshold)

• Returns the number of weapon replacements that would occur among all materials added so far.
• A material is poor if its cost strictly exceeds its damage.
• A weapon must be replaced each time a run of at least threshold consecutive poor materials is encountered. After a replacement, the consecutive count resets — subsequent poor materials begin a new count.
• threshold is a positive integer.

maximumDamage(min_durability)

• Returns the maximum total damage achievable by selecting any subset of materials added so far, such that the weapon's remaining durability is at least min_durability.
• The weapon starts with base_durability (provided at construction). Each selected material reduces the durability by its cost and increases the total damage by its damage.
• Poor materials are not excluded from selection, and a subset that would be considered unstable is still valid — the only constraint is the durability budget.
• min_durability is a non-negative integer.
• If no valid selection exists, return 0.

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Notes

• Query operations do not need to be performed in constant time.
• You do not need to implement any input/output parsing.

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Example

Suppose base_durability = 10, and the following calls are made:

add(3, 2)   # material 0: cost=3, damage=2  → poor (3 > 2)
add(1, 5)   # material 1: cost=1, damage=5  → not poor
add(4, 1)   # material 2: cost=4, damage=1  → poor
add(2, 1)   # material 3: cost=2, damage=1  → poor
add(1, 3)   # material 4: cost=1, damage=3  → not poor

countReplacements(2) → 1

The poor materials are at indices 0, 2, 3. Index 0 is isolated (run of length 1 < threshold, no replacement). Indices 2–3 form a consecutive run of length 2 ≥ threshold, triggering 1 replacement. Total: 1.

maximumDamage(5) → 8

We need the remaining durability ≥ 5, meaning the total cost of selected materials must be ≤ 10 − 5 = 5. We may pick any subset. Some candidates:

Selection	Total Cost	Total Damage	Valid?
{1}	1	5	✓
{4}	1	3	✓
{1, 4}	2	8	✓
{1, 3}	3	6	✓
{0, 1}	4	7	✓
{1, 3, 4}	4	9	✓
{0, 1, 4}	5	10	✓
{1, 2, 4}	6	9	✗
{0, 1, 3, 4}	7	11	✗

The maximum valid damage is 10 from selection {0, 1, 4} (materials 0, 1, and 4), with total cost 3+1+1=5 ≤ 5. → returns 10.