There are buckets buckets of liquid, where exactly one of the buckets is poisonous. To figure out which one is poisonous, you feed some number of (poor) pigs the liquid to see whether they will die or not. Unfortunately, you only have minutesToTest minutes to determine which bucket is poisonous.
You can feed the pigs according to these steps:
\n\nminutesToDie minutes. You may not feed any other pigs during this time.minutesToDie minutes have passed, any pigs that have been fed the poisonous bucket will die, and all others will survive.Given buckets, minutesToDie, and minutesToTest, return the minimum number of pigs needed to figure out which bucket is poisonous within the allotted time.
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Example 1:
\n\n\nInput: buckets = 4, minutesToDie = 15, minutesToTest = 15\nOutput: 2\nExplanation: We can determine the poisonous bucket as follows:\nAt time 0, feed the first pig buckets 1 and 2, and feed the second pig buckets 2 and 3.\nAt time 15, there are 4 possible outcomes:\n- If only the first pig dies, then bucket 1 must be poisonous.\n- If only the second pig dies, then bucket 3 must be poisonous.\n- If both pigs die, then bucket 2 must be poisonous.\n- If neither pig dies, then bucket 4 must be poisonous.\n\n\n
Example 2:
\n\n\nInput: buckets = 4, minutesToDie = 15, minutesToTest = 30\nOutput: 2\nExplanation: We can determine the poisonous bucket as follows:\nAt time 0, feed the first pig bucket 1, and feed the second pig bucket 2.\nAt time 15, there are 2 possible outcomes:\n- If either pig dies, then the poisonous bucket is the one it was fed.\n- If neither pig dies, then feed the first pig bucket 3, and feed the second pig bucket 4.\nAt time 30, one of the two pigs must die, and the poisonous bucket is the one it was fed.\n\n\n
\n
Constraints:
\n\n1 <= buckets <= 10001 <= minutesToDie <= minutesToTest <= 100x such that (T+1)^x >= N"
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