458.PoorPigs.py

"""
    There are 1000 buckets, one and only one of them is poisonous, while the 
    rest are filled with water. They all look identical. If a pig drinks the 
    poison it will die within 15 minutes. What is the minimum amount of pigs 
    you need to figure out which bucket is poisonous within one hour?

    Answer this question, and write an algorithm for the general case.

    General case:
    If there are n buckets and a pig drinking poison will die within m minutes, 
    how many pigs (x) you need to figure out the poisonous bucket within 
    p minutes? There is exactly one bucket with poison.

    Note:
        1. A pig can be allowed to drink simultaneously on as many buckets as 
           one would like, and the feeding takes no time.
        2. After a pig has instantly finished drinking buckets, there has to 
           be a cool down time of m minutes. During this time, only observation 
           is allowed and no feedings at all.
        3. Any given bucket can be sampled an infinite number of times 
           (by an unlimited number of pigs).
"""
#Difficulty: Hard
#17 / 17 test cases passed.
#Runtime: 20 ms
#Memory Usage: 14 MB

#Runtime: 20 ms, faster than 95.71% of Python3 online submissions for Poor Pigs.
#Memory Usage: 14 MB, less than 60.00% of Python3 online submissions for Poor Pigs.

class Solution:
    def poorPigs(self, buckets: int, minutesToDie: int, minutesToTest: int) -> int:
        pigs = 0
        while (minutesToTest//minutesToDie + 1)**pigs < buckets:
            pigs += 1
        return pigs