egg_drop_with_2_eggs_and_n_floors.py

'''
You are given two identical eggs and you have access to a building with n floors labeled from 1 to n.

You know that there exists a floor f where 0 <= f <= n such that any egg dropped at a floor higher than f will break, and any egg dropped at or below floor f will not break.

In each move, you may take an unbroken egg and drop it from any floor x (where 1 <= x <= n). If the egg breaks, you can no longer use it. However, if the egg does not break, you may reuse it in future moves.

Return the minimum number of moves that you need to determine with certainty what the value of f is.
'''

class Solution:
    def twoEggDrop(self, n: int) -> int:
        count = 1
        i = 2
        while(n-count > 0):
            count+=i
            i+=1
        return i-1
      
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class Solution:
    def twoEggDrop(self, n: int) -> int:
        # 1. set up an interval as 1
        interval = 1
        
        # 2. count down from n until it's <= 0, reducing by the interval, and increasing the interval each time
        while n > 0:
            n -= interval
            interval += 1
        
        # 3. return interval - 1
        return interval - 1
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