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Egg Drop Minimum Iterations

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Problem

Eli Lilly and Company's automated laboratory equipment may need to identify a failure threshold while minimizing destructive validation tests. Given a building with floors levels and eggs identical test objects, determine the minimum number of drops required in the worst case to identify the highest floor from which an object can be dropped safely.

An object breaks when dropped above the unknown threshold and survives when dropped at or below it. The threshold may be any integer from 0 through floors. Return the minimum number of drops that guarantees identifying the threshold, regardless of where it is.

Formal Specification

Implement egg_drop(eggs, floors), which accepts two positive integers and returns an integer. The result is the smallest number of drops needed in the worst case. If floors is 0, return 0.

Constraints

  • 1 <= eggs <= 100
  • 0 <= floors <= 10^9
  • The threshold is an integer from 0 through floors
  • A broken egg cannot be reused
  • Return the minimum worst-case number of drops

Function Signature

def egg_drop(eggs, floors):
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