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71 lines
2.5 KiB
Python
71 lines
2.5 KiB
Python
"""
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Calculate the minimum number of attempts needed in the worst case to find the
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critical floor from which eggs start breaking when dropped.
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"""
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# The Egg Dropping Problem is a classic dynamic programming problem.
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# - You are given `k` eggs and a building with `n` floors. Your goal is to determine
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# the minimum number of attempts required to find the highest floor `F` from which
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# if an egg is dropped, it will break. If an egg breaks from floor `F`, it will
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# also break from any floor above `F`. The challenge is to minimize the worst-case
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# number of attempts.
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def egg_dropping(eggs: int, floors: int) -> int:
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"""
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Calculate the minimum number of attempts needed in the worst case for `eggs`
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and `floors` using dynamic programming.
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>>> egg_dropping(1, 5)
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5
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>>> egg_dropping(2, 6)
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3
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>>> egg_dropping(2, 10)
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4
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"""
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# Base case: No floors require 0 trials, one floor requires 1 trial.
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if floors in (0, 1):
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return floors
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if eggs == 1:
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return floors
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# Create a DP table to store the results of subproblems.
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dp = [[0 for _ in range(floors + 1)] for _ in range(eggs + 1)]
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# Fill the base cases for one egg (i.e., we need `i` attempts for `i` floors).
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for i in range(1, floors + 1):
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dp[1][i] = i
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# Compute the minimum number of trials in the worst case for each combination.
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for e in range(2, eggs + 1):
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for f in range(1, floors + 1):
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dp[e][f] = 10**9 # Initialize to infinity.
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for x in range(1, f + 1):
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res = 1 + max(dp[e - 1][x - 1], dp[e][f - x])
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dp[e][f] = min(dp[e][f], res)
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return dp[eggs][floors]
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if __name__ == "__main__":
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print("\n********* Egg Dropping Problem Using Dynamic Programming ************\n")
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print("\n*** Enter -1 at any time to quit ***")
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print("\nEnter the number of eggs and floors separated by a space: ", end="")
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try:
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while True:
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input_data = input().strip()
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if input_data == "-1":
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print("\n********* Goodbye!! ************")
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break
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else:
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eggs, floors = map(int, input_data.split())
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print(
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f"The minimum number of attempts required with {eggs} eggs and "
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f"{floors} floors is:"
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)
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print(egg_dropping(eggs, floors))
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print("Try another combination of eggs and floors: ", end="")
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except (NameError, ValueError):
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print("\n********* Invalid input, goodbye! ************\n")
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