You want to stress test glass jars. You have a ladder with n rungs, and want...
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You want to stress test glass jars. You have a ladder with n rungs, and want to find the highest rung from which you can drop a jar and not have it break. We call this the highest safe rung. Your goal is to find the highest safe rung with the fewest number of drops possible. However, you have a limited supply of jars, and need to find the highest safe rung before breaking all of them. For example, with one jar you could drop it from the first rung, then the second, then the third, and so on, until it breaks, and you are guaranteed to find the highest safe rung with at most n drops. With any other strategy, you would risk breaking the jar before finding the highest safe rung. Now, suppose you have two (identical) jars, so you can break one and still find the highest safe rung. Describe a strategy for finding the highest safe rung that requires you to drop a jar at most f(n) times, for some function f(n) that grows slower than linearly. (In other words, it should be the case that limn f(n)/n = 0.) You want to stress test glass jars. You have a ladder with n rungs, and want to find the highest rung from which you can drop a jar and not have it break. We call this the highest safe rung. Your goal is to find the highest safe rung with the fewest number of drops possible. However, you have a limited supply of jars, and need to find the highest safe rung before breaking all of them. For example, with one jar you could drop it from the first rung, then the second, then the third, and so on, until it breaks, and you are guaranteed to find the highest safe rung with at most n drops. With any other strategy, you would risk breaking the jar before finding the highest safe rung. Now, suppose you have two (identical) jars, so you can break one and still find the highest safe rung. Describe a strategy for finding the highest safe rung that requires you to drop a jar at most f(n) times, for some function f(n) that grows slower than linearly. (In other words, it should be the case that limn f(n)/n = 0.)
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Heres a strategy for finding the highest safe rung with two jars that uses fewer than n drops Initia... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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