design of algorithm and implementation of algorithm in java
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Suppose a container device was designed for the army. The purpose of this container was to be filled with gasoline and dropped from an airplane to resupply the troops. Naturally, the higher the airplane is, the more danger there is that the device will break which turns into a gasoline bomb. On the other hand, the lower the airplane is, the more susceptible it is to enemy fire.
To make things simple, lets make the following assumptions. we will measure the height of the airplane using integer where height n means that the plane is 100n feet off the ground. A container that breaks cannot be used again, but one that survives a fall can be used again. If a test container survives from a certain height, containers will survive from any smaller height. There is a height, above which the planes cannot locate the target zone with sufficient precision to make attempting any drops worthwhile. We will call this the plane limit. Also, the number of containers which are available for testing is limited.
The army needs to know the maximum height from which they can drop these containers without having them break, which could be anywhere from 0 up to the plane limit. We cannot answer this question without knowing the results of a series of tests. What we can do is to help by determining an optimal sequence of drops to make in order to figure out this maximum height. In this project, you will investigate the testing process and the best way to go about it.
Let T(n,k) be the minimum number of tests needed to determine the maximum drop height in the worst case if the plane limit is n ad you have k containers for testing. You are to work on the following tasks (use either Java or Python for tasks 2,3,4):
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