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Unformatted text preview: CMPT 405/705 Design and Analysis of Algorithms Exercises on Dynamic Programming. Due: Thursday, October 15th (at the beginning of the class) Reminder: the work you submit must be your own. Any collaboration and consulting outside resourses must be explicitely mentioned on your submission. 1. The residents of the underground city of Zion defend themselves through a combination of kung fu, heavy artillery, and efficient algorithms. Recently they have become interested in automated methods that can help fend off attacks by swarms of robots. Here is what one of these robot attacks looks like. A swarm of robots arrives over the course of n seconds; in the i-th second, x i robots arrive. Based on remote sensing data, you know this sequence x 1 , x 2 , . . . , x n in advance. You have at your disposal an electromagnetic pulse (EMP), which can destroy some of the robots as they arrive; the EMPs power depends on how long it has been allowed to charge up. To make it precise, there is a function f ( ) so that if j seconds have passed since the EMP was last used, then it is capable of destroying up to f ( j ) robots.) robots....
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