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Unformatted text preview: Introduction to Algorithms April 2, 2004 Massachusetts Institute of Technology 6.046J/18.410J Professors Erik Demaine and Shafi Goldwasser Handout 17 Problem Set 6 This problem set is due in recitation on Friday, April 16 . Reading: Chapter 15, Chapter 17, 16.1-16.3, 22.1-22.2, Chapter 23 There are four problems. Each problem is to be done on a separate sheet (or sheets) of paper. Mark the top of each sheet with your name, the course number, the problem number, your recitation section, the date, and the names of any students with whom you collaborated. As on previous assignments, “give an algorithm” entails providing a description, proof, and runtime analysis. Problem 6-1. Danny’s Daemon Suppose there are bins containing a total of balls, where . Initially, of the bins contain one ball and the other bins are empty. Sitting on top of the bins is a daemon who rearranges the balls by a series of moves . Each move, the daemon will select a bin containing balls, and redistribute each ball to a unique bin. In other words, the bin will lose all balls and other bins will each gain exactly one ball. We define the cost of this move to be . The total number of balls in the system remains constant, i.e.balls in the system remains constant, i....
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- Spring '04
- Algorithms, Shortest path problem, Spanning tree