Quiz2 - Introduction to Algorithms Massachusetts Institute of Technology Professors Piotr Indyk and Charles E Leiserson December 1 2004

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Problem 1. A Dynamic Set A dynamic set Q contains items, where each item x has an associated key key [ x ] . The dynamic set Q supports the following operations: I NSERT ( x, Q ) : Insert item x into Q . x E XTRACT -O LDEST ( Q ) : Remove and return the oldest item x Q . (The oldest item is the one inserted least recently.) x F IND -M AX ( Q ) : Return (but do not remove) the item x Q for which key [ x ] is maximal. Design a data structure for Q that can perform any sequence of n operations efficiently. Problem 2. Great Minds Need Coffee It is a beautiful autumn morning, and Professor Indyk has decided to walk from his apartment to MIT where he will give a lecture for 6.046. To prepare for this trip, the professor has gone online and downloaded a map of the n roads and m intersections in the Boston area. For each road e connecting two intersections, the map lists the length w [ e ] of the road in meters. (Recall that in the Boston area, an arbitrarily large number of roads can meet at a single intersection, e.g., Davis Square.) Like many great theorists, Professor Indyk cannot walk more than 1000 meters without sitting down and assuaging his caffeine addiction. (This is especially true before 9:30 A.M.) Fortunately, the Moonbucks Coffee Company has recently opened a large number of coffee shops throughout the Boston area. Let B = { b1, b2, . . . , bk } be the set of k intersections hosting Moonbucks coffee shops. Thus, Professor Indyk is looking for a route from his apartment (located at one given intersection) to the Stata Center (located at another given intersection) in which he never travels more than 1000
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This note was uploaded on 01/20/2012 for the course CS 6.006 taught by Professor Erikdemaine during the Fall '08 term at MIT.

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Quiz2 - Introduction to Algorithms Massachusetts Institute of Technology Professors Piotr Indyk and Charles E Leiserson December 1 2004

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