introduction to algorithms third edition

... program may need to scale a set of (x, y) data to Þt onto a rectangular display To so, the program must Þrst Þnd the minimum and maximum of each coordinate A simple algorithm to Þnd the minimum ... overview [The treatment in the second edition differs from that of the Þrst edition We use a different partitioning method—known as “Lomuto partitioning”—in the second edition, rather than the “Hoare ... “Hoare partitioning” used in the Þrst edition Using Lomuto partitioning helps simplify the analysis, which uses indicator random variables in the second edition.] Quicksort • • • • Worst-case

Ngày tải lên: 13/08/2014, 18:20

... we increment top[S], set S[top[S]] ← k, set S [top[S]] ← x, and set T [k] ← top[S] D ELETE: To delete object x with key k, assuming that this object is in the dictionary, we need to break the ... pointer in the slot that pointed to j to point to the new slot Then insert the new element in the now-empty slot as usual To update the pointer to j , it is necessary to Þnd it by searching the chain ... the total to exceed 1/2, is the weighted median Notice that the total weight of all elements smaller than xk is less than 1/2, because xk was the Þrst element that caused the total weight to exceed

Ngày tải lên: 13/08/2014, 18:20

... would have to be copied when a new node is inserted To see why, observe that the children of the root would change to point to the new root, then their children would change to point to them, and ... O(h) time, analogous to the changes we made for persistence in insertion But to so without using parent pointers we need to walk down the tree to the node to be deleted, to build up a stack of ... keys are not distinct, because in order to Þnd the path to the node to delete—a particular node with a given key—we have to make some changes to how we store things in the tree, so that duplicate

Ngày tải lên: 13/08/2014, 18:20

... optimality of our way to (i, j ) We also have overlapping subproblems We need the most proÞtable way to (i, j ) to Þnd the most proÞtable way to (i + 1, j − 1), to (i + 1, j ), and to (i + 1, j + 1) ... + | pk p j |} We need to compute b[n, n] In an optimal bitonic tour, one of the points adjacent to pn must be pn−1 , and so we have b[n, n] = b[n − 1, n] + | pn−1 pn | To reconstruct the points ... to (i + 1, j ), and to (i + 1, j + 1) So we’ll need to directly refer to the most proÞtable way to (i, j ) up to three times, and if we were to implement this algorithm recursively, we’d be solving

Ngày tải lên: 13/08/2014, 18:20

... Greedy Algorithms 16-3 Solution to Si j is (solution to Sik ) ∪ {ak } ∪ (solution to Skj ) Since ak is in neither subproblem, and the subproblems are disjoint, |solution to S| = |solution to Sik ... go to get to or 1/4, starting from 1/2, rate of increase of differs • • For α to go from 1/2 to 1, num increases from size /2 to size, for a total increase of size /2 increases from to size Thus, ... called only with j = n + 1, however To avoid this problem altogether, the procedure was changed to the following in the third printing.] R EC -ACTIVITY-S ELECTOR (s, f, i, n) m ←i +1 £ Find Þrst

Ngày tải lên: 13/08/2014, 18:20

... edge it visits to the cycle C, which is then added to the Euler tour T , when we return from a call to V ISIT (u), all edges entering or leaving vertex u have been added to the tour When we advance ... B to the end of A, instead splice B into A right after the Þrst element of A We have to traverse B to update representative pointers anyway, so we can just make the last element of B point to ... add the directed edge (x, y) to E Time: O(E) Thus, the total time is (V + E) Solutions for Chapter 22: Elementary Graph Algorithms 22-21 Solution to Exercise 22.5-7 To determine if G = (V, E)

Ngày tải lên: 13/08/2014, 18:20

... component, so all other edges will be rejected [We could add a test to the main loop of K RUSKAL to stop once |V | − edges have been added to A.] Get the shaded edges shown in the Þgure Suppose we had ... Find a longest path from s to t in G (Section 24.2 discusses how to Þnd a longest path in a dag.) This path corresponds to a longest sequence of nesting boxes The time to Þnd a longest path is ... Solution to Exercise 23.2-4 We know that Kruskal’s algorithm takes O(V ) time for initialization, O(E lg E) time to sort the edges, and O(E α(V )) time for the disjoint-set operations, for a total

Ngày tải lên: 13/08/2014, 18:20

... bitonic 0 0 1 clean bitonic bitonic 0 1 1 0 1 1 bitonic Depth = Lemma If the input to a half-cleaner is a bitonic 0-1 sequence, then for the output: • • • both the top and bottom half are bitonic, ... A bitonic sorting network Constructing a sorting network Step 1: Construct a “bitonic sorter.” It sorts any bitonic sequence A sequence is bitonic if it monotonically increases, then monotonically ... for Chapter 27: Sorting Networks 27-5 Bitonic sorter: n/2 bitonic n bitonic sorter half-cleaner n/2 bitonic sorter n/2 sorted ≤ n/2 sorted sorted bitonic bitonic 0 0 1 0 1 0 0 0 1 0 0 1 sorted Depth:

Ngày tải lên: 13/08/2014, 18:20

... unique simple path from r to x an ancestor of x.Ify is an ancestor of x,thenx is a descendant of y. (Every node is both an ancestor and a descendant of itself.) If y is an ancestor of x and x ¤ y,theny ... vertices of the top graph are mapped to the vertices of the bottom graph by f.1/ D u; f .2/ D ; f .3/ D w; f.4/ D x;f .5/ D y;f .6/ D ´. (b) Two graphs that are not isomorphic, since the top graph ... vertex 2 is adjacent to vertex 1, since the edge .1; 2/ belongs to both graphs. Vertex 1 is not adjacent to vertex 2 in Figure B.2(a), since the edge .2; 1/ does not belong to the graph. The degree

Ngày tải lên: 13/08/2014, 18:20

... of state highways and small towns into one agency is generally called the model a decentralized c centralized b combined d Total ANS: C PTS: REF: p 54 OBJ: To describe the size, scope, ... Alcohol, Tobacco, Firearms and Explosives c Immigration and Naturalization Service d Customs Service ANS: A PTS: REF: p 59 OBJ: To acquaint you with the number and type of jobs available to you ... States 37 Between 1997 and 2006, federal prosecutors rejected nearly two-thirds of the cases brought to them by the FBI and other investigators, more than twice the rejection rate for

Ngày tải lên: 08/09/2017, 09:15

... researcher need to to insure that the research sample is random? a Ask as many people as possible b Ask more than one group of people; try to get all the groups in c Set up the experiment to include ... subject to interviewer bias ANS: B MSC: Applied REF: The Research Process OBJ: 2.2 11 A major drawback of open-ended interviews is that: a some interviews may not cover topics important to the ... of the researcher to subjects c a frequent inability to get at the subtleties and nuances of social interaction d differences between generations in experience e Selecting what to report as significant

Ngày tải lên: 19/10/2017, 16:09

... being referred to by this term is shaped like a string or rope Answer: F Sounds which are more frequently used in a language, acquired earlier, and are simpler to articulate, are said to be unmarked ... feature Answer: F 23 Mandarin is an intonational language and English is a tonal language Answer: F Copyright © 2012 Pearson Education, Inc All rights reserved 24 Tone is a specific pitch or a specific ... your computer see: “Eureka! The Easy Way to Type Foreign Alphabets and Accented Letters in MS Word” and “Adding IPA! The Easy Way to Type Phonetic Symbols, Too, in MS Word” Word Lists for Phonetics

Ngày tải lên: 19/10/2017, 16:16

... development MSC: TYPE: Easy 46 Why does the blastocyst implant on the uterine wall? a To maintain warmth c To create the neural tube b To form the zygote d To provide nourishment ANS: D PTS: DIF: Bloom's: ... ready to be born TYPE: Easy 74 What is the primary event during transition? a Contractions begin b The cervix begins to dilate c The baby’s head crowns d The baby’s head begins to move into the ... Why is an ultrasound used in high risk pregnancies? a To check for gender c To check for height and weight b To check for abnormalities d To check for age ANS: REF: OBJ: MSC: B PTS: DIF: Bloom's:

Ngày tải lên: 19/10/2017, 16:28

... will have to take medication for many months, but it is possible to cure his disease d The course of Alzheimer’s is difficult to describe ANS: A PTS: DIF: Bloom's: Understand REF: 2.1 Introduction, ... synapse and: a fit into specially designed axons b cause the second neuron to open its chemical locks c cause the process known as reuptake d fit into specially designed receptors located on the ... blow to the head, Hector underwent a dramatic personality change A well-organized, extroverted person before the accident, he no longer could plan, or adjust to new social situations Hector would

Ngày tải lên: 19/10/2017, 16:29

... instructor’s manual to accompany Introduction to Algorithms, Second Edition, by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. It is intended for use in a course on algorithms. ... and analyzing algorithms. • Examine two algorithms for sorting: insertion sort and merge sort. • See how to describe algorithms in pseudocode. • Begin using asymptotic notation to express running-time ... invariants is like mathematical induction: Instructor’s Manual by Thomas H. Cormen Clara Lee Erica Lin to Accompany Introduction to Algorithms Second Edition by Thomas H. Cormen Charles E. Leiserson Ronald...

Ngày tải lên: 13/08/2014, 18:20

... hired. • Cost to interview is c i per candidate (interview fee paid to agency). • Cost to hire is c h per candidate (includes cost to Þre current ofÞce assistant + hiring fee paid to agency). • Assume ... of the tree add up to n, the solution to the recurrence is at least n log 3 n = (n lg n). Solution to Exercise 4.2-5 T (n) = T (αn) + T ((1 − α)n) +n We saw the solution to the recurrence T ... for Chapter 5: Probabilistic Analysis and Randomized Algorithms 5-13 Although these probabilities add to 1, none are equal to 1/6. Solution to Exercise 5.3-4 PERMUTE-BY-CYCLIC chooses offset as...

Ngày tải lên: 13/08/2014, 18:20

... Wireless Toolkit includes a document called “J2ME Wireless Toolkit Basic Customization Guide.” This guide describes how to add support for any obfuscator to the toolkit. Obfuscators tend to be ... adapter code to use other obfuscators. If you’re using the 2.2 version of the toolkit, you just need to download ProGuard and copy the proguard.jar file into the toolkit’s bin directory. Then ... Emulator Controls The J2ME Wireless Toolkit emulator appears as a generic mobile phone, as shown in Figure 2-2. Figure 2-2. Buttons on the J2ME Wireless Toolkit emulator SUN’s J2ME Wireless Toolkit...

Ngày tải lên: 17/02/2014, 23:20

... of tobacco smoke to cure hysteria. These examples illustrate the degree to which our species will go to introduce drugs into the body. In this regard, nicotine has probably been delivered into ... addition to providing drugs, plants have also been recently utilized for ecolo- gical purposes via the process of phytoremediation. Phytoremediation refers to the ability of some plants to remove toxic ... pharmacoeconomics. 9 Extracts from which of the following were believed to confer the gift of flight? a mistletoe b tobacco c tomatoes d thorn apple e cannabis. 10 Which of the following produces a...

Ngày tải lên: 06/03/2014, 14:20

... divide-and-conquer algorithms in which a ≠ b.) If we take D(n) time to divide the problem into subproblems and C(n) time to combine the solutions to the subproblems into the solution to the original ... solution.) Exercises 4.3-1 Use the master method to give tight asymptotic bounds for the following recurrences. Introduction to Algorithms, Second Edition Thomas H. Cormen Charles E. Leiserson ... policy not to supply references for problems and exercises, to remove the temptation for students to look up a solution rather than to find it themselves. Changes for the second edition What...

Ngày tải lên: 31/03/2014, 15:58