32 sample documents related to CS 344

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  Homework 1

  Rutgers CS 344
  

  Fall 2012 CS 344: #1 Math Fundamentals Farach-Colton Due by 5:00pm, Due: Sept. 13. 1. Prove, using the denitions, that loga x = logb x. loga b Prove that log x x = . y log y 2. Prove by induction on k : (Remember these formulas, they may be used later) (a
   
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  Homework 2

  Rutgers CS 344
  

  Fall 2012 CS 344: #1 Math Fundamentals Farach-Colton Due by 5:00pm, Due: Sept. 20. 1. Prove that log(n!) (n log n). (15 points) 2. Let f (n) = 2n , g (n) = 3n . Is f (n) in O(g (n)? Is g (n) in O(f (n)? Prove your answer. (10 points) 3. Let f (n) = n2 , g
   
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  Homework 3

  Rutgers CS 344
  

  Fall 2012 CS 344: #3 Sorting Farach-Colton Due by 5:00pm, Sept. 27. 1. The merge algorithm presented in class was not in place. Assume you are given an array A[1], ., A[n] where A[1], ., A[k ] is one sorted list and A[k + 1], ., A[n] is another sorted lis
   
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  Homework 4

  Rutgers CS 344
  

  Fall 2012 CS 344: #4 Trees and Whatnot Farach-Colton Due by 5:00pm, Oct. 4. 1. Prove that a forest consisting of k trees with a total of n nodes has n k edges. (20 points) 2. Let G = (V, E, W ) be a weighted graph such that no two dierent edges in E have
   
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  Homework 5

  Rutgers CS 344
  

  Fall 2012 CS 344: #5 More comparison stu Farach-Colton Due by 5:00pm, Oct. 11. 1. The mode of an array is the most frequent element of the array. Give an algorithm to nd the mode of an array. Analyze its complexity. As always, the faster the algorithm, th
   
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  Homework 6

  Rutgers CS 344
  

  Fall 2012 CS 344: #6 Reductions Farach-Colton Due by 5:00pm, Nov. 1. Suppose there is a C+ library on your machine which has the following function: IS (G, k ): Input: Graph G, and a number k . Output: Yes, if G has an Independent Set of size at least k ;
   
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  Homework 7

  Rutgers CS 344
  

  Fall 2012 CS 344: #7 Graphs and Reductions Farach-Colton Due by 5:00pm, Dec. 4. 1. A graph is said to be bipartite if its vertex set can be partitioned into two sets A, B such that every edge in G has one endpoint in A and other endpoint in B . A Hamilton
   
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  Homework 8

  Rutgers CS 344
  

  Fall 2012 CS 344: #8 More Reductions Farach-Colton Due by 4:00pm, Dec. 11. Consider the following decision problems: V C (G, k ): Input: Graph G, and an integer k . Output: Yes, if G has a Vertex Cover of size k ; No, otherwise. A vertex cover is a set of
   
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  Midterm exam

  Rutgers CS 344
  

  CS344. Algorithms and Data Structures MidTerm Exam I (Thursday October 18, 2012. 5.00 PM to 6.20 PM, Total Points: 100) You may consult your single cheat sheet. Any theorem or algorithm presented in class in class can be used. All other theorems or algo
   
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  Practice exam 1

  Rutgers CS 344
  

  Fall 1994 Farach CS 344: (Practice) Exam #1 Books and notebooks may be consulted. Any theorem proven in class or algorithm presented in class can be used. Theorems or algorithms that were mentioned but not presented can only be used if you prove them. 1.
   
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  Practice questions

  Rutgers CS 344
  

  Fall 2012 CS 344: Practice Questions Farach-Colton Due by 5:00pm, on . 1. Suppose I take an array A[1, . . . , n] of integers and create a new array B [1, . . . , n+ 1] as follows: First, B [1, . . . , n] = A[1, . . . , n]. Now, I pick some i without tell
   
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  Approximate

  Rutgers CS 344
  

  An approximate algorithm is a way of dealing with NP-completeness for optimization problem. This technique does not guarantee the best solution. The goal of an approximation algorithm is to come as close as possible to the optimum value in a reasonable am
   
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  Binary Search Tree

  Rutgers CS 344
  

  Binary Search tree is a binary tree in which each internal node x stores an element such that the element stored in the left subtree of x are less than or equal to x and elements stored in the right subtree of x are greater than or equal to x. This is cal
   
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  Divide and Conquer

  Rutgers CS 344
  

  Divide-and-conquer is a top-down technique for designing algorithms that consists of dividing the problem into smaller subproblems hoping that the solutions of the subproblems are easier to find and then composing the partial solutions into the solution o
   
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  Dynamic Programming

  Rutgers CS 344
  

  Dynamic programming is a fancy name for using divide-and-conquer technique with a table. As compared to divide-and-conquer, dynamic programming is more powerful and subtle design technique. Let me repeat , it is not a specific algorithm, but it is a meta-
   
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  Dynamic Table

  Rutgers CS 344
  

  If the allocated space for the table is not enough, we must copy the table into larger size table. Similarly, if large number of members erased from the table, it is good idea to reallocate the table with a smaller size. Using amortized analysis we shall
   
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  Graph Algorithms

  Rutgers CS 344
  

  Graph Theory is an area of mathematics that deals with following types of problems Connection problems Scheduling problems Transportation problems Network analysis Games and Puzzles. The Graph Theory has important applications in Critical path analysis, S
   
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  Greedy Algorithms

  Rutgers CS 344
  

  Greedy algorithms are simple and straightforward. They are shortsighted in their approach in the sense that they take decisions on the basis of information at hand without worrying about the effect these decisions may have in the future. They are easy to
   
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  Hash Tables

  Rutgers CS 344
  

  Direct-address table If the keys are drawn from the reasoning small universe U = cfw_0, 1, . . . , m-1 of keys, a solution is to use a Table T[0, . m-1], indexed by keys. To represent the dynamic set, we use an array, or direct-address table, denoted by T
   
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  Inequalities

  Rutgers CS 344
  

  Inequalities The term inequality is applied to any statement involving one of the symbols <, >, ,. Example of inequalities are: i. ii. iii. iv. x1 x + y + 2z > 16 p2 + q2 1/2 a2 + ab > 1 Fundamental Properties of Inequalities 1. If a b and c is any real n
   
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  Lec2

  Rutgers CS 344
  

  A vector, u, means a list (or n-tuple) of numbers: u = (u1, u2, . . . , un) where ui are called the components of u. If all the ui are zero i.e., ui = 0, then u is called the zero vector. Given vectors u and v are equal i.e., u = v, if they have the same
   
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  Sets

  Rutgers CS 344
  

  A set is a collection of different things (distinguishable objects or distinct objects) represented as a unit. The objects in a set are called its elements or members. If an object x is a member of a set S, we write x S. On the the hand, if x is not a mem
   
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  Sorting

  Rutgers CS 344
  

  The objective of the sorting algorithm is to rearrange the records so that their keys are ordered according to some well-defined ordering rule. Problem: Given an array of n real number A[1. n]. Objective: Sort the elements of A in ascending order of their
   
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  String

  Rutgers CS 344
  

  String matching consists of finding one or more generally, all of the occurrences of a pattern in a text. Finding a certain pattern in a text is a problem arises in text-editing programs and web \"surfing\". Here we study various fundamental text processing
   
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  BFS

  Rutgers CS 344
  

  CE177 Schlag Fall \'04 Handout # 2 Breadth First Search The input is a simple graph. This algorithm traverses each component of the graph, numbering vertices as they are encountered (bfs[u]) and saving for each vertex u the neighbor (if any) from wh
   
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  Graph Algorythms

  Rutgers CS 344
  

  Elementary Graph Algorithms CSE 680 Suggested Reading: Appendix B4, Chapter 22 1 Graphs G(V, E) - V : vertex set; E: edge set. Directed graphs, undirected graphs, weighted graphs. An edge is incident on, incident from, or incident to a vertex.
   
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  344s2001.ps

  Rutgers CS 344
  

  %!PS-Adobe-2.0 %Creator: dvips(k) 5.83 Copyright 1998 Radical Eye Software %Title: 344s2001.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %DocumentFonts: CMBX12 CMR12 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dv
   
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  344binary.ps

  Rutgers CS 344
  

  %!PS-Adobe-2.0 %Creator: dvips 5.528 Copyright 1986, 1994 Radical Eye Software %Title: 344binary.dvi %CreationDate: Mon Sep 24 14:22:03 2001 %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMMI12 CMMI8 CMSY10 CMEX1
   
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  344bfs.ps

  Rutgers CS 344
  

  %!PS-Adobe-2.0 %Creator: dvips 5.528 Copyright 1986, 1994 Radical Eye Software %Title: 344bfs.dvi %CreationDate: Thu Apr 8 15:02:16 1999 %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX10 CMR10 CMMI10 CMSY10 %EndComments %D
   
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  344krusy2y.ps

  Rutgers CS 344
  

  %!PS-Adobe-2.0 %Creator: dvips 5.528 Copyright 1986, 1994 Radical Eye Software %Title: 344krusy2y.dvi %CreationDate: Fri Apr 7 12:26:55 2000 %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMMI12 CMSY10 CMMI8 %EndC
   
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  344mst2001.ps

  Rutgers CS 344
  

  %!PS-Adobe-2.0 %Creator: dvips(k) 5.83 Copyright 1998 Radical Eye Software %Title: 344mst2001.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMMI12 CMSY10 CMR8 %EndComments %DVIPSWebPage: (www.radicaleye.com)
   
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  kmpshrt.ps

  Rutgers CS 344
  

  %!PS-Adobe-2.0 %Creator: dvips 5.528 Copyright 1986, 1994 Radical Eye Software %Title: kmpshrt.dvi %CreationDate: Wed Apr 19 11:04:36 2000 %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMMI12 CMR8 CMSY10 CMMI8 CM