CS 344
Rutgers - CS 344
  • 2 Pages BFS
    BFS

    School: Rutgers

    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

  • 3 Pages String
    String

    School: Rutgers

    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

  • 1 Page Homework 6
    Homework 6

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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 ;

  • 1 Page Homework 7
    Homework 7

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 1 Page Homework 8
    Homework 8

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 2 Pages Midterm exam
    Midterm Exam

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 1 Page Practice exam 1
    Practice Exam 1

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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.

  • 1 Page Practice questions
    Practice Questions

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 1 Page Homework 1
    Homework 1

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 2 Pages Homework 2
    Homework 2

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 1 Page Homework 3
    Homework 3

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 1 Page Homework 4
    Homework 4

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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

  • 5 Pages Sorting
    Sorting

    School: Rutgers

    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

  • 7 Pages Sets
    Sets

    School: Rutgers

    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

  • 13 Pages Graph Algorythms
    Graph Algorythms

    School: Rutgers

    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.

  • 1 Page Approximate
    Approximate

    School: Rutgers

    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

  • 10 Pages Binary Search Tree
    Binary Search Tree

    School: Rutgers

    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

  • 3 Pages Divide and Conquer
    Divide And Conquer

    School: Rutgers

    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

  • 5 Pages Dynamic Programming
    Dynamic Programming

    School: Rutgers

    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-

  • 7 Pages Dynamic Table
    Dynamic Table

    School: Rutgers

    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

  • 5 Pages Graph Algorithms
    Graph Algorithms

    School: Rutgers

    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

  • 3 Pages Greedy Algorithms
    Greedy Algorithms

    School: Rutgers

    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

  • 8 Pages Hash Tables
    Hash Tables

    School: Rutgers

    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

  • 12 Pages Inequalities
    Inequalities

    School: Rutgers

    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

  • 9 Pages Lec2
    Lec2

    School: Rutgers

    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

  • 1 Page Homework 5
    Homework 5

    School: Rutgers

    Course: Design And Analysis Of Algorithms

    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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