COT 5407 U01/RXA - INTRODUCTION TO ALGORITHMS - FALL 2015
Quiz 02
Advanced Design and Analysis Techniques
Allan Manamel | Panther ID : 5700508
12/3/2015
Q1. Show how to compute the length of an LCS using only 2 * min (m, n) entries in the c
table plus O (
Chapter 13: Red-Black Trees
A red-black tree is a node-colored BST.
Each node is colored either black or red. The
following special rules apply:
1. The root is always black.
2. A nil is considered to be black. This
means that every non-NIL node has two
ch
Recurrence: Solve, Prove, Ruminate.
Chris Brown
September 14, 2005
1
The problem
Solve
T (0) = 0
T (n) =
1 n1
T (i) + cn, n > 0.
n i=0
Prove your answer. What is the asymptotic order of T (n)? What can you say about
generalizations?
2
Solution (creating a
CBs Answers, Asst. 2
CSC 172 8 Sept. 1997
Read the handout on Mathematical Preliminaries. 1. How many different 5-card draw poker hands may be dealt from a 52 card deck? 52 choose 5, or , or
2. How many different 5-card draw poker hands may be dealt from
Example of Inserting Sorted Numbers
x 1 2 3 4 5 6 7 8 9 10
1 Insert 1. A leaf so red. Realize it is root so recolor to black.
1
1
Insert 2
make 2 red. Parent is black so done. 1 2
2
Insert 3
1 Insert 3. Parent is red. Parent's sibling is black (null) 3 is
Order Statistics
Many of the slides are from Prof. Plaisteds resources at University of North Carolina at Chapel Hill
Order Statistic
Selection Problem
Selection problem:
Input: A set A of n distinct numbers and a number i, with 1 i n. Output: the eleme
Chapter 9: Medians and Order Statistics
The selection problem is the problem of
computing, given a set A of n distinct
numbers and a number i, 1 i n, the ithh
order statistics (i.e., the ith smallest
number) of A.
We will consider some special cases of th
Universal Hashing
Suppose that a situation in which an
application that employs hashing is repeatedly
executed and in which the hash function is
selected from a pool of hash functions at
each execution.
Let H be the pool of hash functions.
We say that H i
g v V t v t g f d t u P &d t U X V u iz V wd V X z Wf X bV f d f z V v f z u g u cfw_ W f z U W f d U g W 6V g U X V f z wV Piz wV g d (V &dX V f z g g r t v t " u X V H X V R G u X u 6 W f z f FU V V z V V X V v v v t z t t u V V X V t u &FU Pz d t U e
COT5407 Fall 2006 Quiz #1
Instructor: Tao Li
September 7th, 2006
Student ID:
Name:
1. Let R be the binary relation over the set of real number, dened by
(A, B) R A is a proper subset of B.
For each of the following statements below, answer whether it is t
A Comparison of Dictionary Implementations
Mark P Neyer April 10, 2009
1
Introduction
A common problem in computer science is the representation of a mapping between two sets. A mapping f : A B is a function taking as input a member a A, and returning b,
MST
Many of the slides are from Prof. Plaisteds resources at University of North Carolina at Chapel Hill
Motivation: Minimum Spanning Trees
To minimize the length of a connecting network, it never pays to have cycles. The resulting connection graph is co
Elementary Sorting Algorithms
Many of the slides are from Prof. Plaisted's resources at University of North Carolina at Chapel Hill
Sorting Definitions
Input: n records, R1 . Rn , from a file. Each record Ri has
i
a key K possibly other (satellite) infor
COT-5407-U01: Introduction to Algorithms
Florida International University
Assignment #1
Monday, February 1, 2016
Problem Set 1
This Problem Set as a warm-up is intended to help students master the course material in Part I: Foundation.
You are responsible
COT-5407-U01: Introduction to Algorithms
Florida International University
Assignment #2
Friday, February 19, 2016
Summary Report
Preparing a summary report is an efficient way for learning the literature thoroughly, and will bring you
convenience to fast
COT-5407-U01: Introduction to Algorithms
Florida International University
Assignment #3
Friday, March 11, 2016
Problem Set 3
This Problem Set is intended to help students master the course material in Part III: Data Structures. You
are responsible for the
COT-5407-U01: Introduction to Algorithms
Florida International University
Assignment #4
Friday, April 08, 2016
Problem Set 4
This Problem Set as a warm-up is intended to help students master the course material in Part VI: Graph Algorithms. Students are r
Fibonacci numbers
Fibonacci numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21,
34, .
where each number is the sum of the
preceding two.
Recursive definition:
F(0) = 0;
F(1) = 1;
F(number) = F(number-1)+ F(number2);
Redundant Calculations I
To compute fib(n), we