Recurrences
(CLRS 4.1-4.2)
Last time we discussed divide-and-conquer algorithms Divide and Conquer To Solve P: 1. Divide P into smaller problems P1 , P2 , P3 .Pk . 2. Conquer by solving the (smaller) subproblems recursively. 3. Combine solutions to P1 ,

Jade Yu Cheng ICS 311 Homework 3 Sep 4, 2008
Question for lecture 4
Problem 4-1 on p. 85 Recurrence examples Give asymptotic upper and lower bounds for T (n ) in each of the following recurrences. Assume that T (n ) is constant for n 2 . Make your bounds

Answers to Homework 1
p. 13 1.23 What is the smallest value of n such that an algorithm whose running time is 100n2 runs
faster than an algorithm whose running time is 2n on the same machine?
Solution:
Find the smallest n > 0 such that 100n2 < 2n .
Use a

Elementary Graph Algorithms
Slides adapted from Lin / Devi
Graph Recap
Graph G = (V, E)
V = set of vertices, n = |V|
E = set of edges (VV), m = |E|
Types of graphs
Undirected: edge (u, v) = (v, u)
Directed: (u, v) is edge from u to v, denoted as u v

Set ADT & Hashing
Slides adapted from David A. Plaisted COMP 550
Abstract Data Types (ADT)
Less commonly called Abstract Data Structure
Model for data structures that have similar
behavior
Defined by the operations that can be performed
(and any constr

Graphs
Slides adapted from Ben Choi
Taxonomy of ADTs
ADTs
Binary Relationships
Graphs
Collection of Elements
Manually Positioned
Stack
Queue
Positional
Collection
Algorithmically Positioned
Set
Ordered
Collection
Priority
Queue
.
From S.A. Goldman & K.J.

Balanced Search Trees
Slides adapted from David A. Plaisted COMP 550 and Z. Ras
Binary Search Trees
Implementation of the Ordered Collection ADT
min, max, search, delete, insert, successor,
predecessor
all methods take O(h) time
h is the height of the

Heap sort
2/2/2015
1
Heap sort
Another (n log n) sorting algorithm
In practice quick sort wins
The heap data structure and its variants
are very useful for many algorithms
2/2/2015
2
Selection sort
<=
Sorted
<=
Find minimum
<=
Sorted
2/2/2015
3
Selecti

Data Structures and Algorithms
Solving Recurrence Relations
Chris Brooks Department of Computer Science University of San Francisco
Department of Computer Science University of San Francisco p.1/30
4-0:
for (i=1; i<=n*n; i+) for (j=0; j<i; j+) sum+;
Algor

Topological Sort & Strongly
Connected Components
Slides adapted from David A. Plaisted
Recap
Graphs: G = <V, E>
Data structure made up of vertices & edges
Edges can be (un)directed or (un)weighted
Basic Graph Searching Algorithms
Breadth-First Search

Introduction to Algorithms
Massachusetts Institute of Technology
Professors Erik Demaine and Srini Devadas
November 17, 2011
6.006 Fall 2011
Quiz 2 Solutions
Quiz 2 Solutions
Problem 1. [1 points] Write your name on top of each page.
Problem 2. True/False

November 26, 2012
Fall 2012
Comp 510-Algorithms
Janeth Moran Cervantes
Assignment 6
Chapter 22: Elementary Graph Algorithms
22.2-1) Show the d and values that result from running breadth-rst search on the directed
graph of Figure 22.2(a), using vertex 3 a

Hash Tables
Chapter 11
Aidong Lu
University of North Carolina at Charlotte
[email protected]
September 29, 2015
Knowledge Points
1
Hash table
2
Hash functions
Recommended Videos
https:/www.youtube.com/watch?v=FXEvcP6nLdc
Direct-Address Tables
Scenario
Ma

ITCS 6114/8114 Algorithm and Data structure
Fall 2015
Home work 1
Due on 09/09/2015 @ 11 PM
Please provide a solution for the problems below. Submit your work in single file through
Moodle in .pdf or .doc or .docx format (no other format will be accepted)

ITCS_6114_8114: Algorithms and Data Structures
Fall 2015
Programming Project 3: Design of Demonstration Algorithms
The first phase will be due on November 4th, 2015.
Up to now, we have covered a number of algorithms and you know more about online classes.

ITCS 6114/8114 Algorithm and Data structure
Fall 2015
Homework 4
Due on 10/7/2015 @ 11 PM
Provide a solution for the problems below. Submit your work in single file through Moodle in
.pdf or .doc or .docx format (no other format will be accepted) and make

Sriharish Ranganathan
UNCC ID 800901667
ITCS 6114 Algorithms and Data Structures
a. Prove that CLIQUE p VERTEX-COVER
Solution:
Given an undirected graph G= (V, E), and for that graph, we define the complement of G as, = (, )
where, = cfw_(u, v): V, u v, a

Assignment-3
1) Professor Bunyan thinks he has discovered a remarkable property of binary search trees.
Suppose that the search for key k in a binary search tree ends up in a leaf. Consider three
sets: A, the keys to the left of the search path; B, the ke

CAP 5415 Computer Vision
Fall 2011
Dr. Mubarak Shah
Univ. of Central Florida
www.cs.ucf.edu/~vision/courses/cap5415/fall2012
Office 247-F HEC
Filtering
Lecture-2
General
Binary
Gray Scale
Color
Binary Images
Y
Row 1
1 1 1
1
q
X
0: Black
1: White
Row q
0 0

CAP 5415 Computer Vision
Fall 2012
Dr. Mubarak Shah
Univ. of Central Florida
Alper Yilmaz, Mubarak Shah Fall 2011UCF
Edge Detection
Lecture-3
Alper Yilmaz, Mubarak Shah Fall 2012UCF
Example
Alper Yilmaz, Mubarak Shah Fall 2012UCF
An Application
What is an

E0005E - Industrial Image Analysis
The Hough Transform
Matthew Thurley
slides by Johan Carlson
1
This Lecture
The Hough transform
Detection of lines
Detection of other shapes (the generalized Hough transform)
2
Problem formulation
Lets say we have an edge

CS 675 Computer Vision
Instructor: Marc Pomplun
Practice Midterm Exam
Duration: 75 minutes
No calculators, no books, and no notes are allowed.
Question 1: _ out of _
points
Question 2: _ out of _ points
Question 3: _ out of _
points
Question 4: _ out of _

1
The Pinhole Camera
Y
P (X,Y,Z)
Pc (u,v)
O
u
Center of
Projection
v
Principal Axis
Image Plane
Z
X
Figure 1: A camera.
Figure 1 shows a camera with center of projection O and the principal axis parallel to Z axis. Image plane is at
focus and hence focal

Midterm Exam
Fundamentals of Computer Vision
COMP 558
Oct. 13, 2010
Prof. M. Langer
There are a total of 11 points (10 + 1 bonus on Question 4).
1. (1 point)
Consider a thin lens camera with f-number N = 4 and focal length 30 mm. Suppose the
camera is foc

CSCE 5013 - Computer Vision
Midterm Exam Fall 2011
Instructions:
This is closed book exam. One 8.5 x 11 page of notes are allowed. Calculators can be
used for numerical calculations only (not as electronic notebooks). Please number each
of your answers an

Assignment 3 Solution
Solution 1:
Figure 1: Counter example to Professor Bunyans claim.
The claim is wrong. A simple counter example is shown in figure 1. In the figure, the search is being done for leaf node 3, so the
set B = cfw_8, 4, 3. There is nothin

1. The while loop of lines 5.7 of procedure INSERTION-SORT scans backward through the
sorted array A[1 . . j 1] to find the appropriate place for A[ j ]. The hitch is that the loop
not only searches for the proper place for A[ j ], but that it also moves