The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 17 Disjoint Sets Data Structure
A disjoint-sets data structure maintains a collection of S = {S1 , S2 , , Sk }
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 16 Amortized Analysis
1
Amortized Analysis
Given a data structure that supports certain operations, amortized a
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
NP-completeness Lectures 24-26
1
Feasible Computation
So far, we have been looking at designing algorithms that are as
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 7 Randomized Select
Randomized Selection
The selection problem (Chapter 9) is the following. Input. An array A[1.n] of n
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 6 Randomized Quicksort
Randomized Partition and Randomized Quicksort
Randomized-Partition is a simple modification of Pa
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 5 Randomized algorithms; random permutation
Randomized algorithms
Definition: A randomized algorithm is an algorithm tha
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 4 Quicksort; basic probability
Quicksort
Quicksort(A, p, r) Input. An array A[1.n] of elements from a totally ordered se
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
NP-completeness Lectures 24-26
1
Feasible Computation
So far, we have been looking at designing algorithms that are as efficient
The University of Texas at Austin Lecture 3 Department of Computer Sciences Professor Vijaya Ramachandran Divide & conquer; recurrence relations; master theorem CS357: ALGORITHMS, Spring 2006
Analyzing divide-and-conquer algorithms
A divide-and-conquer al
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 2 Growth of functions; asymptotic analysis; summations
Growth of Functions
A function f (n) is asymptotically nonnegativ
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 11 Greedy, MST
1
The Greedy Framework
Rcall that an optimization problem is one for which an input has a collection of f
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lectures 11-14 Greedy, MST
1
The Greedy Framework
Rcall that an optimization problem is one for which an input has a collection
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Depth-first Search Lectures 23-24
1
Depth-first Search
Let G = (V, E) be a directed or undirected graph. Given a vertex a V , de
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Depth-first Search
1
Depth-first Search
Let G = (V, E) be a directed or undirected graph. Given a vertex a V , depth-first searc
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Breadth-first search Lecture 22
1
Breadth-first search and unweighted shortest paths
We consider here the single-source shortest
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Comparison & Integer Sorting Lecture 21
Lower bound on comparison-based sorting
There are several algorithms that sort n element
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Hashing Lecture 20
1
Hashing
Hashing is a widely-used class of data structures that support the operations of insert, delete and
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Binary Search Trees Lectures 18-19
1
Dictionaries
A dictionary is a data structure that supports the operations of Search, Inser
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 17 Disjoint Sets Data Structure
A disjoint-sets data structure maintains a collection of S = cfw_S1 , S2 , , Sk of disj
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 16 Amortized Analysis
1
Amortized Analysis
Given a data structure that supports certain operations, amortized analysis p
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 15 Priority Queue; Heapsort
1
Data Structures
Sets manipulated by algorithms often grow, shrink or change over time, so
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 1 Merge-sort; algorithm analysis; divide & conquer
Algorithms
An algorithm is a computational procedure that takes value
CS357: ALGORITHMS
The University of Texas at Austin Department of Computer Sciences January 18, 2006 COURSE DESCRIPTION Time/Location/Unique number. MW 11:00-12:30, WEL 2.256, #54045 Professor. Vijaya Ramachandran (vlr"at"cs, TAY 3.152, 471-9554). Office
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 7 Randomized Select
Randomized Selection
The selection problem (Chapter 9) is the following. Input. An array A[1.
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Depth-first Search Lectures 23-24
1
Depth-first Search
Let G = (V, E) be a directed or undirected graph. Given a vertex
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Breadth-first search Lecture 22
1
Breadth-first search and unweighted shortest paths
We consider here the single-source
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Binary Search Trees Lectures 18-19
1
Dictionaries
A dictionary is a data structure that supports the operations of Sear
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Hashing Lecture 20
1
Hashing
Hashing is a widely-used class of data structures that support the operations of insert, d
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Comparison & Integer Sorting Lecture 21
Lower bound on comparison-based sorting
There are several algorithms that sort n
The University of Texas at Austin Department of Computer Sciences Professor Vijaya Ramachandran CS357: ALGORITHMS, Spring 2006
Lecture 15 Priority Queue; Heapsort
1
Data Structures
Sets manipulated by algorithms often grow, shrink or change over