CSCE 310: Decrease and Conquer Algorithms
September 9, 2016
Ryan Patrick
Outline
Homework Questions
Decrease-and-Conquer Algorithms
Permutations
Decrease by a Constant Factor
Decrease by a Variable Factor
Decrease/Conquer
Patrick
Questions
Decrease &
Conq
Introduction to Algorithms
6.046J/18.401J LECTURE 7
Hashing I Direct-access tables Resolving collisions by chaining Choosing hash functions Open addressing Prof. Charles E. Leiserson
October 3, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leise
Introduction to Algorithms
6.046J/18.401J LECTURE 6
Order Statistics Randomized divide and conquer Analysis of expected time Worst-case linear-time order statistics Analysis Prof. Erik Demaine
September 28, 2005 Copyright 2001-5 by Erik D. Demaine and Cha
Introduction to Algorithms
6.046J/18.401J LECTURE 15
Dynamic Programming Longest common subsequence Optimal substructure Overlapping subproblems
Prof. Charles E. Leiserson
November 7, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leiserson L15.1
Introduction to Algorithms
6.046J/18.401J LECTURE 20
Quiz 2 Review
6.046 Staff
November 23, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leiserson L20.1
Theoretical Computer
Science Cheat
Sheet
f (n) = O (g(n) f (n) = f ~(g(n)
f (n) = O (g(n) / (n) = o(g(n)
l im a . = a
"-'=
D efinitions iff q positive c, no such that 0 _< f(n) _< cgCn) vn >_ no. iff 3 positive c, no such that f (n) >_ co(m) >_ 0 V n >_ n
Introduction to Algorithms Massachusetts Institute of Technology Professors Erik D. Demaine and Charles E. Leiserson
December 14, 2005 6.046J/18.410J Handout 35
Problem Set 9 Solutions
Problem 9-1. More parallel merge sort In this problem we will improve
Introduction to Algorithms Massachusetts Institute of Technology Professors Erik D. Demaine and Charles E. Leiserson
December 5, 2005 6.046J/18.410J Handout 30
Problem Set 9
MIT students: This problem set is due in lecture on Friday, December 9, 2005. The
Introduction to Algorithms Massachusetts Institute of Technology Professors Erik D. Demaine and Charles E. Leiserson
November 22, 2005 6.046J/18.410J Handout 27
Problem Set 8 Solutions
Problem 8-1. No left turns Youve just stolen a brand-new Nexus Nano, b
Introduction to Algorithms Massachusetts Institute of Technology Professors Erik D. Demaine and Charles E. Leiserson
November 14, 2005 6.046J/18.410J Handout 23
Problem Set 8
MIT students: This problem set is due in lecture on Monday, November 21, 2005. T
Introduction to Algorithms
6.046J/18.401J LECTURE 8
Hashing II Universal hashing Universality theorem Constructing a set of universal hash functions Perfect hashing Prof. Charles E. Leiserson
October 5, 2005 Copyright 2001-5 by Erik D. Demaine and Charles
Introduction to Algorithms
6.046J/18.401J LECTURE 9
Randomly built binary search trees Expected node depth Analyzing height
Convexity lemma Jensen's inequality Exponential height
Post mortem Prof. Erik Demaine
October 17, 2005 Copyright 2001-5 by Erik D.
CSCE 310: Transform and Conquer Algorithms
September 22, 2016
Ryan Patrick
Outline
Transform & Conquer
Instance Simplification
Gaussian Elimination
Balanced Search Trees
Rotating a Binary Search Tree
2-3 Trees
Transform/Conquer
Patrick
Transform/Conquer
I
CSCE 310: Transform and Conquer Algorithms
September 22, 2016
Ryan Patrick
Outline
Transform & Conquer
2-3 Trees
Transform/Conquer
Insertion
Transform/Conquer
Patrick
2-3 Trees
Insertion
Heaps & Heapsort
Heaps
Heapsort
Representation Change
Horners Rule
B
CSCE 310: Decrease and Conquer Algorithms
September 2, 2016
Ryan Patrick
Outline
Homework Questions
Decrease-and-Conquer Algorithms
Decrease by a Constant
Topological Sorting
Combinatorial Objects
Decrease/Conquer
Patrick
Questions
Decrease &
Conquer
Cons
CSCE 310 Syllabus
Vital Information
Course Number
Section Number
Course Title
Credits
Days
Time
Location
CSCE 310
150
Data Structures and Algorithms
3
Tuesday & Thursday
2:00pm to 3:15pm
Avery Hall Room 110
Prerequisite Courses
CSCE 156
CSCE 235
Textboo
CSCE 310: Data Structures & Algorithms
Ryan Patrick
Outline
The Course
About You
About Me
Office Hours
Assignment Feedback
Academic Honesty
Clicker Questions
MATLAB
Calculating an Average
Algorithm Analysis
Asymptotic Notation
Non-Recursive Algorithms
CSC
CSCE 310: Data Structures and Algorithms
Ryan Patrick
Outline
Algorithm Analysis
Recursive Algorithms
CSCE 310
Patrick
Recurrence Relations
Analysis
Recursive Algorithms
Recurrence Relations
Recursive Algorithm Analysis
The Master Theorem
Counting
Special
CSCE 310: Brute Force Algorithms
January 22, 2017
Ryan Patrick
Figure: xkcd #287
Homework 01 Questions?
Brute Force
Patrick
Brute Force
Closest Pair
Convex Hull
TSP
Knapsack
P, N P, and
N P-hard
Searching
Depth-First
Breadth-First
30
Outline
Brute Force A
CSCE 310: Divide and Conquer Algorithms
January 22, 2017
Ryan Patrick
Homework 01 Questions?
Divide/Conquer
Patrick
Divide and
Conquer
Binary Tree Traversal
Removing Node(s)
Multiplication
Closest Pair &
Quickhull
Branch/Bound
Fast Concurrent
Object Local
CSCE 310: Decrease and Conquer Algorithms
January 25, 2017
Ryan Patrick
Outline
Homework Questions
Decrease-and-Conquer Algorithms
Decrease by a Constant
Topological Sorting
Combinatorial Objects
Decrease/Conquer
Patrick
Questions
Decrease &
Conquer
Const
Introduction to Algorithms Massachusetts Institute of Technology Professors Erik D. Demaine and Charles E. Leiserson
November 18, 2005 6.046J/18.410J Handout 25
Problem Set 7 Solutions
Problem 7-1. Edit distance In this problem you will write a program to
Introduction to Algorithms Massachusetts Institute of Technology Professors Erik D. Demaine and Charles E. Leiserson
November 7, 2005
6.046J/18.410J
Handout 22
Problem Set 7
MIT students: This problem set is due in lecture on Monday, November 14, 2005.
Introduction to Algorithms
6.046J/18.401J LECTURE 19
Shortest Paths III All-pairs shortest paths Matrix-multiplication algorithm Floyd-Warshall algorithm Johnson's algorithm Prof. Charles E. Leiserson
November 21, 2005 Copyright 2001-5 by Erik D. Demaine
Introduction to Algorithms
6.046J/18.401J LECTURE 18
Shortest Paths II Bellman-Ford algorithm Linear programming and difference constraints VLSI layout compaction
Prof. Erik Demaine
November 16, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leis
Introduction to Algorithms
6.046J/18.401J LECTURE 17
Shortest Paths I Properties of shortest paths Dijkstra's algorithm Correctness Analysis Breadth-first search Prof. Erik Demaine
November 14, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leise
Introduction to Algorithms
6.046J/18.401J LECTURE 16
Greedy Algorithms (and Graphs) Graph representation Minimum spanning trees Optimal substructure Greedy choice Prim's greedy MST algorithm Prof. Charles E. Leiserson
November 9, 2005 Copyright 2001-5 by
Introduction to Algorithms
6.046J/18.401J LECTURE 15
Dynamic Programming Longest common subsequence Optimal substructure Overlapping subproblems
Prof. Charles E. Leiserson
November 7, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leiserson L15.1
Introduction to Algorithms
6.046J/18.401J LECTURE 14
Competitive Analysis Self-organizing lists Move-to-front heuristic Competitive analysis of MTF
Prof. Charles E. Leiserson
November 2, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leiserson L1
Introduction to Algorithms
6.046J/18.401J LECTURE 13
Amortized Analysis Dynamic tables Aggregate method Accounting method Potential method Prof. Charles E. Leiserson
October 31, 2005 Copyright 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.1
How l