CS124 Lecture 5 Spring 2011 Minimum Spanning Trees A tree is an undirected graph which is connected and acyclic. It is easy to show that if graph G(V,E) that satisfies any two of the following properties also satisfies the third, and is therefore a tree: • G(V,E) is connected • G(V,E) is acyclic • |E|=|V|−1 […]
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CS 124 Course Notes 1 Spring 2011 An algorithm is a recipe or a well-defined procedure for performing a calculation, or in general, for transforming some input into a desired output. Perhaps the most familiar algorithms are those those for adding and multiplying integers. Here is a multiplication algorithm that is different from the standard
CS 124 Lecture 2 In order to discuss algorithms effectively, we need to start with a basic set of tools. Here, we explain these tools and provide a few examples. Rather than spend time honing our use of these tools, we will learn how to use them by applying them in our studies of actual
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CS124 Lecture 3 Spring 2011 Graphs and modeling Formulating a simple, precise specification of a computational problem is often a prerequisite to writing a computer program for solving the problem. Many computational problems are best stated in terms of graphs. A directed graph G(V,E) consists of a finite set of vertices V and a set
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Section 4: Divide and Conquer & Dynamic Programming Haneul Shin February 2021 Table of Contents ● Divide and Conquer ○ Introduction ○ Merge sort ○ Karatsuba’s algorithm ● Dynamic Programming ○ Introduction ○ Fibonacci ○ Longest path problem ○ Knapsack problem ● Practice Problems Divide and Conquer Divide and Conquer Approach 1. Divide the problem
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CS 124 Section 4 Solutions Haneul Shin February 2021 1. Given an array a with n integers, design a divide and conquer algorithm to find the sum of the maximum sum subarray. This is a subarray with the maximum possible sum, which may be empty. For instance, for a = [2, 3, -7, 1, 5,
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Formal Methods of Software Design, Eric Hehner, segment 0 page 1 out of 3 [talking head] Hi. I’m Eric Hehner. I’m from Toronto, Canada. And I have the pleasure to give this course on formal methods of software engineering. I hope you enjoy it, and I hope it helps you become a better software engineer.
\documentclass[10pt]{article} % \pagestyle{empty} \usepackage{times} % \usepackage{mathptm} \setlength{\oddsidemargin}{-0.25 in} \setlength{\evensidemargin}{-0.25 in} \setlength{\topmargin}{-1.2 in} \setlength{\textwidth}{6.8 in} \setlength{\textheight}{9.5 in} \setlength{\headsep}{0.75 in} \setlength{\parindent}{0.3 in} \setlength{\parskip}{0.1 in} \usepackage{epsf} \def\O{\mathop{\smash{O}}\nolimits} \def\o{\mathop{\smash{o}}\nolimits} \newcommand{\e}{{\rm e}} \newcommand{\R}{{\bf R}} \newcommand{\Z}{{\bf Z}} \begin{document} \section*{CS 124 Homework 3: Spring 2021} \textbf{Your name:} \textbf{Collaborators:} \textbf{No. of late days used on previous psets: }\\ \textbf{No. of late days used
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Section 5: Advanced Dynamic Programming CS 124 March 3, 2021 Outline 1 Dynamic Programming Review 2 Dynamic Programming on Subsets Example: Team Formation Bitmasks 3 Dynamic Programming on Trees Introduction Example: Maximum Weighted Matching 4 Problems Problem 1: Optimal Taxation Problem 2: Stack the Blocks Problem 3: Longest Paths in a Tree CS 124 Advanced
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CS 124 Programming Assignment 1: Spring 2021 Your name(s) (up to two): Collaborators: (You shouldn’t have any collaborators but the up-to-two of you, but tell us if you did.) No. of late days used on previous psets: No. of late days used after including this pset: Homework is due Wednesday 2021-02-24 at 11:59pm ET. You