Topological Sorting (Decrease and Conquer)
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Topological sorting is a linear ordering of vertices in a directed acyclic graph. It is implemented using a decrease and conquer approach where the algorithm identifies a source vertex with no incoming edges, removes it from the graph, and repeats until all vertices are removed, outputting the order of deletions. The example shows the topological sorting of course prerequisites, where the algorithm iteratively deletes courses with all prerequisites completed until all courses are removed in a valid order of C1, C2, C3, C4, C5.
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CS 340 Programming Assignment III:
Topological Sort
Description: You are to implement the Depth-First Search (DFS) based algorithm for (i)
testing whether or not the input directed graph G is acyclic (a DAG), and (ii) if G is a DAG,
topologically sorting the vertices of G and outputting the topologically sorted order.
I/O Specifications: You will prompt the user from the console to select an input graph
filename, including the sample file graphin.txt as an option. The graph input files must be of
the following adjacency list representation where each xij is the j'th neighbor of vertex i (vertex
labels are 1 through n):
1: x11 x12 x13 ...
2: x21 x22 x23 ...
.
.
n: xn1 xn2 xn3 ...
Your output will be to the console. You will first output whether or not the graph is acyclic. If
the graph is NOT acyclic, then you will output the set of back edges you have detected during
DFS. Otherwise, if the graph is acyclic, then you will output the vertices in topologically
sorted order.
Algorithmic specifications:
Your algorithm must use DFS appropriately and run in O(E + V) time on any input graph. You will
need to keep track of edge types and finish times so that you can use DFS for detecting
cyclicity/acyclicity and topologically sorting if the graph is a DAG. You may implement your graph
class as you wish so long as your overall algorithm runs correctly and efficiently.
What to Turn in: You must turn in a single zipped file containing your source code, a Makefile
if your language must be compiled, appropriate input and output files, and a README file
indicating how to execute your program (especially if not written in C++ or Java). Refer to
proglag.pdf for further specifications.
This assignment is due by MIDNIGHT of Monday, February 19. Late submissions
carry a minus 40% per-day late penalty.
Sheet1Name:Possible:Score:Comments:10Graph structure with adjacency list representationDFS16Correct and O(V+E) time10Detecting cycles, is graph DAG?Topological Sort16Correctness of Topo-Sort algorithm and output18No problems in compilation and execution? Non-compiling projects receive max total 10 points, and code that compiles but crashes during execution receives max total 18 points.700Total
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Sheet2
&"Helvetica,Regular"&12&K000000&P
Sheet3
&"Helvetica,Regular"&12&K000000&P
DFS and topological sort
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Search "deeper" whenever possible
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These will be useful ...
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Unit24_TopologicalSort (2).ppt
1. Topological sort is a method for arranging the vertices of a directed acyclic graph (DAG) in linear order such that if vertex A appears before vertex B, then there is no directed edge from B to A.
2. A topological sort is not unique - there can be multiple valid linear orderings of the vertices. An algorithm uses the in-degrees of vertices to iteratively select vertices with no incoming edges until a full ordering is produced.
3. The document provides an example topological sort and discusses implementation using an in-degree array and priority queue to track vertices eligible for the ordering.
20130523 05 - Cyclomatic complexity
This document discusses cyclomatic complexity, a measure of the number of linearly independent paths through a program's source code. It is defined as the number of edges minus the number of nodes plus the number of connected components. Testing all possible paths is impossible due to the exponential increase, so code coverage tools focus on testing requirements, implementations, branches, and cyclomatic paths. The document provides an example graph with 10 nodes, 6 edges, and a cyclomatic complexity of 5. It discusses using the cyclomatic complexity measure for testing, design validation, reuse, and security analysis.
Algorithms and data Chapter 3 V Graph.pptx
This document discusses graphs and graph algorithms. It defines graphs as collections of vertices and edges. It describes different types of graphs like directed, undirected, weighted graphs. It explains graph traversal algorithms like breadth-first search and depth-first search. It also discusses minimum spanning trees and algorithms to find them, like Prim's algorithm and Kruskal's algorithm.
141205 graphulo ingraphblas
This document discusses implementing various graph algorithms using GraphBLAS kernels. It describes how degree filtered breadth-first search, k-truss detection, calculating the Jaccard index, and non-negative matrix factorization can be expressed using operations like sparse matrix multiplication, element-wise multiplication, scaling and reduction. The goal is to demonstrate how fundamental graph problems can be solved within the GraphBLAS framework using linear algebraic formulations of graph computations.
141222 graphulo ingraphblas
This document discusses implementing various graph algorithms using GraphBLAS kernels. It describes how degree filtered breadth-first search, k-truss detection, calculating the Jaccard index, and non-negative matrix factorization can be expressed using operations like SpGEMM, SpMV, element-wise multiplication, and scaling. The goal is to demonstrate how common graph analytics can utilize the linear algebra approach of the GraphBLAS framework.
Topological Sort Algorithm.pptx
Topological sorting is a linear ordering of vertices in a directed acyclic graph (DAG). It is performed by recursively processing vertices with no incoming edges before others. The algorithm uses a stack to push vertices after processing their adjacent vertices. It has applications in project scheduling, circuit design, and detecting cyclic dependencies. The time complexity is O(V+E) where V is vertices and E is edges.
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Analysis of optimization algorithms
This document discusses four key concepts related to optimization algorithms:
1) Algorithms are iterative processes that aim to generate improved solutions over time.
2) Algorithms can be modeled as self-organizing systems with exploration and exploitation.
3) Exploration and exploitation are two conflicting components that require balancing.
4) Genetic algorithms use three main evolutionary operators: crossover, mutation, and selection.
Particle swarm intelligence
The particle swarm optimization (PSO) algorithm was developed in 1995 as a metaheuristic algorithm based on swarm intelligence. It uses a population of candidate solutions called particles that search through the problem space to find the best solution. Each particle adjusts its trajectory based on its own experience and the experience of neighboring particles. The algorithm keeps track of each particle's best solution (personal best) and the best solution in the swarm (global best) to determine the particle's new velocity and position in the search space iteration by iteration until an optimal solution is found.
Nature inspired metaheuristics
The document discusses different types of nature-inspired metaheuristics used for optimization problems. It describes deterministic methods like hill-climbing that always produce the same output for a given input, and stochastic methods like genetic algorithms that can produce different outputs for the same input due to randomness. Gradient-based methods use gradients to find optimal parameters, while gradient-free methods do not. Metaheuristics employ intensification to exploit good solutions locally and diversification to explore globally. Population-based metaheuristics maintain a set of candidate solutions, while trajectory-based methods rely on a single agent. Examples of various metaheuristics are provided.
Darwin's theory of evolution
Genetic algorithms are a family of population-based metaheuristic optimization algorithms inspired by biological evolution, including natural selection and genetics. They maintain and improve a population of candidate solutions by evaluating their fitness and applying operations like selection, crossover and mutation to generate new solutions. Originally developed by John Holland and colleagues in 1960 based on Charles Darwin's theory of evolution, genetic algorithms have become one of the most popular evolutionary algorithms.
no free-lunch theorem
The no-free-lunch (NFL) theorem states that there is no single algorithm that works best for solving all types of problems. While some algorithms may perform better on certain problem types due to their complexity and characteristics, no algorithm will outperform all others across all possible problems. The NFL theorem demonstrates that the performance of any two algorithms will be equal when averaged across all possible problem types, meaning that there is no universally best algorithm and the best choice depends on the specific problem being addressed.
Video and animation
Video and animation involve capturing and displaying sequences of images to depict motion. Video uses real-world images while animation uses drawn or computer-generated images. MPEG standards like MPEG-1, 2, and 4 are used to compress digital video for storage and transmission by removing spatial and temporal redundancies between frames. MPEG compression involves three frame types - I, P, and B frames. I-frames are independent while P and B frames use motion prediction from previous and following frames. Grouping frames into GOPs allows efficient compression. The MPEG encoding and decoding process reconstructs frames using motion vectors and compensating for prediction errors.
Mpeg video compression
MPEG video compression works by reducing both spatial and temporal redundancy. It uses three types of frames - I frames which are intra-coded, P frames which use forward prediction from I or P frames, and B frames which use both forward and backward prediction. I frames provide anchors for the encoding and allow fast forwarding, while P and B frames allow for motion estimation between frames to reduce redundancy over time. MPEG compression groups frames into GOPs and uses motion vectors to predict how objects move between frames, reducing the need to encode redundant pixel data in each frame.
Digital audio
This document discusses digital audio, including its representation and processing. It begins by outlining the uses and applications of digital audio, such as creating moods and enhancing multimedia games. It then covers topics like analog vs. digital audio, producing digital audio through digitization and microphones, representation through sampling and quantization, perceptual encoding, common file formats like MP3 and WAV, and audio streaming using RealAudio. The key aspects of digital audio processing like compression, decompression, and codecs are also summarized.
Designing multimedia
This document discusses the process of designing multimedia projects. It outlines the key phases: conceptualization, analysis, design, development, implementation, and evaluation.
The analysis phase involves studying user needs, content requirements, technical specifications, and constraints. In the design phase, project specifications are created along with storyboards, flowcharts and navigation structures.
The development phase uses authoring tools to create prototypes based on the design. Content like graphics, audio and video are integrated. Formative evaluation tests for bugs during this stage. The implementation phase involves legal/ethical reviews and accessibility testing. Summative evaluation assesses the full project before release.
Testing and Rolling Out Enterprise Applications
The document discusses various aspects of testing and rolling out enterprise applications. It describes different types of testing like functional testing, non-functional testing, white box testing, black box testing and gray box testing. It also discusses different testing levels from unit testing to acceptance testing and production testing. The document then covers testing approaches, environments, performance testing and security testing in detail. Finally, it provides an overview of user acceptance testing and strategies for rolling out enterprise applications.
Constructing Enterprise Applications
The document discusses the process of constructing enterprise applications. It involves translating the design into code components through various activities like achieving construction readiness, constructing solution layers, code review, testing, and creating deployable packages. Construction readiness includes defining a construction plan, package structure, configuration management plan, and development environment. Solution layers include infrastructure, presentation, business, data access, and integration components. Code review and static/dynamic analysis help ensure quality. The overall process aims to fulfill requirements through proper architecture, techniques, and tools.
Architecting and Designing Enterprise Applications
The document discusses the architecture, views, and viewpoints of enterprise applications. It describes how architecture serves as a blueprint and is organized into views and viewpoints representing stakeholder perspectives. The architecture description consists of aspects depicted by models using languages like UML. Enterprise architecture helps conceptualize and analyze business scenarios considering applications, users, and data. Popular frameworks like TOGAF define architecture domains including business, applications, data, and technology. The blueprint of an application includes logical, technical, data, and infrastructure architectures. Logical architecture defines layers like business, data access, and presentation. Technical architecture identifies frameworks, patterns, and integration. Infrastructure services provide common functions.
Incepting Enterprise Applications
This document discusses the key activities involved in incepting an enterprise application, including enterprise analysis, business modeling, requirements elicitation and analysis, requirements validation, and planning and estimation. Enterprise analysis involves identifying business opportunities and stakeholders. Business modeling helps understand business processes and includes creating AS-IS and TO-BE models. Requirements elicitation captures functional and non-functional requirements through use cases and prototypes. Requirements validation ensures requirements meet business needs. Planning and estimation prepares project plans and estimates costs and effort based on techniques like use case points and function points.
Introduction to BEA
This document discusses enterprise applications, including what defines an enterprise application, how they can be categorized, and the challenges they face. Enterprise applications are applications that satisfy an organization's business and functional requirements while also considering efficiency, scalability, security, and other non-functional needs. They can be categorized based on their visibility to end users, the industry domain, type of processing, and whether they are custom-built or readymade. Developing successful enterprise applications requires business case readiness, a clear strategy for execution, and excellence in implementation. It also discusses the key skills needed and how to measure the success of enterprise applications.
Pointers and Structures
Structures in Functions discusses pointers to structures, accessing structure members, passing structures as function arguments by value and by reference, returning structures from functions, arrays of structures, and self-referential structures. Key points include passing a pointer to a structure as a function argument to avoid copying large structures, defining an array of structures to store multiple records, and using a pointer as a member of a structure to create self-referential linked structures like linked lists.
Dynamic memory allocation
The document discusses dynamic memory allocation in C using functions like malloc(), calloc(), free(), and realloc(). It provides:
1) malloc() allocates memory at runtime and returns a pointer to the allocated block. It does not initialize the memory.
2) calloc() also allocates memory at runtime but initializes all bits to zero.
3) free() frees up previously allocated memory so it can be used again.
4) realloc() resizes previously allocated memory blocks, allowing memory usage to grow or shrink as needed.
Function pointer
Pointers can point to functions and be used to call those functions. A function pointer must be initialized with the address of a function before being called. Function pointers allow functions to be passed as parameters and can be used to select between functions at runtime based on some condition.
10. NULL pointer
A null pointer points to nothing or nowhere and is initialized to NULL or 0. Pointers must be initialized to NULL to indicate no memory is allocated yet. Functions returning pointers may need to indicate errors by returning a null pointer. Passing NULL to a function avoids passing an invalid memory address. Dereferencing a null pointer will cause a program to abort, so pointers should be checked against NULL before accessing their value.
13. Pointer and 2D array
A two dimensional array can be accessed using two subscripts, with the first representing the row number and the second representing the column number. Elements are stored in memory row by row. A 2D array can be viewed as a collection of 1D arrays, with each row representing an array of the second dimension size. The base address of the 2D array points to the first element at index [0][0], and any element can be accessed using the generalized form of base_pointer[i][j].
12.string and pointer
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#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
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- Basic understanding of AWS services and architecture
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Findings: Based on findings, the Gumbel approach produced the highest intensity values, whereas the other approaches produced values that were close to each other. The data indicates that 461.9 mm of rain fell during the monsoon season’s 301st week. However, it was found that the 29th week had the greatest average rainfall, 92.6 mm. With 952.6 mm on average, the monsoon season saw the highest rainfall. Calculations revealed that the yearly rainfall averaged 1171.1 mm. Using Weibull’s method, the study was subsequently expanded to examine rainfall distribution at different recurrence intervals of 2, 5, 10, and 25 years. Rainfall and recurrence interval mathematical correlations were also developed. Further regression analysis revealed that short wave irrigation, wind direction, wind speed, pressure, relative humidity, and temperature all had a substantial influence on rainfall.
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Topological Sorting (Decrease and Conquer)
- 1. Topological Sorting Decrease and Conquer Technique
- 2. Definition Topological sorting for a directed acyclic graph(DAG) Linear ordering of vertices For every edge U-V of a directed graph, For every edge U-V of a directed graph, Vertex u will come before vertex v in the ordering
- 3. Source Removal Algorithm Direct implementation of the decrease and conquers method Steps Identify a vertex(source) from a remaining digraph Identify a vertex(source) from a remaining digraph with no incoming edges If there are more than one such vertices, then break the tie randomly. Delete it along with all the edges outgoing from it Solution: deleted order of the vertices
- 4. Example Consider a set of 5 required courses {C1,C2,C3,C4,C5} a part-time student has to take in some degree program. The courses can be taken in any order as long as the following course prerequisites are met: C1 and C2 have no prerequisites C1 and C2 have no prerequisites C3 requires C1 and C2 C4 requires C3 C5 requires C3 and C4 The student can take only one course per term. In which order should the student take the courses?
- 5. Digraph Prerequisite structure of five courses C1 and C2 have no prerequisites C3 requires C1 and C2 C3 requires C1 and C2 C4 requires C3 C5 requires C3 and C4
- 6. Illustration
- 9. Illustration delete C1 delete C2 C1 C2 Topological Sorting
- 11. Illustration delete C1 delete C2 delete C3 C1 C2 C3 Topological Sorting
- 12. Illustration delete C1 delete C2 delete C3
- 13. Illustration delete C1 delete C2 delete C3 delete C4 C1 C2 C3 C4 Topological Sorting
- 14. Illustration delete C1 delete C2 delete C3 delete C4
- 15. Illustration delete C1 delete C2 delete C3 delete C4 delete C5 C1 C2 C3 C4 C5 Topological Sorting