A graph is a data structure consisting of vertices and edges connecting the vertices. Graphs can be directed or undirected. Depth-first search (DFS) and breadth-first search (BFS) are algorithms for traversing graphs by exploring neighboring vertices. DFS uses a stack and explores as far as possible along each branch before backtracking, while BFS uses a queue and explores all neighbors at each depth level first before moving to the next level.
This document defines and provides examples of graphs and their representations. It discusses:
- Graphs are data structures consisting of nodes and edges connecting nodes.
- Examples of directed and undirected graphs are given.
- Graphs can be represented using adjacency matrices or adjacency lists. Adjacency matrices store connections in a grid and adjacency lists store connections as linked lists.
- Key graph terms are defined such as vertices, edges, paths, and degrees. Properties like connectivity and completeness are also discussed.
Graphs are data structures consisting of nodes and edges connecting nodes. They can be directed or undirected. Trees are special types of graphs. Common graph algorithms include depth-first search (DFS) and breadth-first search (BFS). DFS prioritizes exploring nodes along each branch as deeply as possible before backtracking, using a stack. BFS explores all nodes at the current depth before moving to the next depth, using a queue.
This Presentation Explains a very Important topic of Data Structure in Programming which is Graphs and Methods of Graph Traversing.
I think this presentation will help you in understanding the Data Structure Graph and its Traversing Methods.
A graph G is composed of a set of vertices V connected by edges E. It can be represented using an adjacency matrix, with a 1 or 0 in position (i,j) indicating whether vertices i and j are connected, or an adjacency list storing the neighbors of each vertex. Graph search algorithms like depth-first search (DFS) and breadth-first search (BFS) are used to traverse the graph and find paths between vertices, with DFS prioritizing depth and BFS prioritizing breadth of exploration. DFS uses recursion to implicitly store paths while BFS uses queues and must store paths separately.
This document discusses adjacency lists, a method for representing graphs. An adjacency list stores a list of adjacent vertices for each vertex. Each vertex object stores a reference to other adjacent nodes. Common graph terms are defined such as vertices, edges, paths, and weights. Methods for an adjacency list implementation include adding and removing vertices and edges. Pros are that it is easy to retrieve adjacent nodes and check for edges, while a con is that checking for a specific edge is more complex. Graph traversal algorithms and applications of adjacency lists are also discussed.
A graph G consists of a non empty set V called the set of nodes (points, vertices) of the graph, a set E, which is the set of edges of the graph and a mapping from the set of edges E to a pair of elements of V.
Any two nodes, which are connected by an edge in a graph are called "adjacent nodes".
In a graph G(V,E) an edge which is directed from one node to another is called a "directed edge", while an edge which has no specific direction is called an "undirected edge". A graph in which every edge is directed is called a "directed graph" or a "digraph". A graph in which every edge is undirected is called an "undirected graph".
If some of edges are directed and some are undirected in a graph then the graph is called a "mixed graph".
Any graph which contains some parallel edges is called a "multigraph".
If there is no more than one edge but a pair of nodes then, such a graph is called "simple graph."
A graph in which weights are assigned to every edge is called a "weighted graph".
In a graph, a node which is not adjacent to any other node is called "isolated node".
A graph containing only isolated nodes is called a "null graph". In a directed graph for any node v the number of edges which have v as initial node is called the "outdegree" of the node v. The number of edges to have v as their terminal node is called the "Indegree" of v and Sum of outdegree and indegree of a node v is called its total degree.
A graph is a data structure consisting of vertices and edges connecting the vertices. Graphs can be directed or undirected. Depth-first search (DFS) and breadth-first search (BFS) are algorithms for traversing graphs by exploring neighboring vertices. DFS uses a stack and explores as far as possible along each branch before backtracking, while BFS uses a queue and explores all neighbors at each depth level first before moving to the next level.
This document defines and provides examples of graphs and their representations. It discusses:
- Graphs are data structures consisting of nodes and edges connecting nodes.
- Examples of directed and undirected graphs are given.
- Graphs can be represented using adjacency matrices or adjacency lists. Adjacency matrices store connections in a grid and adjacency lists store connections as linked lists.
- Key graph terms are defined such as vertices, edges, paths, and degrees. Properties like connectivity and completeness are also discussed.
Graphs are data structures consisting of nodes and edges connecting nodes. They can be directed or undirected. Trees are special types of graphs. Common graph algorithms include depth-first search (DFS) and breadth-first search (BFS). DFS prioritizes exploring nodes along each branch as deeply as possible before backtracking, using a stack. BFS explores all nodes at the current depth before moving to the next depth, using a queue.
This Presentation Explains a very Important topic of Data Structure in Programming which is Graphs and Methods of Graph Traversing.
I think this presentation will help you in understanding the Data Structure Graph and its Traversing Methods.
A graph G is composed of a set of vertices V connected by edges E. It can be represented using an adjacency matrix, with a 1 or 0 in position (i,j) indicating whether vertices i and j are connected, or an adjacency list storing the neighbors of each vertex. Graph search algorithms like depth-first search (DFS) and breadth-first search (BFS) are used to traverse the graph and find paths between vertices, with DFS prioritizing depth and BFS prioritizing breadth of exploration. DFS uses recursion to implicitly store paths while BFS uses queues and must store paths separately.
This document discusses adjacency lists, a method for representing graphs. An adjacency list stores a list of adjacent vertices for each vertex. Each vertex object stores a reference to other adjacent nodes. Common graph terms are defined such as vertices, edges, paths, and weights. Methods for an adjacency list implementation include adding and removing vertices and edges. Pros are that it is easy to retrieve adjacent nodes and check for edges, while a con is that checking for a specific edge is more complex. Graph traversal algorithms and applications of adjacency lists are also discussed.
A graph G consists of a non empty set V called the set of nodes (points, vertices) of the graph, a set E, which is the set of edges of the graph and a mapping from the set of edges E to a pair of elements of V.
Any two nodes, which are connected by an edge in a graph are called "adjacent nodes".
In a graph G(V,E) an edge which is directed from one node to another is called a "directed edge", while an edge which has no specific direction is called an "undirected edge". A graph in which every edge is directed is called a "directed graph" or a "digraph". A graph in which every edge is undirected is called an "undirected graph".
If some of edges are directed and some are undirected in a graph then the graph is called a "mixed graph".
Any graph which contains some parallel edges is called a "multigraph".
If there is no more than one edge but a pair of nodes then, such a graph is called "simple graph."
A graph in which weights are assigned to every edge is called a "weighted graph".
In a graph, a node which is not adjacent to any other node is called "isolated node".
A graph containing only isolated nodes is called a "null graph". In a directed graph for any node v the number of edges which have v as initial node is called the "outdegree" of the node v. The number of edges to have v as their terminal node is called the "Indegree" of v and Sum of outdegree and indegree of a node v is called its total degree.
Graphs are a non-linear data structure consisting of nodes (vertices) connected by links (edges). There are two main types: undirected graphs where edges are not ordered, and directed graphs where edges have direction from one node to another. Common graph terminology includes adjacent nodes, degrees, isolated nodes, sources, and different graph properties like being connected, complete, or having loops. Graph traversal algorithms like breadth-first search and depth-first search are used to systematically explore the structure of a graph.
A graph consists of vertices and edges, where vertices represent entities and edges represent relationships between vertices. Graphs can be represented sequentially using matrices like adjacency and incidence matrices, or linked using data structures like adjacency lists. Adjacency matrices allow fast addition/removal of edges but use more memory, while adjacency lists use less memory but are slower to modify. The best representation depends on whether the graph is dense or sparse.
Graph in data structure it gives you the information of the graph application. How to represent the Graph and also Graph Travesal is also there many terms are there related to garph
This document defines key graph concepts like paths, cycles, degrees of vertices, and different types of graphs like trees, forests, and directed acyclic graphs. It also describes common graph representations like adjacency matrices and lists. Finally, it covers graph traversal algorithms like breadth-first search and depth-first search, outlining their time complexities and providing examples of their process.
Skiena algorithm 2007 lecture10 graph data strctureszukun
This document summarizes different types of graph data structures and representations. It discusses graphs as consisting of vertices and edges, and describes properties like directed vs undirected, weighted vs unweighted, sparse vs dense. It also covers different representations like adjacency matrices and lists, and provides code examples for initializing, reading, and inserting edges into a graph represented using an adjacency list.
Graphs are a data structure composed of nodes connected by edges. There are two main types: directed graphs where edges show a flow between nodes, and undirected graphs where edges simply show a relationship between nodes. Key terminology includes adjacent nodes, paths, cyclic vs acyclic paths, and representations like adjacency matrices and lists. Graphs can model many real-world applications such as social networks, computer networks, road maps, and more.
This document discusses three types of graphs: directed graphs, undirected graphs, and weighted graphs. It provides examples and definitions of basic graph terminology like vertices, edges, and paths. It also describes two common ways to represent graphs in computer memory: sequential representation using adjacency lists and linked representation using linked lists. Finally, it outlines high-level processes for creating a graph and searching or deleting elements from a graph.
The document defines and describes various graph concepts and data structures used to represent graphs. It defines a graph as a collection of nodes and edges, and distinguishes between directed and undirected graphs. It then describes common graph terminology like adjacent/incident nodes, subgraphs, paths, cycles, connected/strongly connected components, trees, and degrees. Finally, it discusses two common ways to represent graphs - the adjacency matrix and adjacency list representations, noting their storage requirements and ability to add/remove nodes.
The document discusses graphs and their applications. It defines graphs as consisting of vertices and edges. Graphs can be undirected or directed. It also defines concepts like paths, cycles, and connectivity in graphs. Common applications of graphs mentioned are maps, computer networks, and CAD designs. The document then discusses different ways to represent graphs using adjacency matrices and adjacency lists. It also discusses using graphs to model and solve problems like traffic light timing by coloring the vertices.
A graph G is composed of vertices V connected by edges E. It can be represented using an adjacency matrix or adjacency lists. Graph search algorithms like depth-first search (DFS) and breadth-first search (BFS) are used to traverse the graph and find paths between vertices. DFS recursively explores edges until reaching the end of a branch before backtracking, while BFS explores all neighbors at each level before moving to the next.
A graph G consists of a set of vertices V connected by edges E. An edge e is represented as an ordered pair of vertices (u,v). Graphs can be directed or undirected. The degree of a vertex is the number of edges incident to it. A path is a sequence of adjacent vertices, while a cycle is a path where the first and last vertices are the same. Graphs can be represented using an adjacency matrix where a 1 indicates an edge and 0 no edge between two vertices.
The document discusses different types of graphs including directed and undirected graphs. It describes graph implementations using adjacency matrices and adjacency lists. It also covers graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). DFS prioritizes exploring paths as deeply as possible while BFS explores all paths at the same depth level before moving deeper. Real-world examples of graphs include social networks and transportation networks.
A Graph is a non-linear data structure, which consists of vertices(or nodes) connected by edges(or arcs) where edges may be directed or undirected.
Graphs are a powerful and versatile data structure that easily allow you to represent real life relationships between different types of data (nodes).
The document discusses various graph theory concepts including:
- Types of graphs such as simple graphs, multigraphs, pseudographs, directed graphs, and directed multigraphs which differ based on allowed edge connections.
- Graph terminology including vertices, edges, degrees, adjacency, incidence, paths, cycles, and representations using adjacency lists and matrices.
- Weighted graphs and algorithms for finding shortest paths such as Dijkstra's algorithm.
- Euler and Hamilton paths/circuits and conditions for their existence.
- The traveling salesman problem of finding the shortest circuit visiting all vertices.
This document discusses different graph traversal algorithms including depth-first search (DFS) and breadth-first search (BFS). It provides descriptions of how DFS and BFS work by exploring edges and vertices in different orders. It also discusses minimum spanning trees and algorithms for finding minimum spanning trees, including Kruskal's algorithm, Prim's algorithm, and Boruvka's algorithm.
The document discusses various topics related to graphs:
- It defines directed and undirected graphs, paths, connected graphs, trees, degree, isomorphic graphs, cut sets, and labeled graphs.
- Key aspects include paths being sequences of vertices with edges connecting them, connected graphs having paths between all vertex pairs, trees being connected and acyclic graphs, and isomorphic graphs having the same structure.
- It also covers graph concepts such as degrees measuring incident edges, cut sets separating graphs, and labeling providing additional data to graphs' vertices or edges.
Graph Theory: Matrix representation of graphsAshikur Rahman
The document discusses different matrix representations of graphs:
1) Incidence matrices represent the relationship between vertices and edges, with each column having two 1s. Circuit matrices represent circuits, with each row as a circuit vector. Cut-set matrices represent edge sets whose removal disconnects the graph.
2) Path matrices represent paths between vertex pairs, with columns of all 0s/1s indicating edges not/in every path. Adjacency matrices directly encode vertex connectivity.
3) Exercises are provided to construct the incidence matrix, circuit matrix, fundamental circuit matrix, and cut-set matrix for a given graph.
In this chapter we have to Learn Graph Terminologies, Types of Graph, Representation of Graph, Traversal of Graph BFS and DFS. Its Application Use Advantages and Disadvantages
The document discusses graphs and graph theory. It defines graphs as non-linear data structures used to model networks and relationships. The key types of graphs are undirected graphs, where edges have no orientation, and directed graphs, where edges have orientation. Graph traversal algorithms like depth-first search and breadth-first search are discussed. Common graph terminology is defined, including vertices, edges, paths, cycles, degrees. Different graph representations like adjacency matrices and adjacency lists are also covered. Applications of graphs include modeling networks, routes, and relationships.
Graphs are a non-linear data structure consisting of nodes (vertices) connected by links (edges). There are two main types: undirected graphs where edges are not ordered, and directed graphs where edges have direction from one node to another. Common graph terminology includes adjacent nodes, degrees, isolated nodes, sources, and different graph properties like being connected, complete, or having loops. Graph traversal algorithms like breadth-first search and depth-first search are used to systematically explore the structure of a graph.
A graph consists of vertices and edges, where vertices represent entities and edges represent relationships between vertices. Graphs can be represented sequentially using matrices like adjacency and incidence matrices, or linked using data structures like adjacency lists. Adjacency matrices allow fast addition/removal of edges but use more memory, while adjacency lists use less memory but are slower to modify. The best representation depends on whether the graph is dense or sparse.
Graph in data structure it gives you the information of the graph application. How to represent the Graph and also Graph Travesal is also there many terms are there related to garph
This document defines key graph concepts like paths, cycles, degrees of vertices, and different types of graphs like trees, forests, and directed acyclic graphs. It also describes common graph representations like adjacency matrices and lists. Finally, it covers graph traversal algorithms like breadth-first search and depth-first search, outlining their time complexities and providing examples of their process.
Skiena algorithm 2007 lecture10 graph data strctureszukun
This document summarizes different types of graph data structures and representations. It discusses graphs as consisting of vertices and edges, and describes properties like directed vs undirected, weighted vs unweighted, sparse vs dense. It also covers different representations like adjacency matrices and lists, and provides code examples for initializing, reading, and inserting edges into a graph represented using an adjacency list.
Graphs are a data structure composed of nodes connected by edges. There are two main types: directed graphs where edges show a flow between nodes, and undirected graphs where edges simply show a relationship between nodes. Key terminology includes adjacent nodes, paths, cyclic vs acyclic paths, and representations like adjacency matrices and lists. Graphs can model many real-world applications such as social networks, computer networks, road maps, and more.
This document discusses three types of graphs: directed graphs, undirected graphs, and weighted graphs. It provides examples and definitions of basic graph terminology like vertices, edges, and paths. It also describes two common ways to represent graphs in computer memory: sequential representation using adjacency lists and linked representation using linked lists. Finally, it outlines high-level processes for creating a graph and searching or deleting elements from a graph.
The document defines and describes various graph concepts and data structures used to represent graphs. It defines a graph as a collection of nodes and edges, and distinguishes between directed and undirected graphs. It then describes common graph terminology like adjacent/incident nodes, subgraphs, paths, cycles, connected/strongly connected components, trees, and degrees. Finally, it discusses two common ways to represent graphs - the adjacency matrix and adjacency list representations, noting their storage requirements and ability to add/remove nodes.
The document discusses graphs and their applications. It defines graphs as consisting of vertices and edges. Graphs can be undirected or directed. It also defines concepts like paths, cycles, and connectivity in graphs. Common applications of graphs mentioned are maps, computer networks, and CAD designs. The document then discusses different ways to represent graphs using adjacency matrices and adjacency lists. It also discusses using graphs to model and solve problems like traffic light timing by coloring the vertices.
A graph G is composed of vertices V connected by edges E. It can be represented using an adjacency matrix or adjacency lists. Graph search algorithms like depth-first search (DFS) and breadth-first search (BFS) are used to traverse the graph and find paths between vertices. DFS recursively explores edges until reaching the end of a branch before backtracking, while BFS explores all neighbors at each level before moving to the next.
A graph G consists of a set of vertices V connected by edges E. An edge e is represented as an ordered pair of vertices (u,v). Graphs can be directed or undirected. The degree of a vertex is the number of edges incident to it. A path is a sequence of adjacent vertices, while a cycle is a path where the first and last vertices are the same. Graphs can be represented using an adjacency matrix where a 1 indicates an edge and 0 no edge between two vertices.
The document discusses different types of graphs including directed and undirected graphs. It describes graph implementations using adjacency matrices and adjacency lists. It also covers graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). DFS prioritizes exploring paths as deeply as possible while BFS explores all paths at the same depth level before moving deeper. Real-world examples of graphs include social networks and transportation networks.
A Graph is a non-linear data structure, which consists of vertices(or nodes) connected by edges(or arcs) where edges may be directed or undirected.
Graphs are a powerful and versatile data structure that easily allow you to represent real life relationships between different types of data (nodes).
The document discusses various graph theory concepts including:
- Types of graphs such as simple graphs, multigraphs, pseudographs, directed graphs, and directed multigraphs which differ based on allowed edge connections.
- Graph terminology including vertices, edges, degrees, adjacency, incidence, paths, cycles, and representations using adjacency lists and matrices.
- Weighted graphs and algorithms for finding shortest paths such as Dijkstra's algorithm.
- Euler and Hamilton paths/circuits and conditions for their existence.
- The traveling salesman problem of finding the shortest circuit visiting all vertices.
This document discusses different graph traversal algorithms including depth-first search (DFS) and breadth-first search (BFS). It provides descriptions of how DFS and BFS work by exploring edges and vertices in different orders. It also discusses minimum spanning trees and algorithms for finding minimum spanning trees, including Kruskal's algorithm, Prim's algorithm, and Boruvka's algorithm.
The document discusses various topics related to graphs:
- It defines directed and undirected graphs, paths, connected graphs, trees, degree, isomorphic graphs, cut sets, and labeled graphs.
- Key aspects include paths being sequences of vertices with edges connecting them, connected graphs having paths between all vertex pairs, trees being connected and acyclic graphs, and isomorphic graphs having the same structure.
- It also covers graph concepts such as degrees measuring incident edges, cut sets separating graphs, and labeling providing additional data to graphs' vertices or edges.
Graph Theory: Matrix representation of graphsAshikur Rahman
The document discusses different matrix representations of graphs:
1) Incidence matrices represent the relationship between vertices and edges, with each column having two 1s. Circuit matrices represent circuits, with each row as a circuit vector. Cut-set matrices represent edge sets whose removal disconnects the graph.
2) Path matrices represent paths between vertex pairs, with columns of all 0s/1s indicating edges not/in every path. Adjacency matrices directly encode vertex connectivity.
3) Exercises are provided to construct the incidence matrix, circuit matrix, fundamental circuit matrix, and cut-set matrix for a given graph.
In this chapter we have to Learn Graph Terminologies, Types of Graph, Representation of Graph, Traversal of Graph BFS and DFS. Its Application Use Advantages and Disadvantages
The document discusses graphs and graph theory. It defines graphs as non-linear data structures used to model networks and relationships. The key types of graphs are undirected graphs, where edges have no orientation, and directed graphs, where edges have orientation. Graph traversal algorithms like depth-first search and breadth-first search are discussed. Common graph terminology is defined, including vertices, edges, paths, cycles, degrees. Different graph representations like adjacency matrices and adjacency lists are also covered. Applications of graphs include modeling networks, routes, and relationships.
The document defines and explains basic graph terminology and representations. It begins by defining what a graph is composed of, including vertices and edges. It then discusses directed vs undirected graphs and provides examples. It also covers basic graph terminology such as adjacent nodes, degree, paths, cycles, and more. Finally, it discusses different ways of representing graphs, including adjacency matrices, adjacency lists, and traversing graphs using breadth-first and depth-first search algorithms.
Algorithms and data Chapter 3 V Graph.pptxzerihunnana
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.
The document discusses graph representations and algorithms. It describes two common graph representations: adjacency matrix and adjacency list. It then explains traversal algorithms like breadth-first search and depth-first search. Spanning trees and minimum spanning trees are discussed along with Prim's and Kruskal's algorithms. Finally, it covers the single source shortest path problem and Dijkstra's algorithm for solving it on weighted graphs.
The document discusses graphs and graph algorithms. It defines what a graph is - a non-linear data structure consisting of vertices connected by edges. It describes different graph representations like adjacency matrix, incidence matrix and adjacency list. It also explains graph traversal algorithms like depth-first search and breadth-first search. Finally, it covers minimum spanning tree algorithms like Kruskal's and Prim's algorithms for finding minimum cost spanning trees in graphs.
This document discusses topological sorting and strongly connected components in directed graphs. It defines topological sorting as a linear ordering of the vertices in a directed acyclic graph such that for every edge from vertex u to v, u comes before v in the ordering. It presents Kahn's algorithm for performing topological sorting in O(V+E) time. It also defines strongly connected components as maximal sets of vertices such that there is a path between every pair, and presents an algorithm to find the strongly connected components in a graph in O(V+E) time using depth-first search on the transpose graph.
Graphs are propular to visualize a problem . Matrix representation is use to convert the graph in a form that used by the computer . This will help to get the efficent solution also provide a lots of mathematical equation .
This document provides an introduction to graph theory concepts. It defines what a graph is consisting of vertices and edges. It discusses different types of graphs like simple graphs, multigraphs, digraphs and their properties. It introduces concepts like degrees of vertices, handshaking lemma, planar graphs, Euler's formula, bipartite graphs and graph coloring. It provides examples of special graphs like complete graphs, cycles, wheels and hypercubes. It discusses applications of graphs in areas like job assignments and local area networks. The document also summarizes theorems regarding planar graphs like Kuratowski's theorem stating conditions for a graph to be non-planar.
The document describes depth-first search (DFS) and breadth-first search (BFS) graph traversal algorithms. DFS uses a stack and processes each node by first exploring all of its neighbor nodes before backtracking, while BFS uses a queue and processes nodes level-by-level from the starting node outwards. Both algorithms initialize all nodes as ready, process nodes by changing their status, and add neighboring ready nodes to the stack/queue to change their status to waiting.
The document discusses breadth-first search (BFS) algorithms for graphs. It explains that BFS runs in O(n^2) time on adjacency matrices due to checking all elements in each row, but in O(n+m) time on adjacency lists where m is the number of edges. It then describes how to modify BFS to record the shortest path between nodes using a predecessor array. The rest of the document provides examples of how BFS works and applications such as finding connected components and directed acyclic graphs.
This document defines and provides examples of graphs and graph representations. It begins by discussing Euler's use of graphs to solve the Königsberg bridge problem. It then defines graphs formally as G=(V,E) with vertices V and edges E. Examples of undirected and directed graphs are given. Common graph terms like paths, cycles, and connectivity are defined. Methods of representing graphs through adjacency matrices and adjacency lists are described and examples are provided. Finally, the document briefly discusses graph traversal algorithms and the concept of weighted edges.
Breadth First Search & Depth First SearchKevin Jadiya
The slides attached here describes how Breadth first search and Depth First Search technique is used in Traversing a graph/tree with Algorithm and simple code snippet.
This document defines key graph terminology and concepts. It begins by defining what a graph is composed of - vertices and edges. It then discusses directed vs undirected graphs and defines common graph terms like adjacent vertices, paths, cycles, and more. The document also covers different ways to represent graphs, such as adjacency matrices and adjacency lists. Finally, it briefly introduces common graph search methods like breadth-first search and depth-first search.
topologicalsort-using c++ as development language.pptxjanafridi251
topological sort using c++ as programming language to search through a tree structureknljhcffxgchjkjhlkjkfhdffxgchvjbknlkjhgchvjbkjxfghjhiyuighjbyfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffvgvvvvvvvvnbbbbbbbbbfuyfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
Thompson's construction algorithm converts regular expressions to nondeterministic finite automata (NFAs) by recursively building the NFA for each subexpression. The subset construction algorithm converts NFAs to deterministic finite automata (DFAs) by constructing states that correspond to sets of NFA states, and transitions correspond to the reachable states on each input symbol. Converting regular expressions to NFAs to DFAs shows that regular expressions, NFAs, and DFAs all have equivalent expressive power for describing regular languages.
Graphs are useful tools for modeling problems and consist of vertices and edges. Breadth-first search (BFS) is an algorithm that visits the vertices of a graph starting from a source vertex and proceeding to visit neighboring vertices first, before moving to neighbors that are further away. BFS uses a queue to efficiently traverse the graph and discover all possible paths from the source to other vertices, identifying the shortest paths in an unweighted graph. The time complexity of BFS on an adjacency list representation is O(n+m) where n is the number of vertices and m is the number of edges.
This document discusses graphs and graph data structures. It defines a graph as a pictorial representation of a set of objects connected by links, with the objects represented as vertices and the links as edges. It provides definitions and examples of basic graph terminology like vertices, edges, adjacency, and different types of graphs like directed vs undirected graphs. It also covers graph implementations using adjacency matrices and adjacency lists, as well as common graph algorithms like depth-first search and breadth-first search. Finally, it lists some applications of graphs like social networks, maps, and computer networks.
End-to-end pipeline agility - Berlin Buzzwords 2024Lars Albertsson
We describe how we achieve high change agility in data engineering by eliminating the fear of breaking downstream data pipelines through end-to-end pipeline testing, and by using schema metaprogramming to safely eliminate boilerplate involved in changes that affect whole pipelines.
A quick poll on agility in changing pipelines from end to end indicated a huge span in capabilities. For the question "How long time does it take for all downstream pipelines to be adapted to an upstream change," the median response was 6 months, but some respondents could do it in less than a day. When quantitative data engineering differences between the best and worst are measured, the span is often 100x-1000x, sometimes even more.
A long time ago, we suffered at Spotify from fear of changing pipelines due to not knowing what the impact might be downstream. We made plans for a technical solution to test pipelines end-to-end to mitigate that fear, but the effort failed for cultural reasons. We eventually solved this challenge, but in a different context. In this presentation we will describe how we test full pipelines effectively by manipulating workflow orchestration, which enables us to make changes in pipelines without fear of breaking downstream.
Making schema changes that affect many jobs also involves a lot of toil and boilerplate. Using schema-on-read mitigates some of it, but has drawbacks since it makes it more difficult to detect errors early. We will describe how we have rejected this tradeoff by applying schema metaprogramming, eliminating boilerplate but keeping the protection of static typing, thereby further improving agility to quickly modify data pipelines without fear.
State of Artificial intelligence Report 2023kuntobimo2016
Artificial intelligence (AI) is a multidisciplinary field of science and engineering whose goal is to create intelligent machines.
We believe that AI will be a force multiplier on technological progress in our increasingly digital, data-driven world. This is because everything around us today, ranging from culture to consumer products, is a product of intelligence.
The State of AI Report is now in its sixth year. Consider this report as a compilation of the most interesting things we’ve seen with a goal of triggering an informed conversation about the state of AI and its implication for the future.
We consider the following key dimensions in our report:
Research: Technology breakthroughs and their capabilities.
Industry: Areas of commercial application for AI and its business impact.
Politics: Regulation of AI, its economic implications and the evolving geopolitics of AI.
Safety: Identifying and mitigating catastrophic risks that highly-capable future AI systems could pose to us.
Predictions: What we believe will happen in the next 12 months and a 2022 performance review to keep us honest.
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdfGetInData
Recently we have observed the rise of open-source Large Language Models (LLMs) that are community-driven or developed by the AI market leaders, such as Meta (Llama3), Databricks (DBRX) and Snowflake (Arctic). On the other hand, there is a growth in interest in specialized, carefully fine-tuned yet relatively small models that can efficiently assist programmers in day-to-day tasks. Finally, Retrieval-Augmented Generation (RAG) architectures have gained a lot of traction as the preferred approach for LLMs context and prompt augmentation for building conversational SQL data copilots, code copilots and chatbots.
In this presentation, we will show how we built upon these three concepts a robust Data Copilot that can help to democratize access to company data assets and boost performance of everyone working with data platforms.
Why do we need yet another (open-source ) Copilot?
How can we build one?
Architecture and evaluation
Learn SQL from basic queries to Advance queriesmanishkhaire30
Dive into the world of data analysis with our comprehensive guide on mastering SQL! This presentation offers a practical approach to learning SQL, focusing on real-world applications and hands-on practice. Whether you're a beginner or looking to sharpen your skills, this guide provides the tools you need to extract, analyze, and interpret data effectively.
Key Highlights:
Foundations of SQL: Understand the basics of SQL, including data retrieval, filtering, and aggregation.
Advanced Queries: Learn to craft complex queries to uncover deep insights from your data.
Data Trends and Patterns: Discover how to identify and interpret trends and patterns in your datasets.
Practical Examples: Follow step-by-step examples to apply SQL techniques in real-world scenarios.
Actionable Insights: Gain the skills to derive actionable insights that drive informed decision-making.
Join us on this journey to enhance your data analysis capabilities and unlock the full potential of SQL. Perfect for data enthusiasts, analysts, and anyone eager to harness the power of data!
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The Building Blocks of QuestDB, a Time Series Databasejavier ramirez
Talk Delivered at Valencia Codes Meetup 2024-06.
Traditionally, databases have treated timestamps just as another data type. However, when performing real-time analytics, timestamps should be first class citizens and we need rich time semantics to get the most out of our data. We also need to deal with ever growing datasets while keeping performant, which is as fun as it sounds.
It is no wonder time-series databases are now more popular than ever before. Join me in this session to learn about the internal architecture and building blocks of QuestDB, an open source time-series database designed for speed. We will also review a history of some of the changes we have gone over the past two years to deal with late and unordered data, non-blocking writes, read-replicas, or faster batch ingestion.
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataKiwi Creative
Harness the power of AI-backed reports, benchmarking and data analysis to predict trends and detect anomalies in your marketing efforts.
Peter Caputa, CEO at Databox, reveals how you can discover the strategies and tools to increase your growth rate (and margins!).
From metrics to track to data habits to pick up, enhance your reporting for powerful insights to improve your B2B tech company's marketing.
- - -
This is the webinar recording from the June 2024 HubSpot User Group (HUG) for B2B Technology USA.
Watch the video recording at https://youtu.be/5vjwGfPN9lw
Sign up for future HUG events at https://events.hubspot.com/b2b-technology-usa/
2. What is a Graph?
A data Structure that consists of a set of
nodes(vertices) and a set of edges that relate the node
to each other.
The set of edges describes relationship among the
vertices.
edge
Node
3. Formal Definition Of Graphs
A graph G is defined as follows:
G=(V,E)
V: set of vertices
E:set of edges connecting the vertices in V
An edge e=(u , v) is a pair of vertices
Example:
a b
c d
e
V={a,bc,d,e}
E={(a,b),(a,c),(a,d),(b,e)
,(c,d),(c,e),(d,e)}
4. When the edges in a graph have no direction , the
graph is called undirected.
When the edges in a graph have a direction , the graph
is called directed.
Undirected edge Directed edge
a b a b
1
2
5
4
3
1
2
5
4
3
Undirected Graph Directed Graph
5. Adjacent nodes : two nodes are adjacent if they are
connected by an edge.
Path : a sequence of vertices that connect two nodes
in a graph
Simple path : A simple path is a path in which all
vertices , except possibly in the first and last ,are
different.
Complete Graph: a graph in which every vertex is
directly connected to every other vertex
a b
A is adjacent to b
7. Adjacency matrix
Let G=(V , E) be a graph with n vertices.
The adjacency matrix of G is a two dimensional array n by
n , say A[5][5].
A B
C D
E
(A) 1
(B) 2
(C) 3
(D)4
(E)5
(A)1 (B)2 (C)3 (D)4 (E)5
0 1 1 1 0
01 0 1 0
1 0 0 1 1
1 1 1 0 1
0 0 1 1 0
When the adjacent vertices of a graph is represented in the form of matrix
then such type of representation is called Adjacency Matrix
Representation of graph. E.g. A[i][j]
Number of rows = Number of Column
A ij =
O , if Vi is not adjacent to Vj
1 , if Vi , Vj is adjacent
8. Adjacency lists
B C
E
A D
NODE ADJACENCY LIST
A B , C , D
B C
C NULL
D C , E
E C
When the vertices of graph are represented by the linked
list then such type of representation is called adjacency list
representation of graph.
9. Traverse all node in the graph.
Methods
* Breadth – First Search
*Depth - First Search
10. Breadth First Search(BFS)
*BFS uses queue.
Logic
*During execution of algorithms , each node N of G will be
in one of three states called status of N:
- STATUS = 1(Ready state)
- STATUS = 2(Waiting state)
- STATUS= 3(Processed state)
11. ED
C
F
A
B
Algorithm
1.Initialize all nodes to the ready state
(STATUS=1)
2.Put the starting node A in Queue and
change its status to the waiting state
(STATUS=2)
3. [LOOP]
Repeat steps 4 and 5 until queue is empty
4. Remove the front node N of Queue.
Process N and change the status of N to
the processed state (STATUS=3)
5. Add to the rear of queue all the
neighbors of N that are in ready state
(STATUS=1), and change their status to
waiting state (STATUS=2).
[End of Loop]
6. Exit
12. A
ED
CB
F
1.Initialize all nodes to the ready state
(STATUS=1)
1
1
1
1
1
1
2.Put the starting node A in Queue and
change its status to the waiting state
(STATUS=2)
A
2 1.Initialize all nodes to the ready state
(STATUS=1)
2.Put the starting node A in Queue and
change its status to the waiting state
(STATUS=2)
3. [LOOP]
Repeat steps 4 and 5 until queue is
empty
4. Remove the front node N of Queue.
Process N and change the status of N
to the processed state (STATUS=3)
5. Add to the rear of queue all the
neighbors of N that are in ready state
(STATUS=1), and change their status to
waiting state (STATUS=2).
[End of Loop]
6. Exit
3
B C E
2 2
2
D F
3
2
2
3
3
3
3
B
A
C E
D F
Traversing order – A B C E D F
13. Depth First Search (DFS)
* DFS uses stack
*During execution of algorithms , each node N of G will be
in one of three states called status of N:
- STATUS = 1(Ready state)
- STATUS = 2(Waiting state)
- STATUS= 3(Processed state)
Logic
14. A F
D
C E
B
1.Initialize all nodes to the ready state
(STATUS=1)
2.Push the starting node A onto stack
and change its status to the waiting state
(STATUS=2)
3. [LOOP]
Repeat steps 4 and 5 until stack is
empty
4. Pop the top node N of Stack.
Process N and change the status of N
to the processed state (STATUS=3)
5. Push onto Stack all the neighbors of
N that are still in ready state
(STATUS=1), and change their status to
waiting state (STATUS=2).
[End of Loop]
6. Exit
Algorithm
15. A F
D
C E
B
1.Initialize all nodes to the ready state
(STATUS=1)
1
1
11
1
1
2.Push the starting node A onto stack
and change its status to the waiting state
(STATUS=2)
A
2
A
1.Initialize all nodes to the ready state
(STATUS=1)
2.Push the starting node A onto stack
and change its status to the waiting state
(STATUS=2)
3. [LOOP]
Repeat steps 4 and 5 until stack is
empty
4. Pop the top node N of Stack.
Process N and change the status of N
to the processed state (STATUS=3)
5. Push onto Stack all the neighbors of
N that are still in ready state
(STATUS=1), and change their status to
waiting state (STATUS=2).
[End of Loop]
6. Exit
A
B
C
3
2
2
C
3
D
E
2
2
E
3
F
2
F
3
3 3
D B