Kamran Ahmed
2 years ago
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# Directed graph |
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# Directed Graph |
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A directed graph is graph, i.e., a set of objects (called vertices or nodes) that are connected together, where all the edges are directed from one vertex to another. A directed graph is sometimes called a digraph or a directed network. In contrast, a graph where the edges are bidirectional is called an undirected graph. |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://en.wikipedia.org/wiki/Directed_graph'>Directed Graph</BadgeLink> |
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# Undirected graph |
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# Undirected Graph |
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An undirected graph is graph, i.e., a set of objects (called vertices or nodes) that are connected together, where all the edges are bidirectional. An undirected graph is sometimes called an undirected network. In contrast, a graph where the edges point in a direction is called a directed graph. |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://mathinsight.org/definition/undirected_graph'>Undirected Graph</BadgeLink> |
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# Spanning tree |
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# Spanning Tree |
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A spanning tree is a subset of Graph G, which has all the vertices covered with minimum possible number of edges. Hence, a spanning tree does not have cycles and it cannot be disconnected.. |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.tutorialspoint.com/data_structures_algorithms/spanning_tree.htm'>Spanning Tree</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=oolm2VnJUKw&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=13'>CSE373 2020 - Lecture 13 - Minimum Spanning Trees</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=RktgPx0MarY&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=14'>CSE373 2020 - Lecture 14 - Minimum Spanning Trees (con't)</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=tKwnms5iRBU&index=16&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp'>Greedy Algorithms: Minimum Spanning Tree</BadgeLink> |
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# Graph representation |
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# Graph Representation |
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A graph can either be represented as an adjacency matrix or an adjacency list. |
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The adjacency matrix is a 2D array of size `V x V` where `V` is the number of vertices in a graph. Let the 2D array be `adj[][]`, a slot `adj[i][j] = 1` indicates that there is an edge from vertex `i` to vertex `j`. |
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Adjacency list is an array of vectors. Size of the array is equal to the number of vertices. Let the array be `array[]`. An entry `array[i]` represents the list of vertices adjacent to the ith vertex. This representation can also be used to represent a weighted graph. The weights of edges can be represented as lists of pairs. |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.programiz.com/dsa/graph-adjacency-matrix'>Adjacency Matrix - Graph Representation</BadgeLink> |
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.programiz.com/dsa/graph-adjacency-list'>Adjacency List - Graph Representation</BadgeLink> |
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# Graph |
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# Graph |
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Graphs in data structures are non-linear data structures made up of a finite number of nodes or vertices and the edges that connect them. Graphs in data structures are used to address real-world problems in which it represents the problem area as a network like telephone networks, circuit networks, and social networks. |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.simplilearn.com/tutorials/data-structure-tutorial/graphs-in-data-structure'>Graph Data Structure</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=0sQE8zKhad0'>Graph Data Structure | Illustrated Data Structures</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=Sjk0xqWWPCc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=10'>CSE373 2020 - Lecture 10 - Graph Data Structures</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=ZTwjXj81NVY&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=11'>CSE373 2020 - Lecture 11 - Graph Traversal</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=KyordYB3BOs&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=12'>CSE373 2020 - Lecture 12 - Depth First Search</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=oolm2VnJUKw&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=13'>CSE373 2020 - Lecture 13 - Minimum Spanning Trees</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=RktgPx0MarY&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=14'>CSE373 2020 - Lecture 14 - Minimum Spanning Trees (con't)</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=MUe5DXRhyAo&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=15'>CSE373 2020 - Lecture 15 - Graph Algorithms (con't 2)</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=Aa2sqUhIn-E&index=15&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb'>6.006 Single-Source Shortest Paths Problem</BadgeLink> |
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# Bellman fords algorithm |
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# Bellman Ford's Algorithm |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=f9cVS_URPc0&ab_channel=MITOpenCourseWare'>Bellman-Ford - MIT</BadgeLink> |
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# Dijkstras algorithm |
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# Dijkstra's Algorithm |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=NSHizBK9JD8&t=1731s&ab_channel=MITOpenCourseWare'>Dijkstra's Algorithm - MIT</BadgeLink> |
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# Graph algorithms |
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# Graph Algorithms |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=i_AQT_XfvD8&index=6&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>Graph Algorithms I - Topological Sorting, Minimum Spanning Trees, Prim's Algorithm - Lecture 6</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=ufj5_bppBsA&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=7'>Graph Algorithms II - DFS, BFS, Kruskal's Algorithm, Union Find Data Structure - Lecture 7</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=DiedsPsMKXc&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=8'>Graph Algorithms III: Shortest Path - Lecture 8</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=XIAQRlNkJAw&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=9'>Graph Alg. IV: Intro to geometric algorithms - Lecture 9</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=RpgcYiky7uw'>Strongly Connected Components Kosaraju's Algorithm Graph Algorithm</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/playlist?list=PL9xmBV_5YoZO-Y-H3xIC9DGSfVYJng9Yw'>Shortest Path Algorithms (playlist) in 16 minutes</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/playlist?list=PL9xmBV_5YoZObEi3Hf6lmyW-CBfs7nkOV'>Minimum Spanning Trees (playlist) in 4 minutes</BadgeLink> |
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<BadgeLink colorScheme='purple' badgeText='Course' href='https://www.coursera.org/learn/algorithms-on-graphs'>Algorithms on Graphs - Coursera</BadgeLink> |
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# Dijkstras algorithm |
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# Dijkstra's Algorithm |
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<ResourceGroupTitle>Free Content</ResourceGroupTitle> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=NSHizBK9JD8&t=1731s&ab_channel=MITOpenCourseWare'>Dijkstra's Algorithm - MIT</BadgeLink> |
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=CHvQ3q_gJ7E&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb&index=18'>Speeding Up Dijkstra's Algorithm - MIT</BadgeLink> |
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