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- 1. Title Layout • Subtitle
- 2. Course: CSE134 (Data Structure) Course Teacher: Mr. A. S. M. Farhan Al Haque (ASMFH) Section: P Group: A Depertment: CSE(43 Batch) Group Members: 01. Md. Ashaf Uddaula (161-15-7473) 02. Alamin Hossain (161-15-7483) 03. Md. Khasrur Rahman (161-15-7214) 04. Md. Eram Talukder (161-15-7485) 05. Ijaz Ahmed Utsa (161-15-7180)
- 3. Going to tell about……. Graph • Definition of Graph • Adjacent Node • Degree of Graph • Isolated Node • Path • Closed Path • Simple Path • Connected Graph • Labelled Graph • Multiple Edges & Loop • Multi Graph • Graph Types • Directed Graph • Complete Graph • Null Graph • Sub-Graph Heap • Definition of Heap • Type of heap • Min Heap • Max Heap • Representation of Heap • Determine Child • Heapify Process
- 4. What is Graph? • A collection of Nodes(v1,v2,v3,v4,v5,v6) & connected by Edges(e1,e2,e3,e4,e5,e6). • Abstract Data Type. • In Mathematically, A graph G is composed by a set V of vertices or node connected through a set E of edges or links. Here, V={v1,v2,v3,v4,v5,v6} & E={e1,e2,e3,e4,e5,e6} Then , Graph G will be the sets of V & E, Graph, G = {V,E}
- 5. Adjacent Node • Two Nodes are adjacent if they are connected via only one edge. • Here, (1,7),(7,6),(6,5),(5,4),(4,3), (3,2),(2,1) every node of every pair is an adjacent node.
- 6. Degree of Graph • The number of edges of a node Here, the degree of Node Number , 1 is 2(5,2) Node Number , 2 is 4(2,5,4,14) Node Number , 3 is 2(14,34) Node Number , 4 is 3(5,5,58) Node Number , 5 is 3(4,34,58)
- 7. Isolated Node • If the degree of a node is 0, that means , a node which has no connection with other other nodes is called Isolated Node. Here, f is an isolated node.
- 8. Path • A sequence of vertices that connected two nodes in a graph Here, p=n-1 ;p=the length of a path which is called the length of number of edges. ;n=Number of Nodes
- 9. Closed Path • The path said to be closed if the starting point of path from a node & finishing point of that path will same , that type of path can called closed path. Here, H->D->G->H is a closed path B->D->C->B is a closed path F->D->E->F is a closed path
- 10. Simple Path • A path where is no repeatation of any node which is involved in that path previously. Here, bec is a simple path but, acda is not a simple path, that type of path is called cycle.
- 11. Connected Graph • A graph is connected when there is a path between every pair of vertices.
- 12. Labelled Graph • A graph is to be labeled if its edges & vertices are assigned data.
- 13. Multiple Edges & Loop • MULTIPLE EDGES: Edges have the same pair of end points. • LOOP: An edge whose end points are equal.
- 14. Multiple Graph • A graph consisting of Multiple Edges & Loop
- 15. Graph Types • There are two type of graph: Directed Graph Undirected Graph
- 16. Directed Graph • A graph where every node has a direction by using edges of that node. Here , A -> B , A->C & B->C are directed .
- 17. Complete Graph A graph where every Node is interconnected with all nodes in a graph.
- 18. Null Graph • A graph which has no edges between nodes
- 19. Sub-Graph • All the edges and vertices of (a) might not be present in M1,M2,M3,M4; but if a vertex is present in M1,M2,M3,M4, it has a corresponding vertex in (a) and any edge that connects two vertices in M1,M2,M3,M4 will also connect the corresponding vertices in (a).
- 20. What is Heap? • Heap is a tree with some special properties. • The basic requirement of a heap is that the value of a node must be >=(or,<=) to the values of its children. • Tree must be made an almost binary tree(ABT).
- 21. Type of heap • Heap is two type basically. 1. Min Heap 2. Max Heap
- 22. Min Heap • A min-heap is a binary tree such that. - the data contained in each node is less than (or equal to) the data in that node's children. - the binary tree is complete.
- 23. Max Heap • ● A max-heap is a binary tree such that. - the data contained in each node is greater than (or equal to) the data in that node's children
- 24. Representation of Heap • Heap can be represent by using arrays Data of Node from Almost Binary Tree(ALT) will serially input in a declare array with the sequence of Root Left Right
- 25. Determine Child Process of Determine Child of a Heap from an array
- 26. Heapify Process Process of Determine Parent of a Heap from an array

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