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Title Layout
• Subtitle
Course: CSE134 (Data Structure)
Course Teacher: Mr. A. S. M. Farhan Al Haque (ASMFH)
Section: P Group: A Depertment: CSE(4...
Going to tell about…….
Graph
• Definition of Graph
• Adjacent Node
• Degree of Graph
• Isolated Node
• Path
• Closed Path
...
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.
•...
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,...
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(2,5,4,1...
Isolated Node
• If the degree of a node is 0, that
means , a node which has no
connection with other other
nodes is called...
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 ...
Closed Path
• The path said to be closed if the
starting point of path from a node &
finishing point of that path will sam...
Simple Path
• A path where is no repeatation of any
node which is involved in that path
previously.
Here, bec is a simple ...
Connected Graph
• A graph is connected when there is
a path between every pair of
vertices.
Labelled Graph
• A graph is to be labeled if its edges
& vertices are assigned data.
Multiple Edges & Loop
• MULTIPLE EDGES: Edges have the same pair of end points.
• LOOP: An edge whose end points are equal.
Multiple Graph
• A graph consisting of
Multiple Edges &
Loop
Graph Types
• There are two type of graph:
Directed Graph Undirected Graph
Directed Graph
• A graph where every node has a
direction by using edges of that node.
Here , A -> B , A->C & B->C are dir...
Complete Graph
A graph where every Node is
interconnected with all nodes in a
graph.
Null Graph
• A graph which has no edges between nodes
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,...
What is Heap?
• Heap is a tree with some special properties.
• The basic requirement of a heap is that the value of a node...
Type of heap
• Heap is two type basically.
1. Min Heap
2. Max Heap
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...
Max Heap
• ● A max-heap is a binary tree
such that. - the data contained in
each node is greater than (or
equal to) the da...
Representation of Heap
• Heap can be represent by using
arrays
 Data of Node from Almost Binary
Tree(ALT) will serially i...
Determine Child
Process of Determine Child of a Heap from an array
Heapify Process
Process of Determine Parent of a Heap from an array
Graph & Heap in Data Structure (Basic Information)
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Graph & Heap in Data Structure (Basic Information)

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This Slide is made of many basic thoughts of Graph & Heap which are a part of data structure.It's was our university group presentation slide which was completely made by me with the help of some information from google.I hope that will help us for understanding Graph & Heap easily.

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Graph & Heap in Data Structure (Basic Information)

  1. 1. Title Layout • Subtitle
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 11. Connected Graph • A graph is connected when there is a path between every pair of vertices.
  12. 12. Labelled Graph • A graph is to be labeled if its edges & vertices are assigned data.
  13. 13. Multiple Edges & Loop • MULTIPLE EDGES: Edges have the same pair of end points. • LOOP: An edge whose end points are equal.
  14. 14. Multiple Graph • A graph consisting of Multiple Edges & Loop
  15. 15. Graph Types • There are two type of graph: Directed Graph Undirected Graph
  16. 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. 17. Complete Graph A graph where every Node is interconnected with all nodes in a graph.
  18. 18. Null Graph • A graph which has no edges between nodes
  19. 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. 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. 21. Type of heap • Heap is two type basically. 1. Min Heap 2. Max Heap
  22. 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. 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. 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. 25. Determine Child Process of Determine Child of a Heap from an array
  26. 26. Heapify Process Process of Determine Parent of a Heap from an array

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