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![Multidimensional arrays
• A multi-dimensional array is an array of arrays. 2-dimensional
arrays are the most commonly used. They are used to store data in
a tabular manner.
• Consider following 2D array, which is of the size 3×5. For an array
of size N×M, the rows and columns are numbered
from 0 to N−1 and columns are numbered from 0 to M−1,
respectively. Any element of the array can be accessed
by arr[i][j] where 0≤i<N and 0≤j<M. For example, in the following
array, the value stored at arr[1][3] is 14.](https://image.slidesharecdn.com/datastructurepart2-210125170513/75/Data-structure-Part-2-13-2048.jpg)
![Cont…
• 2D array declaration:
• To declare a 2D array, you must specify the following:
• Row-size: Defines the number of rows
• Column-size: Defines the number of columns
• Type of array: Defines the type of elements to be stored in the
array i.e. either a number, character, or other such datatype. A
sample form of declaration is as follows:
• type arr[row_size][column_size]](https://image.slidesharecdn.com/datastructurepart2-210125170513/75/Data-structure-Part-2-14-2048.jpg)
Uploaded byDr. SURBHI SAROHA
Data structure(Part 2)
This document discusses different types of data structures including trees, binary search trees, and multidimensional arrays. It defines key tree terminology like root, child, parent, leaf nodes, and describes properties of binary search trees where the left subtree contains nodes with keys less than the parent node and the right subtree contains nodes with greater keys. It also provides an example of declaring and accessing elements in a two-dimensional array with rows and columns.
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Data structure(Part 2)
- 1.
- 2. Syllabus • Trees • Binarysearch trees • Multidimensional arrays
- 3. Trees • Trees: UnlikeArrays, Linked Lists, Stack and queues, which are linear data structures, trees are hierarchical data structures. • Tree Vocabulary: The topmost node is called root of the tree. • The elements that are directly under an element are called its children. • A tree is a nonlinear hierarchical data structure that consists of nodes connected by edges. • The element directly above something is called its parent. • For example, ‘a’ is a child of ‘f’, and ‘f’ is the parent of ‘a’. Finally, elements with no children are called leaves.
- 4. Example • tree • ---- •j <-- root • / • f k • / • a h z <-- leaves
- 5.
- 6. Tree Terminologies • Node •A node is an entity that contains a key or value and pointers to its child nodes. • The last nodes of each path are called leaf nodes or external nodes that do not contain a link/pointer to child nodes. • The node having at least a child node is called an internal node. • Edge • It is the link between any two nodes.
- 7. Cont… • Root • Itis the topmost node of a tree. • Height of a Node • The height of a node is the number of edges from the node to the deepest leaf (ie. the longest path from the node to a leaf node). • Depth of a Node • The depth of a node is the number of edges from the root to the node. • Height of a Tree • The height of a Tree is the height of the root node or the depth of the deepest node.
- 8. Cont…. • Degree ofa Node • The degree of a node is the total number of branches of that node. • Forest • A collection of disjoint trees is called a forest. • Types of Tree • Binary Tree • Binary Search Tree • AVL Tree • B-Tree
- 9. Binary search trees •Binary Search Tree is a node-based binary tree data structure which has the following properties: • The left subtree of a node contains only nodes with keys lesser than the node’s key. • The right subtree of a node contains only nodes with keys greater than the node’s key. • The left and right subtree each must also be a binary search tree.
- 10.
- 11. Cont….. • A BinarySearch Tree (BST) is a tree in which all the nodes follow the below- mentioned properties − • The value of the key of the left sub-tree is less than the value of its parent (root) node's key. • The value of the key of the right sub-tree is greater than or equal to the value of its parent (root) node's key. • Following are the basic operations of a tree − • Search − Searches an element in a tree. • Insert − Inserts an element in a tree. • Pre-order Traversal − Traverses a tree in a pre-order manner. • In-order Traversal − Traverses a tree in an in-order manner. • Post-order Traversal − Traverses a tree in a post-order manner.
- 12. Node • Define anode having some data, references to its left and right child nodes. • struct node { • int data; • struct node *leftChild; • struct node *rightChild; • };
- 13. Multidimensional arrays • Amulti-dimensional array is an array of arrays. 2-dimensional arrays are the most commonly used. They are used to store data in a tabular manner. • Consider following 2D array, which is of the size 3×5. For an array of size N×M, the rows and columns are numbered from 0 to N−1 and columns are numbered from 0 to M−1, respectively. Any element of the array can be accessed by arr[i][j] where 0≤i<N and 0≤j<M. For example, in the following array, the value stored at arr[1][3] is 14.
- 14. Cont… • 2D arraydeclaration: • To declare a 2D array, you must specify the following: • Row-size: Defines the number of rows • Column-size: Defines the number of columns • Type of array: Defines the type of elements to be stored in the array i.e. either a number, character, or other such datatype. A sample form of declaration is as follows: • type arr[row_size][column_size]
- 15.
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