Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

Basic Element of Data Structures like linked list, stack and queue, trees, Graph,recursion Introduction to basic element of data structure • Basic technique for improving algorithm is to structure the data in such a way that the resulting operation can be efficiently carried out. • They are 1. Linked list 2. Stack 3. Queue 4. Tree 5. Graph Linked list • Linked list is a collection of element in which each element is pointing to next element. Types of linked list are 1. Single linked list 2. Double linked list Operation on linked list are 1. Add 2. Delete 3. Traverse Stack • Stack is a list in which insertion & deletion are taking place at only one end called as top of the stack • Stack is a LIFO (Last in first out ) structure. E D C B A Top Stack Stack is implemented using 1. Array Representation 2. Linked list representation Basic operation on stack are 1. Add 2. Delete 3. Stack Top Operation on stack using array representation Algorithm Add(item) { If(top ≥ n-1) then { write(“Stack is full”);return false;} Else {top:=top+1;stack[top]:=item; return true;} } Algorithm Delete(item) { If(top<0) then {write(“Stack is empty!”); return false;} Else { item:=stack[top];top:=top-1;return true;} } Operation on stack using Linked representation of stack Node = record{ Type data; node*link; } Algorithm Add(item) { Temp:=new node; If(temp->data):=item;(temp->link):=top; Top:=temp; return true; } Algorithm delete(item) { If(top=0) then { Write(“Stack is empty!”); return false;} Else {item:=(top->data); temp:=top; top:=(top->link); delete temp; return true;} } Queue • An efficient Queue representation can be obtained by taking an array q[0:n-1] & treating it as if it were circular • Element are inserted by increasing the variable rear to the next free position • When rear=n-1, the next element is entered at q[0] in case that spot is free • Front always point one position counterclockwise from the first element in the queue • Time require to add & delete element in queue is o(1). Basic queue operation Algorithm AddQ(item) { Rear:=(rear+1) mod n; If(front=rear)then {Write(“Queue is full!”);If(front=0) then rear:=n-1;else rear:=rear-1;return false;} Else {q[rear]:=item; return true;} } Algorithm DeleteQ(item) { If(front=rear) then { write(“Queue is empty!”); return false; } Else {front :=(front + 1) mod n; item:=q[front]; return true; } } Tree • A tree is finite set of one or more nodes such that there is specially designed node called the root and remaining node are partitioned into n≥0 disjoint set.T1, T2,.. Tn, where each of these subset is a tree. The set set.T1, T2,.. Tn are called the sub tree of the root. Level & Degree • node (13) Level 1 A • • • • • • • • • • degree of a node B leaf (terminal) nonterminal E F parent children K L sibling degree of a tree (3) ancestor level of a node height of a tree (4) C G 2 D H M I J 3 4 Binary tree • Binary tree is a tree node where each node have 0, 1 or 2 children • Example A B D C E F Binary search tree • A binary search tree is a binary tree. It may be empty. If not empty, then it satisfies the following property. 1. Every element has a key and no two elements have the same key. 2. The key in the left subtree are smaller than the key in the root 3. The key in the right subtree are larger than the key in the root Graph • A data structure that consists of a set of nodes (vertices) and a set of edges that relate the nodes to each other • The set of edges describes relationships among the vertices . • A graph G is defined as follows: G=(V,E) V(G): a finite, nonempty set of vertices E(G): a set of edges (pairs of vertices) Directed vs. undirected graphs • When the edges in a graph have no direction, the graph is called undirected Graph terminology • 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 • Complete graph: a graph in which every vertex is directly connected to every other vertex Graph terminology (cont.) • What is the number of edges in a complete directed graph with N vertices? N * (N-1) 2 O( N ) Graph terminology (cont.) • What is the number of edges in a complete undirected graph with N vertices? N * (N-1) / 2 2 O(N ) Graph terminology (cont.) • Weighted graph: a graph in which each edge carries a value Graph implementation • Array-based implementation – A 1D array is used to represent the vertices – A 2D array (adjacency matrix) is used to represent the edges Array-based implementation Graph implementation (cont.) • Linked-list implementation – A 1D array is used to represent the vertices – A list is used for each vertex v which contains the vertices which are adjacent from v (adjacency list) Linked-list implementation Recursion? • Sometimes, the best way to solve a problem is by solving a smaller version of the exact same problem first • Recursion is a technique that solves a problem by solving a smaller problem of the same type Example of Recursion: factorial function • Recursive implementation int Factorial(int n) { if (n==0) // base case return 1; else return n * Factorial(n-1); } Coding the factorial function (cont.) • Iterative implementation int Factorial(int n) { int fact = 1; for(int count = 2; count <= n; count++) fact = fact * count; return fact; } Application • Application of stack is decimal to binary no. conversion, parse a tree. • Application of Queue is Memory queue • Application of tree is MST • Application of graph is Network