data structures acm executive body 2k11. a series of elements of same type placed in contiguous...

DATA STRUCTURESACM EXECUTIVE BODY

2k11

A series of elements of same type

Placed in contiguous memory locations

Can be individually referenced by adding an index to a unique identifier

Example: Sort 10^7 numbers ranging from 100 to

200.

ARRAY

Abstract Data Types (ADTs) or data structures or collections store data and allow various operations on the data to access and change it

Why Abstract?◦ Specify the operations of the data structure and

leave implementation details to later

Every collection ADT provides a way to : insert, remove, find and access a data item

Abstract Data Type (ADT)

Last In First Out (LIFO)

Operations◦ Push◦ Pop◦ Top◦ isEmpty (Underflow)◦ isFull (Overflow)

STACK

Data 4

Data 3

Data 2

Data 1

Infix to Postfix Conversion

Matching tags in XML/HTML

Undo sequence in a text editor

Implementing functional calls (Recursion)

History of Web Browsers

Applications of Stack

Balancing Of Parenthesis◦ Given a sequence of ‘(‘ and ‘)’◦ Validate the sequence◦ A sequence is valid if for every ‘(‘, there is a

counter-balancing ‘)’ which occurs only later in the sequence

◦ Examples (()()()) : Valid (()(() : Invalid )()()( : Invalid

Problems

Nearest Smaller Element◦ Given a sequence of integers◦ For every integer, output the nearest integers to

the left and to the right which are smaller to it.◦ If there is no such number, output -1.

◦ Example 3 1 5 4 6 (-1,1) (-1,-1) (1,4) (1,-1) (4,-1)

Problems

Maximum Rectangle Area in a Histogram

Maximum Rectangular Area = 4x6 = 24

Problems

7

3

8

6

9

78

Water Harvesting◦ Find the maximum volume of water that can be collected in

between the adjacent buildings

◦ Maximum Volume Of Water Collected = 1 + 4 + 4 = 9

Problems

7

3

8

67 7

84

1

4

First In First Out (FIFO)

Operations◦ Enqueue (Insert)◦ Dequeue (Remove)◦ Front◦ Rear / Back◦ isEmpty◦ isFull

Queue

Data 1 Data 2 Data 3 Data 4

Operating System Job Scheduling

Breadth First Traversal of a Graph

Level Order Traversal of a Binary Tree

Applications

Print first 100 numbers comprising only of 1s, 3s and 5s.

The first few numbers in the sequence are 1,3,5, 11,13,15,31,33,35,51,53,55, 111,113,115,131,133,135,151,153,155,311,313...

and so on.

Problem

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Circular Queue Complete use of

space

Uses single, fixed size buffer, as if it were connected from end to beginning

An generalized queue, for which elements can be added to or removed from either the front or the rear.

Operations:◦ PushBack◦ PushFront◦ PopBack◦ PopFront◦ Front◦ Back

Deque

Given an array and an integer k, find the maximum element for each and every sub-array of size k

Example:

◦ a = [ 8 , 5, 10, 7, 9, 4, 15, 12, 19, 13 ]◦ k = 4

◦ Output : [ 10, 10, 10, 15, 15, 19, 19 ]

Problems on Deque

Input Restricted Deque◦ Deletion can be made from both ends◦ Insertion can be made at one end only

Output Restricted Deque◦ Insertion can be made at both ends◦ Deletion can be made at one end only

Variations of Deque

Standard Template Library

Part of ISO standard C++ library

Why Use STL◦ Reduces Development time

◦ Highly Reliable Code ( no or small amount of debugging effort required )

◦ Highly Robust ( Container size grows automatically )

◦ Portable and easily maintainable

STL

Templates allow the usage of generic types◦ Advantage: no need of writing the same code all over again

for a different data type

Example:◦ template <class X> // X can represent any data type that support the operations

class ABC { ABC() { }

public: getMax(X a, X b)

{ return (a > b ? a: b); } };

ABC <double> a; max_val = a.getMax(15.30, 53.12);

Templates

Including the library◦ #include<stack>

Declaration◦ stack <int> s;

Push Operation◦ s.push(5);

Pop Operation◦ s.pop();

Access the Top Element◦ int x = s.top();

Check if Stack is Empty◦ if ( s.empty() ) cout<< “ Stack is Empty ” << endl;

STL - Stack

Including the library◦ #include<queue>

Declaration◦ queue <int> q;

Push Operation◦ q.push(5);

Pop Operation◦ q.pop();

Access the Top Element◦ int x = q.front();

Check if Stack is Empty◦ if ( q.empty() ) cout<< “ Queue is Empty ” << endl;

STL - Queue

Including the library◦ #include<deque>

Declaration◦ deque <int> dq;

Push Operation◦ dq.push_back(5);◦ dq.push_front(5);

Pop Operation◦ dq.pop_back();◦ dq.pop_front();

Access the front and back elements◦ int x = dq.front(); int y = dq.back();

Check if Stack is Empty◦ if ( dq.empty() ) cout<< “ Deque is Empty ” << endl;

STL - Deque

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STL-Map Introduction Associative data structure

◦ a value is associated with the key

Stores the values in an order, sorted by the key values.

Internally implemented as a balanced BST

Multimap is used if multiple associated entries are allowed for same key values.

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STL- Map Including the library

◦ #include<map>

Declaring a map◦ map<string, int>m;

Inserting a value◦ m.insert( pair<string, int > ("abc", 2);◦ m["abc"]=2;

Finding a value◦ if( m.find("abc") != m.end() ) cout << "Not found" << endl;

Clear all entries◦ m.clear();

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STL- Pair and Vector Vector

◦ Dynamic array of variables, struct or objects of same type

◦ Resizes itself when inserting or erasing an element

Pair◦ A simple associative container consisting of a 2-

tuple of data elements or objects, denoted by ‘first' and ‘second'

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STL- Vector Including the library

◦ #include<vector>

Declaration◦ vector<int>v; //1-D◦ vector<int>v[10000] ; //2-D

Pushing a value◦ v.push_back(5); //1-D◦ v[i].push_back(5); //2-D

Removing a value◦ v.pop_back(); //1-D

Accessing an element at position i◦ int x= v[i]; //1-D

Clear all entries◦ v.clear(); //1-D

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STL- Pair Including the library

◦ #include<utility>

Declaration◦ pair<string, int> p;

Definition◦ p = make_pair("abc",10);

Accessing the elements◦ p.first ◦ p.second

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STL-Set Used to store unique elements in a sorted

order

Elements in a set can't be modified once they has been inserted. But they can be inserted or removed from the container.

Internally implemented as balanced BST

Multiset can be used to allow duplicate entries

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STL-Set Library to be included

◦ #include<set>

Declaration◦ set<int>s;

Inserting an element◦ s.insert(5);

Removing an element◦ s.erase(5);

Get the size of the set◦ int x= s.size();

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Useful functions int a[]={1,2,2,3,5}; vector<int> v ( a, a+5 ) ;

◦ sort ( a, a+5 ); // sort an array◦ sort ( v.begin(), v.end() ); // sort a vector

◦ next_permutation( a, a+5 ); find next permutation of elements of array

◦ prev_permutation( a, a+5 );

◦ lower_bound( v.begin(), v.end(), 2); find the first occurence of a value in a sorted container

◦ upper_bound( v.begin(), v.end(), 2 );

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Using Iterators Used with map, vector and set

Iterator: vector<int>::iterator it; //declaration it = v.begin(); // points to start of the container it = v.end(); //points to end of the container

◦ Other operations: it++ ; it-- ; it != m.end() ;

Reverse Iterator: iterates in a reverse fashion from end to beginning vector<int>::reverse_iterator it; it = v.rbegin(); it = v.rend();

If you have any problem solving a question or understanding some concept , feel free to bug us, we will be happy to debug you…

ACM Executive body 2014-15

o Nimesh Ghelani: nimeshghelani@gmail.como Prem Kamal: premkamal008@gmail.como Utkarsh Raj: raj.utkarsh1992@gmail.como Rishikesh Jha: rishi.jha15@gmail.como Vivek Verma: verma.vivek0786@gmail.como Nischal Kumar: nischal1251.11@bitmesra.ac.ino Chandan Agarwal: agarwalchand23@gmail.com o Sanket Singhal: sanketsinghal19@gmail.como Aparajita Choudhary: aparchoudhary@gmail.como Bhavini Mishra: bhavini.shruti@gmail.com

Happy Coding…

04/19/23