Introduction to Data Structure and Algorithm Presented By: Pratik Mota

Objectives Basics of Data Structure and Algorithm

Practical Examples of where Data Structure Algorithms is used

Asymptotic Notations [ O(n), o(n), θ(n), Ω(n), ω(n) ]

Time and Space Complexity

GNU gprof basic

Basics of Data structure and Algorithm

Data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently.

Some Well-know Data structure

1) Array

2) List [Singly and Doubly Linked List]

3) Tree [ Binary,AVL, Red Black..etc ]

4) B+ Tree

5) Heap [ Max and Min Heap ]

6) Hashing

7) Graph [ BFS, DFS,..etc ]

Basics of Data structure and Algorithm

Algorithm is a step-by-step procedure for calculations OR you can tell it is sequence of program instructions designed to compute a particular result.

Examples:- Sorting, Searching, Shortest Path, Dynamic Programming, Numerical Algorithms etc..

Sort

INPUTsequence of numbers

a1, a2, a3,….,anb1,b2,b3,….,bn

OUTPUTa permutation of the sequence of numbers

2 5 4 10 7 2 4 5 7 10

Sorting Algorithm

Use of Data Structure and Algorithm

Practical Examples (Cont.)Backtrackin

g Indexing in Database

B-Tree and B+ Tree

Practical Examples (Cont.)Query Optimization

Algorithms

Parse Tree

Relational algebra Apply Optimization Mechanisms

Asymptotic Notations

1n

2n

3n

4n

5n

6n

Runnin

g t

ime

1 2 3 4 5 6 7 8 9 10 11 12 …..

best-case Ω(n)

average-case θ(n)

worst-case O(n)

Input instance size

o(n)

ω(n)

Basics of Complexity

O(1) < O(log n ) < O(n) < O(n log n ) < O(n^2) < ….. < O(n^k) < O(2^n)

O( n^2 + n + 1 ) => O(n^2) MAX ( f(n), g(n) )

O(N + a)^b O(N^b)

Time Complexity :- Amount of time taken by an algorithm to run.

Space Complexity:- Extra/Temporary Space use by algorithm .

MIN MAX

Time and Space Complexity

O(n) O(n^2) O( log n )

Time Complexity

Space Complexity :- Normally used/consider when Recursive functions comes. It is Depth of Recursion tree.

GNU gprof

Gprof is a profiling program which collects performance statistics of our programs.

For Performance analysis -pg option needed for GCC / g++ Compiler.

Ex:- g++ -pg gprof_test.cpp -o gprof_test

After running ./gprof_test , It generates gmon.out file.

gmon.out file contain Performance analysis statistics, which can be analyze using gprof tool. Ex:- gprof gprof_test gmon.out > analysis.txt

It provides mainly two type of Performance Analysis

1) Flat Profile [ Total amount of time your program spent executing each function ]

2) Call graph [ How much time was spent in each function and its children ]

Thank you..!!