COL106: Data Structures and Algorithms (IIT Delhi, Semester-II-2016-17)
Programming-4
There are 1 questions for a total of 100 points.
(100)
1. We would like to develop some software for Training and Placement (T&P cell) at IIT Delhi for helping
them to m
COL106: Data Structures and Algorithms (IIT Delhi, Semester-II-2016-17)
Programming-1
There are 1 questions for a total of 100 points.
(100)
1. The first programming assignment will involve working with large binary numbers and understanding
running time
COL106: Data Structures and Algorithms (IIT Delhi, Semester-II-2016-17)
Programming-3
There are 1 questions for a total of 100 points.
(100)
1. We would like to develop some software for Rendezvouz-2017 which will help you keep track of scores
in various
COL106: Data Structures and Algorithms (IIT Delhi, Semester-II-2016-17)
Programming-2
There are 1 questions for a total of 100 points.
(100)
1. The second programming assignment will involve using one data structure to implement another.
In lectures, we d
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COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Graph Algorithms
BFS application
Bipartite graph: A graph is bipartite i the vertices can be
partitioned into two sets such t
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Graph Algorithms
Connectivity
A graph may not always be connected.
A connected component in an undirected graph is a maximal
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures: Heaps and Priority Queues
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
H
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures: Tree
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
Tree ! Binary Tree
A b
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures: Balanced Binary Search Trees
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structure
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
Linked List
Linked List: A collection of nodes with linear ordering defined on
them.
Each node holds an eleme
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures: Hashing
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
Hashing
We have see
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures: Balanced Binary Search Trees
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structure
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
Multiway Search Trees ! (2,4)-Trees
Definition (2-4)-Tree)
A (2, 4)-Tree is a multiway search tree with the f
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures: Universal Hashing
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
Universal
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
Balanced Binary Search Trees ! AVL Trees
Question: How do we perform remove(k) operation on an AVL
tree?
Algo
COL106: Data Structures and Algorithms
Ragesh Jaiswal, IIT Delhi
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures: Heaps and Priority Queues
Ragesh Jaiswal, IIT Delhi
COL106: Data Structures and Algorithms
Data Structures
H
Chapter 5
Vector spaces and signal space
In the previous chapter, we showed that any L2 function u(t) can be expanded in various orthogonal expansions, using such sets of orthogonal functions as the T -spaced truncated sinusoids or
the sinc-weighted sinus
An Overview of Vector Spaces
ELL205 Signals and Systems
Prof. Shankar Prakriya
Indian Institute of Technology Delhi
August 8, 2016
Prof. Shankar Prakriya
An Overview of Vector Spaces ELL205 Signals and Systems
Contents
General Motivation
Introduction to M
Chapter 2
Systems
A system is a quantitative description of a physical process which transforms signals
(at its input) to signals (at its output). More precisely, a system is a black
box (viewed as a mathematical abstraction) that deterministically transf
Module 1 : Signals in Natural Domain
Problem 1
We are given a certain linear time - invariant system with impulse response
. We are told that when the input is
the output is
, which is sketched in figure below. We are then giventhe following set of inputs
ELL205 Signals and Systems
Tutorial II, 2016-2017
1. Perform GS orthogonalization to find a basis for the space spanned by x1 = [1, 1, 0]T , x2 =
[0, 1, 1]T and x3 = [1, 1, 1]T .
2. Find an orthonormal basis for the space spanned by u(t + 1) u(t 1), tu(t
k=0
with p(t), and sketch y(t) in the space provided below. Note: you need to clearly indicate
all important points on the axes - the sketch should be clear and unambiguous.
4. (8 marks) Consider ELL205
a system defined
by an impulse
h[n] = [n 4] + [n + 4
COL106: Data Structures, I Semester 2015-16
Assignment 4
A small search engine
October 2, 2015
In this assignment we will build the basic data structure underlying search
engines: an inverted index. We will use this inverted index to answer some
simple se
COL106: Data Structures, I Semester 2015-16
Assignment 6 and 7
An app-based taxi service
October 26, 2015
Nowadays services like Ola and Uber have become very popular. One
feature that makes them particularly attractive is that their apps inform you
of th
Department of Mathematics
MAL 145: Number Theory
Problems on Primes
These problems are taken from An Introduction to the Theory of Numbers by Niven, Zuckerman & Montgomery with minor changes.
1. Starting with any positive integer n, subtract double the un
Department of Mathematics
MTL 145: Number Theory
Problems on Divisibility
These problems are taken from An Introduction to the Theory of Numbers by Niven, Zuckerman & Montgomery with minor changes.
1. Find all integers x, y, z such that 6x + 10y + 15z = 1