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Live Training on data structure and algorithms

Course Content


 Introduction

  • Analysis of Algorithm 
  • Background analysis through a Program and its functions.
  • Order of Growth 
  • A mathematical explanation of the growth analysis through limits and functions.
  • A direct way of calculating the order of growth
  • Asymptotic Notations
  • Best, Average and Worst case explanation through a program.
  • Big O Notation
  • Graphical and mathematical explanation.
  • Calculation
  • Applications at Linear Search
  • Omega Notation
  • Graphical and mathematical explanation.
  • Calculation.
  • Theta Notation
  • Graphical and mathematical explanation.
  • Calculation.
  • Analysis of common loops
  • Single, multiple and nested loops
  • Analysis of Recursion
  • Various calculations through Recursion Tree method
  • Space Complexity 
  • Basic Programs
  • Auxiliary Space
  • Space Analysis of Recursion
  • Space Analysis of Fibonacci number


 Mathematics

  • Finding the number of digits in a number.
  • Arithmetic and Geometric Progressions.
  • Quadratic Equations.
  • Mean and Median.
  • Prime Numbers.
  • LCM and HCF
  • Factorials
  • Permutations and Combinations
  • Modular Arithmetic
  • Problems(With Video Solutions):
  • Count Digits
  • Palindrome Numbers
  • Factorial of Numbers
  • GCD of Two Numbers
  • LCM of Two Numbers
  • Check for Prime
  • Prime Factors
  • Sieve of Eratosthenes
  • Computing Power


 Bit Magic

  • Bitwise Operators
  • Operation of AND, OR, XOR operators
  • Operation of Left Shift, Right Shift and Bitwise Not
  • Method 1: Simple method
  • Method 2: Brian and Kerningham Algorithm
  • Method 3: Using Lookup Table
  • To check whether a number is a power of 2 or not
  • Odd occurrences in an array.
  • Two numbers having odd occurrences in an array.
  • Generate power set using bitwise operators.


 Recursion

  • Introduction to Recursion
  • Applications of Recursion
  • Writing base cases in Recursion
  • Factorial
  • N-th Fibonacci number
  • Various problems on Recursion(With Video Solutions)
  • Print n to 1
  • Print 1 to n
  • Tail Recursion
  • Checking Palindrome
  • Sum of digits
  • Rod cutting
  • Subsets of a set
  • Tower of Hanoi Problem
  • Josephus Problem


 Arrays

  • Types of Arrays
  • Fixed-sized array
  • Dynamic-sized array
  • Operations on Arrays
  • Searching
  • Insertions
  • Deletion
  • Arrays vs other DS
  • Reversing - Explanation with complexity
  • Problems(With Video Solutions)
  • Left Rotation of the array by 1
  • Check if Sorted
  • Left Rotation of the array by D places
  • Leaders in an Array
  • Maximum Difference Problem
  • Frequencies in Sorted Array
  • Stock Buy and Sell Problem
  • Trapping Rainwater Problem
  • Maximum Consecutive 1s
  • Maximum Subarray Sum
  • Longest Even-Odd Subarray
  • Maximum Circular sum subarray.
  • Majority Element
  • Minimum Consecutive Flips
  • Sliding Window Technique
  • Prefix Sum Technique


 Searching

  • Binary Search Iterative and Recursive
  • Binary Search and various associated problems
  • Index of First Occurence in Sorted Array
  • Index of Last Occurence in Sorted Array
  • Count of occurrences of x in sorted element
  • Count of 1s in a binary sorted array
  • Find an element in sorted and rotated array
  • Peak element
  • Find an element in an infinite sized sorted array
  • The square root of an integer
  • Find pair in an unsorted array which gives sum X
  • Find pair in a sorted array which gives sum X
  • Find triplet in an array which gives sum X
  • Median of two sorted arrays 
  • Majority Element 


 Sorting

  • Overview of Sorting Algorithms
  • Insertion Sort
  • Merge Sort
  • Problems(With Video Solutions)
  • Intersection of 2 sorted arrays
  • Union of 2 sorted arrays
  • Count Inversions in arrays
  • Partitions(With Video Solutions)
  • Naive
  • Lomuto
  • Hoare
  • Quick Sort
  • Using Lomuto and Hoare
  • Time and Space analysis
  • Choice of Pivot and Worst case
  • Tail call elimination
  • Problems(With Video Solutions)
  • Kth Smallest element
  • Chocolate Distribution Problem
  • Sorting arrays with 2 and3 types of elements
  • Merge Overlapping Intervals
  • Meeting the Maximum Guests
  • Cycle Sort
  • Counting Sort
  • Radix Sort
  • Bucket Sort


 Matrix

  • Introduction to Matrix
  • Multidimensional Matrix
  • Pass Matrix as Argument
  • Printing matrix in a snake pattern
  • Transposing a matrix
  • Rotating a Matrix
  • Check if the element is present in a row and column-wise sorted matrix.
  • Boundary Traversal
  • Spiral Traversal
  • Matrix Multiplication
  • Search in row-wise and column-wise Sorted Matrix


 Hashing

  • Introduction and Time complexity analysis
  • Application of Hashing
  • Discussion on Direct Address Table
  • Working and examples on various Hash Functions
  • Introduction and Various techniques on Collision Handling
  • Chaining and its implementation
  • Open Addressing and its Implementation
  • Chaining V/S Open Addressing
  • Double Hashing


 Strings

  • Given a string, check if they are an anagram of each other.
  • Given a string, find the leftmost character that repeats.
  • Given a string, find the leftmost character that does not repeat.
  • Given a string, find the lexicographic rank of it in O(n) time.
  • Implementation of the previously discussed lexicographic rank problem.
  • Given a text string and a pattern string, find if a permutation of the pattern exists in the text.
  • Given two strings, check if they are rotations of each other or not.
  • Various Pattern Searching Algorithms.
  • Rabin Karp Algorithm
  • KMP Algorithm


 Linked List

  • Introduction
  • Doubly Linked List
  • Circular Linked List
  • Loop Problems
  • Detecting Loops
  • Detecting loops using Floyd cycle detection
  • Detecting and Removing Loops in Linked List
  • Middle of Linked List
  • Nth node from the end of linked list
  • Deleting a Node without accessing Head pointer of Linked List
  • An iterative method to Reverse a linked list 
  • Recursive method to reverse a linked list
  • Reverse in group of size k
  • Segregating even-odd nodes of linked list
  • The intersection of two linked list
  • Pairwise swap nodes of linked list
  • Clone a linked list using a random pointer
  • LRU Cache Design
  • Merge two Sorted Linked Lists
  • Palindrome Linked List


 Stack

  • Understanding the Stack data structure 
  • Applications of Stack
  • Implementation of Stack in Array and Linked List
  • Balanced Parenthesis 
  • Two stacks in an array 
  • K Stacks in an array 
  • Stock span problem with variations
  • Previous Greater Element 
  • Next Greater Element 
  • Largest Rectangular Area in a Histogram
  • Understanding getMin() in Stack with O(1)


 Queue

  • Implementation of the queue using array and LinkedList
  • Stack using queue
  • Problems
  • Reversing a Queue
  • Generate numbers with given digits
  • First Circular Tour


 Deque


 Tree

  • Introduction
  • Tree
  • Application
  • Binary Tree
  • Tree Traversal
  • Implementation of:
  • Inorder Traversal 
  • Preorder Traversal 
  • Postorder Traversal 
  • Level Order Traversal (Line by Line)
  • Tree Traversal in Spiral Form 
  • Problems
  • Size of Binary Tree 
  • Maximum in Binary Tree 
  • Height of Binary Tree 
  • Print Nodes at K distance 
  • Print Left View of Binary Tree 
  • Children Sum Property 
  • Check for Balanced Binary Tree 
  • Maximum Width of Binary Tree 
  • Convert Binary Tree to Doubly Linked List 
  • Construct Binary Tree from Inorder and Preorder 
  • Tree Traversal Spiral Form
  • The diameter of a Binary Tree 
  • LCA problem with an efficient solution
  • Burn A Binary Tree from a Leaf
  • Count Nodes in a complete Binary Tree
  • Serialize and Deserialize a Binary tree


 Binary Search Tree


 Heap

  • Introduction & Implementation
  • Binary Heap 
  • Insertion
  • Heapify and Extract
  • Decrease Key, Delete and Build Heap
  • Heap Sort 
  • Problems
  • Sort K-Sorted Array 
  • Buy Maximum Items with Given Sum 
  • K Largest Elements 
  • Merge K Sorted Arrays 
  • Median of a Stream


 Graph

  • Introduction to Graph 
  • Graph Representation 
  • Adjacency Matrix
  • Adjacency List
  • Adjacency Matrix VS List
  • Breadth-First Search 
  • Applications
  • Depth First Search 
  • Applications
  • Problems
  • Shortest Path in an Unweighted Graph 
  • Detecting Cycle
  • In the Undirected Graph 
  • In the Directed Graph
  • Topological Sorting 
  • Kahn's BFS Based Algorithm
  • DFS Based Algorithm
  • Shortest Path in Directed Acyclic Graph 
  • Prim's Algorithm/Minimum Spanning Tree
  • Dijkstra's Shortest Path Algorithm
  • Bellman-Ford Shortest Path Algorithm
  • Kosaraju's Algorithm
  • Articulation Point
  • Bridges in Graph
  • Tarjan’s Algorithm


 Greedy


 Backtracking


 Dynamic Programming

  • Introduction 
  • Dynamic Programming
  • Memoization 
  • Tabulation
  • Problems(With Video Solutions):
  • Longest Common Subsequence
  • Coin Change Count Combinations 
  • Edit Distance Problem
  • Naive Approach
  • DP Approach
  • Longest Increasing Subsequence Problem
  • Naive Approach
  • Efficient Approach
  • Maximum Cuts 
  • Minimum coins to make a value 
  • Minimum Jumps to reach at the end 
  • 0-1 knapsack problem 
  • Naive Approach
  • Efficient Approach
  • Optimal Strategy for a Game 
  • Variation of Longest Common Subsequence 
  • Variation of Longest Increasing Subsequence 
  • Egg Dropping Problem 
  • Count BST with nkeys
  • Maximum Sum with No Consecutive
  • Subset Sum Problem
  • Matrix Chain Multiplication
  • Palindrome Parititioning


 Trie

  • Introduction
  • Representation
  • Search
  • Insert
  • Delete
  • Count Distinct Rows in a Binary Matrix


 Segment Tree

  • Introduction
  • Construction
  • Range Query 
  • Update Query


 Disjoint Set

  • Introduction
  • Find and Union Operations
  • Union by Rank
  • Path Compression
  • Kruskal's Algorithm



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