# DSA Beginner to Advanced Roadmap by Sandeep Jain

## A detailed roadmap designed for aspiring programmers looking to kickstart their Data Structures and Algorithms journey, created, curated and organised by the CEO himself.

25

Chapters

3

Quizzes

50+

Articles

500

Problems

Discover a smoother learning journey through our effortless roadmap

Start your journey## Chapters

### Analysis of Algorithms

Asymptotic Notation and Analysis (Based on input size) in Complexity Analysis of Algorithms

Asymptotic Notations and how to calculate them

Worst, Average and Best Case Analysis of Algorithms

Big O Notation Tutorial - A Guide to Big O Analysis

Analysis of Algorithms | Big-Omega â„¦ Notation

Analysis of Algorithms | Big - Î˜ (Big Theta) Notation

How to Analyse Loops for Complexity Analysis of Algorithms

How to analyse Complexity of Recurrence Relation

How to solve time complexity Recurrence Relations using Recursion Tree method?

What does 'Space Complexity' mean?

### Arrays

Introduction to Getting Started with Array Data Structure

Types of Arrays

How do Dynamic arrays work?

Search, Insert, and Delete in an Unsorted Array | Array Operations

Search, Insert, and Delete in an Sorted Array | Array Operations

Array Reverse in C/C++/Java/Python/JavaScript

Sort an array of 0s, 1s and 2s | Dutch National Flag problem

Find a peak element which is not smaller than its neighbours

Program to find the minimum (or maximum) element of an array

Count number of occurrences (or frequency) in a sorted array

Find Subarray with given sum | Set 1 (Non-negative Numbers)

Program to cyclically rotate an array by one

Find the Missing Number

Count pairs with given sum

Find duplicates in O(n) time and O(1) extra space | Set 1

Find first non-repeating element in a given Array of integers

Count subarrays with equal number of 1's and 0's

Subarray with 0 sum

Largest Sum Contiguous Subarray (Kadane's Algorithm)

Minimize the maximum difference between the heights

Find the row with maximum number of 1s

Find whether an array is subset of another array

Majority Element

Sort an array in wave form

Maximum Sum Path in Two Arrays

Find the missing and repeating number

Given a sorted array and a number x, find the pair in array whose sum is closest to x

Find the smallest positive integer value that cannot be represented as sum of any subset of a given array

### Matrix

Introduction to Matrix or Grid Data Structure - Two Dimensional Array

Search in a row wise and column wise sorted matrix

Print matrix in zig-zag fashion

Print a given matrix in spiral form

Shift matrix elements row-wise by k

Program to find transpose of a matrix

Inplace (Fixed space) M x N size matrix transpose

Inplace rotate square matrix by 90 degrees | Set 1

Mirror of matrix across diagonal

Program for Conway's Game Of Life

Check if all rows of a matrix are circular rotations of each other

Count zeros in a row wise and column wise sorted matrix

Minimum flip required to make Binary Matrix symmetric

Program to multiply two matrices

Queries in a Matrix

Find pairs with given sum such that elements of pair are in different rows

Find all permuted rows of a given row in a matrix

Find number of transformation to make two Matrix Equal

Magic Square | ODD Order

A Boolean Matrix Question

Print K'th element in spiral form of matrix

Find size of the largest '+' formed by all ones in a binary matrix

Validity of a given Tic-Tac-Toe board configuration

### Strings

Introduction to Strings - Data Structure and Algorithm Tutorials

Reverse words in a given string

Longest Common Prefix using Sorting

Find the minimum distance between the given two words

Check if two given Strings are Isomorphic to each other

Check if a string can be obtained by rotating another string 2 places

Find largest word in dictionary by deleting some characters of given string

How to replace a substring of a string

Multiply Large Numbers represented as Strings

Find Excel column name from a given column number

Find the longest substring with k unique characters in a given string

Smallest window in a String containing all characters of other String

Length of the longest substring without repeating characters

Count of substrings of length K with exactly K distinct characters

Count number of substrings with exactly k distinct characters

Given a sequence of words, print all anagrams together | Set 1

Minimum number of deletions to make a string palindrome

KMP Algorithm for Pattern Searching

Longest prefix which is also suffix

Rabin-Karp Algorithm for Pattern Searching

Z algorithm (Linear time pattern searching Algorithm)

Number of distinct words of size N with at most K contiguous vowels

Longest substring whose characters can be rearranged to form a Palindrome

### Linked List

Introduction to Linked List - Data Structure and Algorithm Tutorials

Linked List vs Array

Find Middle of the Linked List

Reverse a Linked List

Reverse a Doubly Linked List

Rotate a Linked List

Program for Nth node from the end of a Linked List

Delete last occurrence of an item from linked list

Detect loop or cycle in a linked list

Traversal of Circular Linked List

Pairwise Swap Nodes of a given Linked List

Reverse a Linked List in groups of given size

Merge two sorted linked lists

Detect and Remove Loop in a Linked List

Delete all occurrences of a given key in a linked list

Write a function to get the intersection point of two Linked Lists

Intersection of two Sorted Linked Lists

Remove duplicates from an unsorted doubly linked list

Add two numbers represented by Linked List

Multiply two numbers represented by Linked Lists

Swap Kth node from beginning with Kth node from end in a Linked List

Construct a linked list from 2D matrix

Reverse a sublist of linked list

Rearrange a given linked list in-place.

Reverse alternate K nodes in a Singly Linked List

Merge K sorted linked lists | Set 1

Flattening a Linked List

Clone a Linked List with next and Random Pointer

### Mathematical Programs

Program to count digits in an integer (4 Different Methods)

Check if a number is Palindrome

Program for factorial of a number

Program to Find GCD or HCF of Two Numbers

Program to find LCM of two numbers

Prime Numbers

Prime Factorization using Sieve O(log n) for multiple queries

Sieve of Eratosthenes

Compute power of power k times % m

LCM of given array elements

GCD of more than two (or array) numbers

Modular Exponentiation (Power in Modular Arithmetic)

Nth Fibonacci Number

### Bitwise Manipulations

Set the K-th bit of a given number

Program to clear K-th bit of a number N

Toggling k-th bit of a number

Count set bits in an integer

Program to find whether a given number is power of 2

Count number of bits to be flipped to convert A to B

Position of rightmost set bit

How to swap two numbers without using a temporary variable?

Highest power of 2 less than or equal to given number

Count set bits in a range

Find the two numbers with odd occurrences in an unsorted array

Check if binary representation of a number is palindrome

Find the missing and repeating number

Minimum XOR Value Pair

Count total set bits in first N Natural Numbers (all numbers from 1 to N)

Find the n-th number whose binary representation is a palindrome

Find the element that appears once

Count subarrays with equal number of 1's and 0's

Count number of subsets having a particular XOR value

Find the maximum subset XOR of a given set

### Searching

Linear Search Algorithm - Data Structure and Algorithms Tutorials

Binary Search - Data Structure and Algorithm Tutorials

Find the first repeating element in an array of integers

Find the missing and repeating number

Given Array of size n and a number k, find all elements that appear more than n/k times

Two elements whose sum is closest to zero

Find a pair with the given difference

Kth smallest element in a row-wise and column-wise sorted 2D array

Ceiling in a sorted array

Find the closest pair from two sorted arrays

Find the Minimum element in a Sorted and Rotated Array

Find k closest elements to a given value

Find a Fixed Point (Value equal to index) in a given array

Median of two Sorted Arrays of Different Sizes

Search in an almost sorted array

Find if there is a pair with a given sum in the rotated sorted Array

### Sorting

Introduction to Sorting Techniques â€“ Data Structure and Algorithm Tutorials

Bubble Sort - Data Structure and Algorithm Tutorials

Selection Sort â€“ Data Structure and Algorithm Tutorials

Insertion Sort - Data Structure and Algorithm Tutorials

QuickSort - Data Structure and Algorithm Tutorials

Merge Sort - Data Structure and Algorithms Tutorials

Sort elements by frequency

Sort numbers stored on different machines

Sort even-placed elements in increasing and odd-placed in decreasing order

Sort a nearly sorted (or K sorted) array

Sort a Matrix in all way increasing order

Count distinct occurrences as a subsequence

K-th smallest element after removing some integers from natural numbers

Merge Overlapping Intervals

Maximum difference between frequency of two elements such that element having greater frequency is also greater

Minimum swaps to reach permuted array with at most 2 positions left swaps allowed

Find whether it is possible to make array elements same using one external number

Sort an array after applying the given equation

Count minimum number of subsets (or subsequences) with consecutive numbers

Choose k array elements such that difference of maximum and minimum is minimized

### Hashing

Introduction to Hashing - Data Structure and Algorithm Tutorials

Find whether an array is subset of another array

Frequency of each character in a String using unordered_map in C++

Find first non-repeating character of given String

Find Union and Intersection of two unsorted arrays

Find missing elements of a range

Check if pair with given Sum exists in Array (Two Sum)

Remove duplicates from Sorted Array

Longest Consecutive Subsequence

Given a sequence of words, print all anagrams together | Set 1

Longest sub-array having sum k

Largest subarray with equal number of 0s and 1s

Sort an array according to the order defined by another array

Smallest subarray with k distinct numbers

Find the length of largest subarray with 0 sum

Count the number of subarrays having a given XOR

Transform One String to Another using Minimum Number of Given Operation

Longest subarray with sum divisible by K

Count distinct elements in every window of size k

Check if an array can be divided into pairs whose sum is divisible by k

### Stack

What is Stack? A Complete Tutorial

Implement a stack using singly linked list

Convert Infix expression to Postfix expression

Evaluation of Postfix Expression

Convert Infix To Prefix Notation

Evaluation of Prefix Expressions

Check for Balanced Brackets in an expression (well-formedness)

How to Reverse a String using Stack

Reverse individual words

Next Greater Element (NGE) for every element in given Array

Previous greater element

Trapping Rain Water

The Stock Span Problem

Delete consecutive same words in a sequence

Lexicographically largest subsequence containing all distinct characters only once

Minimize length by removing subsequences forming valid parenthesis from a given string

Clone a stack without using extra space | Set 2

Length of the longest valid substring

Next Greater Frequency Element

Maximum product of indexes of next greater on left and right

Largest Rectangular Area in a Histogram using Stack

Design a stack that supports getMin() in O(1) time and O(1) extra space

Stack Permutations (Check if an array is stack permutation of other)

Check if two expressions with brackets are same

Design custom Browser History based on given operations

Find maximum of minimum for every window size in a given array

### Queue

Introduction to Queue - Data Structure and Algorithm Tutorials

Reversing a Queue

Reversing the first K elements of a Queue

Introduction and Array Implementation of Queue

Implement Stack using Queues

Find the first circular tour that visits all petrol pumps

An Interesting Method to Generate Binary Numbers from 1 to n

Check if a queue can be sorted into another queue using a stack

Interchange elements of Stack and Queue without changing order

### Deque

Deque | Set 1 (Introduction and Applications)

Implementation of Deque using circular array

Lexicographically largest permutation by sequentially inserting Array elements at ends

Generate Bitonic Sequence of length N from integers in a given range

Length of all prefixes that are also the suffixes of given string

Sliding Window Maximum (Maximum of all subarrays of size K)

Complete Tutorial on LRU Cache with Implementations

Reduce the given Array of [1, N] by rotating left or right based on given conditions

Generate Linked List consisting of maximum difference of squares of pairs of nodes from given Linked List

Substring of length K having maximum frequency in the given string

### Heap

Introduction to Heap - Data Structure and Algorithm Tutorials

Binary Heap

Insertion and Deletion in Heaps

Introduction to Max-Heap â€“ Data Structure and Algorithm Tutorials

Introduction to Min-Heap â€“ Data Structure and Algorithm Tutorials

Minimum product of k integers in an array of positive Integers

Print K largest(or smallest) elements in an array

Find K most occurring elements in the given Array

K'th largest element in a stream

Largest triplet product in a stream

Minimum sum of two numbers formed from digits of an array

Connect n ropes with minimum cost

K maximum sum combinations from two arrays

Maximum sum of at most two non-overlapping intervals in a list of Intervals | Interval Scheduling Problem

Merge k sorted arrays | Set 1

Find Median from Running Data Stream

Find smallest range containing elements from k lists

Merge two sorted arrays in O(1) extra space using Heap

### Recursion Algorithm

Introduction to Recursion - Data Structure and Algorithm Tutorials

Sum of natural numbers using recursion

Print reverse of a string using recursion

Sum of digit of a number using recursion

Program for factorial of a number

Recursive Programs to find Minimum and Maximum elements of array

Count Set-bits of number using Recursion

Print Fibonacci Series in reverse order using Recursion

Flood Fill Algorithm

Recursively remove all adjacent duplicates

Binary to Gray code using recursion

Delete a linked list using recursion

Length of longest palindromic sub-string : Recursion

Program for Tower of Hanoi Algorithm

Print all possible paths from top left to bottom right in matrix

Find the value of a number raised to its reverse

Print all Palindromic Partitions of a String using Backtracking

Check if a string is a scrambled form of another string

Print all Palindromic Partitions of a String using Bit Manipulation

### Backtracking

Introduction to Backtracking - Data Structure and Algorithm Tutorials

Rat in a Maze

N Queen Problem

Algorithm to Solve Sudoku | Sudoku Solver

Permutations of given String

Subset Sum Problem using Backtracking

Longest Possible Route in a Matrix with Hurdles

Find shortest safe route in a path with landmines

Word Break Problem using Backtracking

Remove Invalid Parentheses

Printing all solutions in N-Queen Problem

Find if there is a path of more than k length from a source

Partition of a set into K subsets with equal sum

Tug of War

### Tree

Introduction to Tree - Data Structure and Algorithm Tutorials

Tree Traversal Techniques - Data Structure and Algorithm Tutorials

Types of Trees in Data Structures

Level Order Traversal (Breadth First Search or BFS) of Binary Tree

Level order traversal in spiral form

Find the Maximum Depth or Height of given Binary Tree

Program to Determine if given Two Trees are Identical or not

Convert a Binary Tree into its Mirror Tree (Invert Binary Tree)

Symmetric Tree (Mirror Image of itself)

How to determine if a binary tree is height-balanced?

Largest value in each level of Binary Tree

ZigZag Tree Traversal

Print Right View of a Binary Tree

Print Nodes in Top View of Binary Tree

Bottom View of a Binary Tree using Recursion

Diameter of a Binary Tree in O(n) [A new method]

Vertical order traversal of Binary Tree using Map

Construct Tree from given Inorder and Preorder traversals

Convert Binary Tree to Doubly Linked List by keeping track of visited node

Construct BST from given preorder traversal | Set 1

Find distance between two nodes of a Binary Tree

Find the maximum sum leaf to root path in a Binary Tree

Difference between sums of odd level and even level nodes of a Binary Tree

Maximum sum of nodes in Binary tree such that no two are adjacent

Print Ancestors of a given node in Binary Tree

Lowest Common Ancestor in a Binary Tree

Check if a given Binary Tree is Sum Tree

Print Left View of a Binary Tree

Maximum Path Sum in a Binary Tree

Boundary Traversal of binary tree

Print all nodes at distance k from a given node

Serialize and Deserialize a Binary Tree

Count number of nodes in a complete Binary Tree

Find the maximum path sum between two leaves of a binary tree

Count all k-sum paths in a Binary Tree

Burn the binary tree starting from the target node

Clone a Binary Tree with Random Pointers

### Binary Search Tree

Introduction to Binary Search Tree - Data Structure and Algorithm Tutorials

Searching in Binary Search Tree (BST)

Deletion in Binary Search Tree (BST)

Self-Balancing Binary Search Trees

AVL Tree Data Structure

Introduction to Red-Black Tree

Iterative searching in Binary Search Tree

A program to check if a Binary Tree is BST or not

Find the node with minimum value in a Binary Search Tree

Check if an array represents Inorder of Binary Search tree or not

Check for Identical BSTs without building the trees

Second largest element in BST

Check if two BSTs contain same set of elements

Construct BST from given preorder traversal | Set 1

Transform a BST to greater sum tree

BST to a Tree with sum of all smaller keys

Lowest Common Ancestor in a Binary Search Tree.

Find k-th smallest element in BST (Order Statistics in BST)

K'th Largest element in BST using constant extra space

Largest number in BST which is less than or equal to N

Shortest distance between two nodes in BST

Inorder predecessor and successor for a given key in BST

Find a pair with given sum in BST

Maximum element between two nodes of BST

Find the largest BST subtree in a given Binary Tree | Set 3

Two nodes of a BST are swapped, correct the BST

How to handle duplicates in Binary Search Tree?

Construct all possible BSTs for keys 1 to N

Merge two BSTs with limited extra space

K'th Largest Element in BST when modification to BST is not allowed

Maximum Unique Element in every subarray of size K

Inversion count in Array Using Self-Balancing BST

Merge Two Balanced Binary Search Trees

### Greedy Algorithm

Introduction to Greedy Algorithm - Data Structures and Algorithm Tutorials

Activity Selection Problem | Greedy Algo-1

Fractional Knapsack Problem

Job Sequencing Problem

Ford-Fulkerson Algorithm for Maximum Flow Problem

What is Dijkstraâ€™s Algorithm? | Introduction to Dijkstra's Shortest Path Algorithm

Kruskalâ€™s Minimum Spanning Tree (MST) Algorithm

Primâ€™s Algorithm for Minimum Spanning Tree (MST)

Huffman Coding | Greedy Algo-3

Buy Maximum Stocks if i stocks can be bought on i-th day

Find the minimum and maximum amount to buy all N candies

Divide cuboid into cubes such that sum of volumes is maximum

Minimum rooms for m events of n batches with given schedule

Minimum cost to make array size 1 by removing larger of pairs

Minimum increment by k operations to make all elements equal

Smallest subset with sum greater than all other elements

Minimum Number of Platforms Required for a Railway/Bus Station

Divide 1 to n into two groups with minimum sum difference

Paper Cut into Minimum Number of Squares

Minimum difference between groups of size two

Largest palindromic number by permuting digits

Find smallest number with given number of digits and sum of digits

Greedy Algorithm to find Minimum number of Coins

Graph Coloring Using Greedy Algorithm

Greedy Approximate Algorithm for K Centers Problem

Shortest Superstring Problem

Approximate solution for Travelling Salesman Problem using MST

### Dynamic Programming

Dynamic Programming (DP) Tutorial with Problems

What is memoization? A Complete tutorial

Tabulation vs Memoization

Minimize steps to reach K from 0 by adding 1 or doubling at each step

Count number of ways to cover a distance

Minimum number of deletions and insertions to transform one string into another

Find the longest path in a matrix with given constraints

Maximum sum path in a Matrix

Longest Increasing Subsequence (LIS)

Longest Common Subsequence (LCS)

Word Wrap Problem

Maximum Product Cutting | DP-36

Cutting a Rod | DP-13

Maximum Length Chain of Pairs | DP-20

Maximum Sum Increasing Subsequence | DP-14

Minimum perfect squares to add that sum to given number.

Longest Palindromic Substring

Number of Unique BST with a given key | Dynamic Programming

Minimum insertions to form a palindrome | DP-28

Count All Palindromic Subsequence in a given String

Partition problem | DP-18

Palindrome Partitioning

Find if a string is interleaved of two other strings | DP-33

Partition a set into two subsets such that the difference of subset sums is minimum

Boolean Parenthesization Problem | DP-37

Longest Zig-Zag Subsequence

Maximum profit by buying and selling a share at most k times

The Painter's Partition Problem

Matrix Chain Multiplication | DP-8

### Graph

Introduction to Graphs - Data Structure and Algorithm Tutorials

Graph and its representations

Breadth First Search or BFS for a Graph

Depth First Search or DFS for a Graph

Print Adjacency List for a Directed Graph

Search a Word in a 2D Grid of characters (Word Search)

Boggle (Find all possible words in a board of characters) | Set 1

Word Ladder (Length of shortest chain to reach a target word)

Flood fill Algorithm - how to implement fill() in paint?

Given a matrix of â€˜Oâ€™ and â€˜Xâ€™, replace 'O' with 'X' if surrounded by 'X'

Minimum time required to rotten all oranges

Minimum number of swaps required to sort an array

Minimum steps to reach target by a Knight | Set 1

Count all possible Paths between two Vertices

Find whether there is path between two cells in matrix

Kahn's algorithm for Topological Sorting

Check if it is possible to finish all task from given dependencies (Course Schedule I)

Find the ordering of task from given dependencies (Course Schedule II)

How to find Shortest Paths from Source to all Vertices using Dijkstra's Algorithm

Floyd Warshall Algorithm

Find number of closed islands in given Matrix

Minimum Cost Path with Left, Right, Bottom and Up moves allowed

Strongly Connected Components

Tarjan's Algorithm to find Strongly Connected Components

Hamiltonian Cycle

Bridges in a graph

Articulation Points (or Cut Vertices) in a Graph

Alien Dictionary

Print all possible shortest chains to reach a target word

Shortest path by removing K walls

Shortest Path in Directed Acyclic Graph

Find minimum weight cycle in an undirected graph

Detect cycle in an undirected graph

### Trie

Introduction to Trie - Data Structure and Algorithm Tutorials

Trie | (Insert and Search)

Trie | (Delete)

Longest Common Prefix using Trie

Count number of Distinct Substring in a String

Maximum XOR of Two Numbers in an Array

Maximum number of Strings with Common Prefix of length K

Maximize Bitwise XOR of K with two numbers from Array

Maximum common prefix of all strings

Count of Strings of Array having given prefixes for Q query

Search a string in the dictionary with a given prefix and suffix for Q queries

Queries to calculate maximum Bitwise XOR of X with any array element not exceeding M

Spell Checker using Trie

### Segment Tree

Introduction to Segment Trees - Data Structure and Algorithm Tutorials

Segment Tree | Sum of given range

Segment Tree | Range Minimum Query

Lazy Propagation in Segment Tree

Min-Max Range Queries in Array

Querying maximum number of divisors that a number in a given range has

Flipping Sign Problem | Lazy Propagation Segment Tree

Queries to check if any non-repeating element exists within range [L, R] of an Array

Range LCM Queries

Range query for Largest Sum Contiguous Subarray

Maximum Occurrence in a Given Range

Queries to find maximum product pair in range with updates

Queries to evaluate the given equation in a range [L, R]

Length of Longest Subarray with same elements in atmost K increments

Calculate the Sum of GCD over all subarrays

Range Queries for Longest Correct Bracket Subsequence

Range and Update Query for Chessboard Pieces

Generate original permutation from given array of inversions

Count number of increasing sub-sequences : O(NlogN)

Reconstructing Segment Tree

### Disjoint Set

Introduction to Disjoint Set (Union-Find Algorithm)

Union By Rank and Path Compression in Union-Find Algorithm

Detect Cycle in Graph using DSU

Connected Components in an Undirected Graph

Find the number of islands using DFS

Replace all occurrences of X by Y for Q queries in given Array

Minimum cost to connect all cities

The Earliest Moment When Everyone Become Friends

Minimum cost required to connect all houses in a city

Lexicographically minimum String possible

Job Sequencing Problem using Disjoint Set

Path queries through restricted weighted edges

### DSA Quiz for Beginners to Advanced

## About DSA Roadmap for Beginner to Advanced

An extensive interview-centric roadmap designed by the CEO to help you ace your DSA preparations. We will help you enhance your conceptual knowledge about DSA and improve your problem-solving and coding skills. The main focus of this DSA Roadmap will be to help you get started and become a Pro in Data Structures and Algorithms, with additional benefit to prepare for coding interviews of product-based companies like Microsoft, Uber, Amazon, and many more!

### Why take this DSA Roadmap for Beginners to Advanced by Sandeep Jain?

With a passion for teaching, our CEO has taken countless sessions and has provide proven tailored guidance to all the aspiring coders over the years. Launch a successful tech career with his structured learning methods, and gain his:

- Industry Expertise
- Extensive Teaching Experience
- Student Friendly Approach

## Why Data Structures and Algorithms Are Important to Learn?

Data structures and algorithms play a major role in implementing software and in the hiring process as well. In our daily life, we always go with the choice which can complete the task in a short amount of time and with efficiency, using fewer resources. The same happens with these companies. The problem faced by these companies is much harder and on a much larger scale. Software developers also have to make the right decisions when it comes to solving the problems of these companies. Knowledge of Data Structures and Algorithms goes a long way in solving these problems efficiently and the interviewers are more interested in seeing how candidates use these tools to solve a problem.

### If you want to know more about Why Data Structures and Algorithms, then you must opt this DSA Roadmap for Beginners to Advanced by Mr. Sandeep Jain (CEO & Founder, GeeksforGeeks).

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## FAQ's

How can I start this course?

You just need to click on the button that says START YOUR JOURNEY, and that's it. You will be taken to your first chapter.

Is this a language-specific course?

No. Majority topics in the course include implementations in popular programming languages like C, C++, Java, Python, C#, and Javascript.

Does the course include programming questions?

Yes, the course focuses on DS & Algo with a mix of theoretical topics and programming questions.

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