📊 *Big O Notation Cheatsheet* 🚀

Understand how your code performs as data grows!

🔹 *O(1) – Constant Time*
✅ Time is the same no matter the input size
📌 Example: Accessing an element in a hash table
💡 Fastest possible performance

🔹 *O(log n) – Logarithmic Time*
✅ Performance grows slowly even with large input
📌 Example: Binary search on a sorted array
💡 Very efficient for large data sets

🔹 *O(n) – Linear Time*
✅ Time grows in direct proportion to input
📌 Example: Looping through an array
💡 Good for simple iterations

🔹 *O(n log n) – Linearithmic Time*
✅ Grows faster than linear but better than quadratic
📌 Example: Efficient sorting like Merge Sort, Quick Sort
💡 Common in real-world sorting algorithms

🔹 *O(n²) – Quadratic Time*
❌ Time grows with square of input size
📌 Example: Bubble sort, selection sort
💡 Avoid for large inputs

🔹 *O(n³) – Cubic Time*
❌ Time grows with cube of input size
📌 Example: Triple nested loops
💡 Very slow for large n

🔹 *O(2ⁿ) – Exponential Time*
⚠️ Time doubles with each input addition
📌 Example: Recursive Fibonacci
💡 Impractical for even moderate inputs

🔹 *O(n!) – Factorial Time*
⚠️ Time grows factorially with input
📌 Example: Solving Traveling Salesman with brute force
💡 Used in brute-force permutations or combinations

🧠 *Tips:*
✅ Prefer O(1) > O(log n) > O(n) > O(n log n)
❌ Avoid O(n²), O(2ⁿ), O(n!) unless absolutely necessary
✅ Use the right data structures & algorithms

💬 *Tap ❤️ if this helped you!*

Array Sorting Algorithms

100+ Practice Questions

❍ C/C++
❍ Python
❍ JavaScript
❍ Java
❍ C#
❍ Golang

➊ Simple Numbers

➀ Find a digit at a specific place in a number
➁ Find count of digits in a number
➂ Find the largest digit
➃ Find the 2nd largest digit
➄ Find the kth largest digit
➅ Find the smallest digit
➆ Find the 2nd smallest digit
➇ Find the kth smallest digit
➈ Find generic root (sum of all digits) of a number
➉ Reverse the digits in a number
➀➀ Rotate the digits in a number
➀➁ Is the number a palindrome?
➀➂ Find sum of 'n' numbers
➀➃ Check if a number is perfect square
➀➄ Find a number in an AP sequence
➀➅ Find a number in a GP sequence
➀➆ Find a number in fibonacci sequence
➀➇ Check number divisibility by 2, 3, 5, 9
➀➈ Check if a number is primary or not
20. Given a number, print all primes smaller than it
➁➀ Check if a number is circular prime or not
➁➁ Find all prime factors of a number
➁➂ Find the GCD of 2 numbers
➁➃ Find the LCM of 2 numbers
➁➄ Find the factorial of a number
➁➅ Find the exponentiation of a number

➋ Unit Conversion

➀ Number Base (Binary, Octal, Hexadecimal, Decimal)
➁ Weight (gram, kg, pound)
➂ Height (cm, m, inch, feet)
➃ Temperature (centigrade, fahrenhite)
➄ Distance (km, mile)
➅ Area (m², km², acre)
➆ Volume (ltr, gallon)
➇ Time (sec, min, hour)
➈ Currency

➌ Calculator

➀ Loan EMI Calculator
➁ Fixed Deposit Returns Calculator
➂ Interest Calculator
➃ BMI Calculator
➄ Item Price (considering tax, discount, shipping)
➅ Tip Calculator

➍ Geometry

➀ Find distance between 2 points
➁ Given 2 sides of a right angle triangle, find the 3rd
➂ Find 3rd angle of a triangle when 2 are given
➃ Area of a triangle when 3 sides are given
➄ Area of a right angle triangle
➅ Perimeter of a Square
➆ Area of a Square
➇ Perimeter of a Rectangle
➈ Area of a Rectangle
➉ Circumference of a Circle
➀➀ Area of a Circle
➀➁ Circumference of a Semi-Circle
➀➂ Area of a Semi-Circle
➀➃ Area of a Ring
➀➄ Circumference of an Ellipse
➀➅ Area of an Ellipse
➀➆ Suface Area of a Sphere
➀➇ Volume of a Sphere
➀➈ Surface Area of a Hemisphere
20. Volume of a Hemisphere
➁➀ Surface area of a Cube
➁➁ Volume of a Cube
➁➂ Surface area of a Cylinder
➁➃ Volume of a Cylinder

➎ Vector

➀ Find Scalar Multiplication of a vector
➁ Find addition/subtraction of vectors
➂ Find magnitude of a vector
➃ Find an unit vector along a given vector
➄ Find dot product of 2 vectors
➅ Find cross product of 2 vectors
➆ Check if 2 vectors are orthogonal

➏ Matrix

➀ Find the determinant of a matrix
➁ Find Scalar Multiplication of a matrix
➂ Find addition/subtraction of matrices
➃ Find the transpose of a matrix
➄ Find if 2 matrices are orthogonal
➅ Find inverse of a 2x2 and 3x3 matrix

➐ Set

➀ Find Union of 2 sets
➁ Find Intersection of 2 sets
➂ Find the Difference of 2 sets
➃ Find the Symmetric Difference of 2 sets
➄ Find if a set is subset/superset of another set
➅ Find if 2 sets are disjoints

➑ Special Numbers

➀ Strong Number
➁ Perfect Number
➂ Armstrong Number
➃ Harshad Number
➄ Kaprekar Number
➅ Lychrel Number
➆ Narcissistic Decimal Number
➇ Lucus Number
➈ Catalan Number
➉ Duck Number
➀➀ Ugly Number
➀➁ Abundant Number
➀➂ Deficient Number
➀➃ Automorphic Number
➀➄ Magic Number
➀➅ Friendly Pair Numbers
➀➆ Neon Number
➀➇ Spy Number
➀➈ Happy Number
20. Sunny Number
➁➀ Disarium Number
➁➁ Pronic Number
➁➂ Trimorphic Number
➁➃ Evil Number
➁➄ Amicable Pairs

✅ *Beginner’s Roadmap to Learn DSA* 🧠💻

1️⃣ *Foundations* – Understand programming basics & core math
2️⃣ *Data Structures* – Arrays, Linked Lists, Stacks, Queues
3️⃣ *Searching & Sorting* – Binary Search, Quick Sort, Merge Sort
4️⃣ *Trees & Graphs* – Binary Trees, BFS, DFS, Graph theory
5️⃣ *Recursion* – Learn base & recursive cases, backtracking
6️⃣ *Advanced Structures* – Heaps, Hash Maps, Tries
7️⃣ *Algorithms* – Greedy, Divide & Conquer, DP
8️⃣ *Advanced Topics* – String, Bit Manipulation, Sliding Window
9️⃣ *Problem Solving* – Daily practice on LeetCode, Codeforces, etc.
🔟 *Projects + GitHub* – Build & share to showcase your DSA skills


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