Algorithms Tutorial & Complete Learning Path

If you’re on a quest to conquer the world of algorithms, you’ve arrived at the right place. This guide is designed to take you through the world of algorithms, unravelling their complexities in a simple, approachable manner.

The Essence of Algorithms

Algorithms are the heartbeats of computer science; they are step-by-step instructions that dictate how tasks are performed. From sorting a list of numbers to finding the shortest path in a network, algorithms empower computers to solve problems with precision and speed.

Starting Your Journey

1. Understanding the Basics: Begin with the fundamentals—what algorithms are, why they matter, and how they are used in everyday computing.

2. Sorting and Searching: Dive into classic algorithms like QuickSort and Binary Search, which form the foundation of efficient data manipulation.

3. Complex Problem Solving: Learn about algorithms that tackle complex problems, such as Dijkstra’s for pathfinding or Knapsack for optimization.

Advanced Learning

1. Algorithmic Paradigms: Explore different approaches like Greedy, Divide and Conquer, and Dynamic Programming.

2. Data Structures: Pair your algorithm knowledge with the right data structures for optimal performance.

3. Real-World Applications: See how algorithms shape technology, from Google’s search engine to Netflix’s recommendation system.

Practical Tips

1. Code Along: Implement algorithms in your preferred programming language to solidify your understanding.

2. Analyze and Optimize: Learn to evaluate the efficiency of algorithms with Big O notation and improve them where possible.

3. Stay Curious: Keep exploring. The field of algorithms is vast and ever-evolving.

Complete Algorithms Tutorial

Bellow are a complete tutorials of a Algorithms

1. Introduction to Algorithms:

What is Algorithm | Introduction to Algorithms
Definition, Types, Complexity, Examples of Algorithms
Algorithms Design Techniques
Why is analysis of an Algorithm important?

2. Analysis of Algorithms:

Asymptotic Analysis
Worst, Average and Best Cases
Asymptotic Notations
Lower and Upper Bound Theory
Introduction to Amortized Analysis
What does ‘Space Complexity’ mean?
Polynomial Time Approximation Scheme
Accounting Method | Amortized Analysis
Potential Method in Amortized Analysis

3. Searching and Sorting:

Introduction to Searching Algorithms
Introduction to Sorting Algorithm
Stable and Unstable Sorting Algorithms
Lower bound for comparison based sorting algorithms
Can Run Time Complexity of a comparison-based sorting algorithm be less than N logN?
Which sorting algorithm makes minimum number of memory writes?

4. Greedy Algorithms:

Introduction to Greedy Algorithms
Activity Selection Problem
Huffman Coding
Job Sequencing Problem
Quiz on Greedy Algorithms
Minimum Number of Platforms Required for a Railway/Bus Station

5. Dynamic Programming:

Introduction to Dynamic Programming
Overlapping Subproblems Property
Optimal Substructure Property
Longest Increasing Subsequence
Longest Common Subsequence
Min Cost Path
Coin Change
Matrix Chain Multiplication

0-1Knapsack Problem
Longest Palindromic Subsequence
Palindrome Partitioning

6. Pattern Searching:

Introduction to Pattern Searching
Naive Pattern Searching
KMP Algorithm
Rabin-Karp Algorithm
Pattern Searching using a Trie of all Suffixes
Aho-Corasick Algorithm for Pattern Searching
Z algorithm (Linear time pattern searching Algorithm)

7. Backtracking:

Introduction to Backtracking
Print all permutations of a given string
The Knight’s tour problem
Rat in a Maze
N Queen Problem
Subset Sum
M Coloring Problem
Hamiltonian Cycle
Sudoku

8. Divide and Conquer:

Introduction to Divide and Conquer
Merge Sort
Write your own pow(x, n) to calculate x*n
Count Inversions
Closest Pair of Points
Strassen’s Matrix Multiplication

9. Geometric Algorithm:

Introduction to Geometric Algorithms
Closest Pair of Points | O(nlogn) Implementation
How to check if a given point lies inside or outside a polygon?
How to check if two given line segments intersect?
Given n line segments, find if any two segments intersect
How to check if given four points form a square
Convex Hull using Jarvis’ Algorithm or Wrapping

10. Mathematical Algorithms:

Introduction to Mathematical Algorithms
Write an Efficient Method to Check if a Number is Multiple of 3
Write a program to add two numbers in base 14
Program for Fibonacci numbers
Average of a stream of numbers
Multiply two integers without using multiplication, division and bitwise operators, and no loops
Babylonian method for square root
Sieve of Eratosthenes
Pascal’s Triangle
Given a number, find the next smallest palindrome
Program to add two polynomials
Multiply two polynomials
Count trailing zeroes in factorial of a number

11. Bitwise Algorithms:

Introduction to Bitwise Algorithms
Little and Big Endian
Detect opposite signs
Swap bits
Turn off the rightmost set bit
Rotate bits
Next higher number with same number of set bits
Swap two nibbles in a byte

12. Graph Algorithms:

Introduction to Graph Algorithms
BFS, DFS
Cycles in Graph
Shortest paths
MST
Topological Sorting
Connectivity
Max Flow

13. Randomized Algorithms:

Introduction to Randomized Algorithms
Linearity of Expectation
Expected Number of Trials until Success
Randomized Algorithms | Set 0 (Mathematical Background)
Randomized Algorithms | Set 1 (Introduction and Analysis)
Randomized Algorithms | Set 2 (Classification and Applications)
Randomized Algorithms | Set 3 (1/2 Approximate Median)
Reservoir Sampling

14. Branch and Bound:

Branch and Bound | Set 1 (Introduction with 0/1 Knapsack)
Branch and Bound | Set 2 (Implementation of 0/1 Knapsack)
Branch and Bound | Set 3 (8 puzzle Problem)
Branch And Bound | Set 4 (Job Assignment Problem)
Branch and Bound | Set 5 (N Queen Problem)
Branch And Bound | Set 6 (Traveling Salesman Problem)

15. Quizzes:

Analysis of Algorithms
Sorting
Divide and Conquer
Greedy Algorithms
Dynamic Programming
Backtracking
NP Complete
Searching
Recursion
Bit Algorithms

This is the complete Roadmap and articles of algorims to learn DSA.

Before you move on to the world of development, master the fundamentals of DSA on which every advanced algorithm is built upon. Choose your preferred language and start learning today:

Conclusion

Embarking on this learning path will equip you with the tools to tackle complex computational problems. Remember, mastering algorithms is not just about memorizing steps; it’s about developing a mind-set to approach problems logically and creatively. Happy coding, and may your journey through the algorithmic landscape be as enlightening as it is exhilarating.

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