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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