What is an Algorithm?
Simple Definition
An algorithm is just a step-by-step set of instructions to solve a problem or complete a task.
Think of it like a recipe in cooking: it tells you exactly what to do, in what order, to get the result you want.
Key Components
- Input: What you start with
- Process: The steps you follow
- Output: The result you get
Why Learn Algorithms?
Foundation of Software
Used in GPS, Search Engines, AI ChatBots, Gaming Apps, Databases, Web Applications
Career Opportunities
Top companies like Google, Microsoft, Amazon, Apple, Meta focus heavily on algorithms in interviews
Problem-Solving Skills
Boosts your problem-solving abilities and makes you a stronger programmer
Simple Example: Finding the Largest Number
Algorithm Steps:
- 1Look at the first number, remember it as biggest
- 2Look at the next number; if it's bigger, remember that
- 3Repeat until you check all numbers
- ✓The remembered one is the largest
Interactive Demo:
Big O Notation - Algorithm Efficiency
What is Big O?
Big O notation is a way to measure how fast an algorithm runs as the input size grows. It helps us compare different algorithms and predict their performance.
Key Points:
- Describes the upper bound of complexity
- Focuses on worst-case scenario
- Ignores constants and lower-order terms
- Helps choose the right algorithm
Common Complexities (Best to Worst):
Big O Complexity Comparison
Interactive visualization showing how different complexities grow with input size
Interactive Big O Calculator
Operations for n = 100:
Essential Data Structures
Data Structures Visualization
Array
Linear data structure with elements in contiguous memory locations.
Linked List
Linear data structure where elements are stored in nodes connected by pointers.
Stack
LIFO (Last In, First Out) data structure. Like a stack of plates.
Queue
FIFO (First In, First Out) data structure. Like a line of people.
Binary Tree
Hierarchical data structure with nodes connected by edges.
Hash Table
Key-value pairs with fast access using hash functions.
Essential Algorithms
Searching Algorithms
Linear Search
Checks each element one by one until the target is found.
def linear_search(arr, target):
for i in range(len(arr)):
if arr[i] == target:
return i
return -1Binary Search
Divides sorted array in half repeatedly to find target.
def binary_search(arr, target):
left, right = 0, len(arr) - 1
while left <= right:
mid = (left + right) // 2
if arr[mid] == target:
return mid
elif arr[mid] < target:
left = mid + 1
else:
right = mid - 1
return -1Sorting Algorithms
Sorting Algorithms Comparison
| Algorithm | Best Case | Average Case | Worst Case | Space | Stable |
|---|---|---|---|---|---|
| Bubble Sort | O(n) | O(n²) | O(n²) | O(1) | ✅ |
| Selection Sort | O(n²) | O(n²) | O(n²) | O(1) | ❌ |
| Insertion Sort | O(n) | O(n²) | O(n²) | O(1) | ✅ |
| Merge Sort | O(n log n) | O(n log n) | O(n log n) | O(n) | ✅ |
| Quick Sort | O(n log n) | O(n log n) | O(n²) | O(log n) | ❌ |
Interactive Sorting Demo
Algorithm Design Patterns
Algorithm Patterns & Problem-Solving
Divide & Conquer
Break problem into smaller subproblems, solve them, then combine results.
Greedy
Make the locally optimal choice at each step.
Dynamic Programming
Solve complex problems by breaking them into overlapping subproblems.
Backtracking
Try all possibilities and backtrack when a solution path fails.
Two Pointers
Use two pointers to traverse data structure efficiently.
Sliding Window
Maintain a window of elements and slide it through the data.
Complete Learning Roadmap
Your Journey from Beginner to Expert
🌱 Beginner Level (2-4 weeks)
What to Learn:
- • Basic programming concepts
- • Arrays and strings
- • Simple loops and conditions
- • Basic input/output
Practice Problems:
- • Find maximum in array
- • Reverse a string
- • Count vowels
- • Simple calculator
📚 Fundamental Level (4-6 weeks)
What to Learn:
- • Big O notation basics
- • Linear search algorithm
- • Bubble sort algorithm
- • Basic recursion
- • Stack and queue concepts
Practice Problems:
- • Implement linear search
- • Implement bubble sort
- • Calculate factorial recursively
- • Balanced parentheses
🚀 Intermediate Level (6-8 weeks)
What to Learn:
- • Binary search algorithm
- • Merge sort and quick sort
- • Hash tables/maps
- • Linked lists
- • Two pointers technique
Practice Problems:
- • Two sum problem
- • Merge two sorted arrays
- • Remove duplicates
- • Implement hash table
🎯 Advanced Level (8-12 weeks)
What to Learn:
- • Trees and binary search trees
- • Graph algorithms (BFS, DFS)
- • Dynamic programming
- • Greedy algorithms
- • Backtracking
Practice Problems:
- • Tree traversals
- • Shortest path problems
- • Knapsack problem
- • N-Queens problem
🏆 Expert Level (12+ weeks)
What to Learn:
- • Advanced graph algorithms
- • Complex dynamic programming
- • String algorithms
- • Computational geometry
- • Network flows
Practice Problems:
- • Minimum spanning tree
- • Longest common subsequence
- • String matching algorithms
- • Convex hull problems
Learning Resources & Practice
🌐 Online Platforms
- LeetCode - Coding interview practice
- HackerRank - Programming challenges
- Codeforces - Competitive programming
- CodeChef - Programming contests
🎨 Visualization Tools
- VisuAlgo - Algorithm animations
- Algorithm Visualizer - Interactive visualizations
- USF Visualizations - Data structure animations
📚 Books & Courses
- Grokking Algorithms - Beginner-friendly
- Introduction to Algorithms - Comprehensive
- Cracking the Coding Interview - Interview prep
- Khan Academy - Free courses
💻 Recommended Languages
- Python - Beginner-friendly, clean syntax
- Java - Industry standard, object-oriented
- C++ - Performance-oriented, competitive programming
- JavaScript - Web development, versatile
💡 Study Tips
- • Practice coding problems daily
- • Understand concepts before memorizing
- • Use visualization tools
- • Join coding communities
- • Build projects to apply knowledge
🎯 Interview Prep
- • Master Big O analysis
- • Practice whiteboard coding
- • Learn to explain your thinking
- • Study system design basics
- • Mock interviews with peers