Algorithmic Foundations
Master the mathematical foundations: asymptotic analysis, recurrences, and proof techniques that underpin all algorithm design.
Big-O Notation Playground
Big-O notation describes how an algorithm's runtime or space requirements grow as input size increases. Adjust the input size below to see how different complexity classes compare.
Common Algorithms by Complexity
Array Access
O(1)arr[i] Direct index lookup
Binary Search
O(log n)binarySearch(arr, x) Divide and conquer search
Linear Search
O(n)arr.find(x => x === target) Check each element
Merge Sort
O(n log n)mergeSort(arr) Efficient comparison sort
Bubble Sort
O(n²)bubbleSort(arr) Simple but slow sorting
Fibonacci (naive)
O(2^n)fib(n) Exponential recursion
Key Concepts
Asymptotic Analysis
We focus on how algorithms behave as input grows toward infinity. Constants and lower-order terms are dropped because they become insignificant at scale.
Why This Matters for AI Coding
When AI generates code, it might produce working solutions that are inefficient. Understanding complexity helps you:
- • Spot O(n²) solutions where O(n log n) exists
- • Ask AI to optimize with specific complexity targets
- • Verify that generated code will scale
Chapters
Asymptotic Analysis
Understanding Big-O, Big-Θ, and Big-Ω notation for algorithm analysis
Recurrence Relations
Solving recurrences using substitution, recursion trees, and the Master Theorem
Ready to continue?
After mastering the foundations, explore Sorting & Searching algorithms.