Big O Complexity Calculator
Free Big O notation calculator. Analyze algorithm complexity, compare time complexities, and look up data structure and sorting algorithm performance. Visualize complexity growth with interactive charts.
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Understand Algorithm Complexity
Big O notation describes how algorithm performance scales with input size. This calculator helps you analyze, compare, and understand time and space complexities for algorithms and data structures—essential knowledge for coding interviews and system design.
What is Big O Notation?
Big O notation expresses the upper bound of an algorithm's growth rate. It describes the worst-case scenario of how time or space requirements grow as input size approaches infinity. Common complexities range from O(1) constant time to O(n!) factorial time.
Big O Definition
T(n) = O(f(n)) as n → ∞Why Analyze Complexity?
Interview Preparation
Big O analysis is crucial for technical interviews. Understand complexity to discuss trade-offs and optimize solutions.
Performance Optimization
Identify bottlenecks in your code. A O(n²) algorithm may work fine for 100 items but fail at 1 million.
Algorithm Selection
Choose the right algorithm for your use case. Sometimes O(n log n) sorting beats O(n) counting sort depending on constraints.
System Design
Scale systems effectively by understanding how components behave under load. Database indices, caching, and sharding all involve complexity trade-offs.
How to Use This Calculator
Common Use Cases
Comparing Algorithms
See how O(n log n) merge sort compares to O(n²) bubble sort as input size grows. At n=10,000, the difference is 132,000 vs 100,000,000 operations.
Choosing Data Structures
Need fast lookups? Hash tables offer O(1) average. Need sorted data? Consider BST with O(log n). Frequent insertions? Linked lists provide O(1).
Estimating Performance
Calculate how long an algorithm might take. If O(n²) takes 1 second for n=1,000, it takes ~17 minutes for n=100,000.
Interview Practice
Review complexity classes and their characteristics before technical interviews. Know which algorithms fall into which category.
Frequently Asked Questions
O(n) grows linearly—doubling n doubles the time. O(n log n) grows slightly faster due to the log factor. For n=1,000,000, O(n) is 1M operations while O(n log n) is about 20M operations. Both are efficient and considered 'fast' algorithms.