Compare Big O Complexity Curves

Name: Compare Big O Complexity Curves
Author: Kitmul

Visualize and compare Big O complexity curves from O(1) to O(n!) on an interactive chart.

Visualize and compare Big O complexity curves side by side on an interactive chart. Toggle O(1), O(log n), O(n), O(n log n), O(n2), O(n3), O(2n), and O(n!) to see how operations scale with input size. Adjust n with a slider, switch to logarithmic scale, and view a comparison table with operation counts at different sizes. Everything runs in your browser with zero server calls.

n =50Log scale

Complexity	Type	n=10	n=100	n=1000	Example
O(1)	Constant	1	1	1	Array access, hash lookup
O(log n)	Logarithmic	3.3	6.6	10.0	Binary search
O(n)	Linear	10	100	1.0K	Linear scan, single loop
O(n log n)	Linearithmic	33.2	664.4	10.0K	Merge sort, heap sort
O(n²)	Quadratic	100	10.0K	1.0M	Bubble sort, nested loops

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Tutorial

How to Use

Select Complexities

Click the complexity buttons to toggle which curves appear on the chart. Each has a distinct color for easy comparison.

Adjust Input Size

Use the n slider to change the maximum input size. Watch how different complexities diverge as n grows larger.

Compare in Table

Review the table below the chart to see exact operation counts at n=10, n=100, and n=1000 for each selected complexity.

Guide

Complete Guide to Big O Notation

Why Big O Matters

Big O notation is the universal language for describing algorithm efficiency. It lets you compare algorithms independently of hardware, language, or implementation details. Understanding Big O is essential for choosing the right data structure and algorithm for any problem.

Common Complexity Classes

From fastest to slowest: O(1) constant, O(log n) logarithmic, O(n) linear, O(n log n) linearithmic, O(n2) quadratic, O(n3) cubic, O(2n) exponential, O(n!) factorial. Most practical algorithms fall between O(log n) and O(n2).

Best, Average, and Worst Case

Big O typically describes worst-case performance. Some algorithms like quicksort have O(n2) worst case but O(n log n) average case. Understanding all three cases helps you choose algorithms that perform well under real conditions.

Space vs Time Complexity

Big O applies to both time and space. An algorithm might be O(n) in time but O(n2) in space. Trading time for space or vice versa is a fundamental design decision in algorithm selection.

Sources

Examples

Worked Examples

Example: Linear vs Quadratic at Scale

Compare O(n) and O(n2) for n=1000.

Step 1: O(n) at n=1000 = 1,000 operations.

Step 2: O(n2) at n=1000 = 1,000,000 operations.

Step 3: The quadratic algorithm does 1000x more work than linear.

Result: At n=1000, O(n2) is 1000 times slower than O(n). This gap widens as n grows.

Example: When Exponential Becomes Impractical

Compare O(n log n) and O(2n) for increasing n.

Step 1: At n=10, O(n log n) = 33, O(2n) = 1,024.

Step 2: At n=20, O(n log n) = 86, O(2n) = 1,048,576.

Step 3: At n=30, O(n log n) = 147, O(2n) = 1,073,741,824.

Result: O(2n) becomes impractical around n=25-30 even on modern hardware, while O(n log n) handles millions of inputs easily.

Use Cases

Study Algorithm Efficiency

“Toggle O(n) and O(n log n) to see why merge sort outperforms bubble sort. The visual gap between curves makes the theoretical difference concrete and memorable.”

Prepare for Technical Interviews

“Interviewers often ask about time complexity. Seeing O(n2) explode compared to O(n log n) builds the intuition needed to choose the right algorithm under time pressure.”

Evaluate Scaling Decisions

“Compare your algorithm's complexity class against alternatives. If your solution is O(n2) and an O(n log n) option exists, the chart shows exactly when the difference matters.”

Frequently Asked Questions

?What is Big O notation?

Big O describes how an algorithm's time or space grows as input size increases. O(n) means linear growth; O(n2) means quadratic. It focuses on the dominant term and ignores constants.

?Why does O(n log n) matter?

O(n log n) is the best possible time complexity for comparison-based sorting. Algorithms like merge sort and heap sort achieve this, making it a key benchmark for efficiency.

?What is the difference between O(2n) and O(n!)?

Both grow extremely fast, but O(n!) grows far faster. At n=20, O(2n) is about 1 million while O(n!) is 2.4 quintillion. Neither is practical for large inputs.

?Does Big O include constants?

No. Big O drops constants and lower-order terms. An algorithm that takes 3n+5 steps is O(n). This simplification focuses on scaling behavior rather than exact speed.

?What does logarithmic scale show?

Log scale compresses the Y axis so you can see all complexities on one chart. Without it, exponential and factorial curves make polynomial curves invisible.

?Is my data private when using this tool?

Completely. All calculations and rendering happen in your browser. No data is sent to any server.

?Is this tool free to use?

Yes. Fully free with no sign-up, no limits, and no ads.

?Can I add custom complexity functions?

The current version includes the eight most common complexity classes. These cover virtually all standard algorithm analysis scenarios.

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Boost Your Capabilities

Compare Big O Complexity Curves

How to Use

Select Complexities

Adjust Input Size

Compare in Table

Complete Guide to Big O Notation

Why Big O Matters

Common Complexity Classes

Best, Average, and Worst Case

Space vs Time Complexity

Worked Examples

Example: Linear vs Quadratic at Scale

Example: When Exponential Becomes Impractical

Use Cases

Study Algorithm Efficiency

Prepare for Technical Interviews

Evaluate Scaling Decisions

Frequently Asked Questions

?What is Big O notation?

?Why does O(n log n) matter?

?What is the difference between O(2n) and O(n!)?

?Does Big O include constants?

?What does logarithmic scale show?

?Is my data private when using this tool?

?Is this tool free to use?

?Can I add custom complexity functions?

How do you like this tool?

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Abstract Syntax Tree (AST) Visualizer

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