Big O Calculator – Analyze Code Time & Space Complexity

Ever wondered how fast your code runs or how much memory it uses? The Big O Calculator helps you analyze the time and space complexity of your code so you can optimize performance like a pro.

Understanding Big O notation is key for cracking coding interviews, writing efficient programs, and scaling real-world applications.

What is Big O Notation?

Big O notation describes how the runtime or memory usage of an algorithm grows relative to the input size.

Here are some common types:

• O(1) – Constant Time
• O(n) – Linear Time
• O(n²) – Quadratic Time
• O(log n) – Logarithmic Time

Real-life analogy:

• Looking for a name in an unsorted list = O(n)
• Looking in a phonebook with alphabetical order = O(log n)
• Doing the same task repeatedly = O(n²)

To deepen your understanding of Big O, check out this Big O Cheatsheet – a visual guide to time and space complexities.

How the Big O Calculator Works

Inputs:
Paste your code snippet into the input box.

Output:
The calculator analyzes your code’s loops, recursion, and control structures to estimate time and space complexity.

Logic Behind It:
The tool uses static code analysis and heuristics based on known algorithmic patterns (like loop nesting, recursion depth, etc.).

Common Time Complexities

Here’s a quick reference:

Big O	Description	Example Use
O(1)	Constant time	Accessing array index
O(log n)	Logarithmic time	Binary search
O(n)	Linear time	Iterating through array
O(n log n)	Log-linear time	Merge sort, quick sort
O(n²)	Quadratic time	Nested loops (bubble sort)
O(2ⁿ)	Exponential time	Recursive Fibonacci
O(n!)	Factorial time	Solving permutations

Code Examples of Time Complexities

Example 1: Linear Search – O(n)

def linear_search(arr, target):
    for i in arr:
        if i == target:
            return True
    return False

Example 2: Binary Search – O(log n)

def binary_search(arr, target):
    low, high = 0, len(arr) - 1
    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == target:
            return True
        elif arr[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return False

Best, Worst, and Average Case Analysis

Algorithms perform differently depending on input:

• Best Case: Minimum work needed
• Worst Case: Maximum effort required
• Average Case: Typical performance over random inputs

Example:

• Linear Search
  • Best: O(1) (found at start)
  • Worst: O(n) (found at end)
• Binary Search
  • Best: O(1)
  • Worst: O(log n)

Space Complexity – The Other Side of the Equation

Space complexity measures how much memory your program uses as input grows.

Key Points:

• Independent memory = O(1)
• Creating new arrays/lists = O(n) or more
• Recursive calls = O(depth)

It’s essential for apps running on limited-memory devices or when handling huge datasets.

For further reading, check out this Wikipedia article on Space Complexity that covers its importance in algorithm analysis.

Big O Cheat Sheet Table

Complexity	Performance	Example	Best Use
O(1)	Fastest	Hash table lookup	Small, fixed-size operations
O(log n)	Very efficient	Binary search	Sorted data structures
O(n)	Scalable	For loop	List iteration
O(n log n)	Efficient sorting	Merge/Quick sort	Most practical sorts
O(n²)	Slow with growth	Nested loops	Small datasets only
O(2ⁿ)	Explosive growth	Recursive brute-force	Avoid when possible
O(n!)	Impractical	Permutations	Rare use cases

Why You Should Use a Big O Calculator

• ✅ Helps in cracking coding interviews
• ✅ Quickly spots inefficient logic
• ✅ Ideal for students and devs learning DSA
• ✅ Encourages writing scalable code

Want more tools to help with math-related calculations? Browse our full collection on the Math Calculators page.

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