Technology

Space Complexity Calculator

Free space complexity analyzer for algorithms and data structures. Calculate memory usage, compare data structure overhead, and optimize memory consumption for better performance.

Optimize Your Program's Memory Usage

Space complexity determines how much memory your code needs. Understanding memory usage is crucial for embedded systems, mobile apps, large-scale data processing, and anywhere resources are limited. This calculator helps you analyze and optimize memory consumption.

What is Space Complexity?

Space complexity measures the total memory an algorithm uses relative to input size. It includes input space (storing the data) and auxiliary space (extra memory for computation). While time complexity gets more attention, space complexity often determines what's actually feasible.

Space Complexity

S(n) = Input Space + Auxiliary Space

Why Analyze Memory Usage?

Prevent Out-of-Memory Errors

A O(n²) matrix for 100,000 items needs 80GB of RAM. Know your limits before crashing in production.

Choose Right Data Structures

Hash tables trade O(n) space for O(1) lookup. Linked lists use extra pointer memory. Make informed trade-offs.

Optimize for Constraints

Mobile apps, embedded systems, and serverless functions have memory limits. Design algorithms that fit your constraints.

Reduce Cloud Costs

Memory costs money. Reducing memory usage from O(n²) to O(n) can cut cloud bills significantly at scale.

How to Use This Calculator

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Common Memory Patterns

O(1) - Constant Space

In-place algorithms like quicksort partitioning or two-pointer techniques. Uses fixed variables regardless of input size.

O(n) - Linear Space

Hash tables, arrays, merge sort auxiliary array. Memory grows proportionally with input. Most common for practical algorithms.

O(n²) - Quadratic Space

Adjacency matrices, 2D DP tables. Memory explodes quickly—a 10,000×10,000 matrix needs 800MB for 8-byte elements.

O(log n) - Recursion Stack

Binary search, balanced tree traversal. Stack depth grows logarithmically—very memory efficient for recursive solutions.

Frequently Asked Questions

Space complexity includes ALL memory: input + auxiliary. Auxiliary space is ONLY the extra memory beyond the input. For example, merge sort has O(n) space complexity (input + temp array) but O(n) auxiliary space (just the temp array). When comparing algorithms, auxiliary space is often more relevant.