Just like time complexity helps us measure how fast an algorithm runs, space complexity measures how much memory an algorithm needs. This is important because efficient memory use can be as crucial as fast execution, especially when working with large data sets or memory-limited devices.

What is Space Complexity?

Space complexity is the total amount of memory an algorithm requires, including:

1. Auxiliary Space: The temporary memory used by the algorithm to perform operations, excluding the input data and output spaces.
2. Output Space: The memory used to store the output.

So, space complexity = auxiliary space + Output Space.

Why Does Space Complexity Matter?

Efficient space usage allows algorithms to run smoothly without causing memory overflows or slowing down the system due to excessive memory consumption. It’s especially important when:

• Working with Large Data: Managing large files, big databases, or streams of data.
• Running on Memory-Limited Devices: Devices like smartphones or embedded systems have limited memory, making space efficiency essential.
• Improving Performance: Sometimes reducing space can also improve speed since less memory use often means fewer operations for memory management.

Measuring Space Complexity

To measure space complexity, we look at the amount of memory an algorithm needs as the input size grows, often using asymptotic notations like O(n), O(1), etc.

Here we have covered some commonly used space complexities.

1. Constant Space – O(1): Algorithms that don’t grow in memory usage with input size. They only use a fixed amount of extra space, regardless of the data size.

2. Linear Space – O(n): Algorithms that require memory proportional to the input size, such as those storing additional information for each input element.

3. Quadratic or Higher Space: Less common, these algorithms use memory that grows quadratically (O(n^2)) or even faster, often due to nested data structures or recursive calls.

In the next lesson, Analyzing Space Requirements, we’ll break down how to calculate the space complexity of specific algorithms and go over examples in detail.