1. Big-O notation: space complexity
Welcome back! In our previous video, we explored time complexity and how it helps us understand the performance of our code as input size grows. Now, let's dive into an equally important concept: Space Complexity.
2. What is space complexity?
While time complexity measures how input size affects runtime, space complexity measures how input size affects memory usage.
For Java developers, understanding space complexity is crucial for building applications that only use memory when absolutely needed and avoid crashing with errors such as `OutOfMemoryError`.
3. Big-O Notation
Just like with time complexity, we use Big-O notation to describe space complexity. Let's review some common space complexity classes through practical examples.
4. A maximum-finder method
First, let's look at operations with `O(1)` or constant space complexity. This means the amount of extra memory used doesn't depend on input size.
In this example, we're only using a single variable `max` regardless of the input array size. Whether our array of integers has 10 elements or 10 million, we still use the same amount of extra memory. That's why we classify it as `O(1)` or constant space.
5. A doubling method
Now, let's look at an example with `O(n)` linear space complexity, where memory usage grows in direct proportion to input size.
Here, we have some code that, given an array of integers, returns another array with those integers doubled.
You can see that in this implementation we create a new array that's the same size as our input array.
If our input has `n` elements, we need space for `n` additional elements. The space complexity is `O(n)` because the extra memory needed grows linearly with the input size.
6. A multiplication table method
Finally, let's examine a case with `O(n²)` space complexity.
This function creates a multiplication table of size `n×n`. The space required grows quadratically with the input - if `n` is 10, we need 100 cells; if `n` is 100, we need 10,000 cells. That's why we classify it as `O(n²)`.
7. Why is space complexity important?
Understanding space complexity matters because memory is a finite resource - applications that consume too much memory can crash or slow down systems.
To see this in action, let's compare how our examples would behave with different input sizes. For an input size of 10 thousand elements:
- `findMax`, which is O(1), uses just a few bytes of extra memory
- `doubleValues`, which is O(n), uses approximately 40KB of extra memory (assuming 4 bytes per integer)
- `multiplicationTable`, which is O(n²), would need around 400MB of extra memory!
This shows why the complexity considerations are so important.
8. Space complexity vs. time complexity
When optimizing Java applications, we often face trade-offs between time and space complexity. Sometimes we can save time by using more memory, and other times we might accept slower performance to reduce memory usage. The right choice depends on your specific application constraints.
In the next chapters of this course, we'll see examples where this trade-off has significant impact.
9. Let's practice!
Now, let's practice applying these concepts with some real Java code examples!