I know what static is, but just not sure when to use it.
static variable: I only used it for constant fields. Sometimes there are tens of constants in a class, so using static constants can save lots of memory. Is there any other typical use cases?
static method: I use it when I make a class about algorithms. For example, a class which provides different sorting algorithms. Is it against OOP design? I think it is better to maintain this way rather than implementing sorting algorithms inside each class that needs to use them. Am I wrong? What are some good use cases?
Also, are there any performance difference between using static and non-static fields/methods?
You are describing cases where you've used static, but this doesn't quite explain fundamentally why you would use static vs non-static - they are more than just keywords for constants and utility methods.
When something is not static (instance), it means that there is an instance of it for each instance of the class. Each one can change independently.
When something is static, it means there is only one copy of it for all instances of the class, so changing it from any location affects all others.
Static variables/methods typically use less memory because there is only one copy of them, regardless of how many instances of the class you have. Statics, when used appropriately, are perfectly fine in object oriented design.
If you have a method/variable that you only need one instance of (e.g. a constant or a utility method), then just make it static. Understand though that making a method static means it cannot be overridden. So if you have a method you want to override in a subclass, then don't make it static.
The general rule of thumb is - if you need only one copy of it, make it static. If you need a copy per instance, then make it non static.
Is there any other typical use cases?
Global Variables
Is it against OOP design?
Not exaclty, the point is that static methods are stateless since you don't need a particular instance of a class. My favorite approach is for utility methods (like Apache Commons). But you may be aware that some methods may be better placed as class members instead of static.
Also static methods can make class testability harder once you can't override these methods or replace by mock implementation.
Performance difference ?
There's a performance Android recommendation from Google that says "prefer static over virtual":
http://developer.android.com/training/articles/perf-tips.html#PreferStatic
I'm not sure it's true for JVM since Android uses a different VM, but it makes sense given the reasons the link points out:
If you don't need to access an object's fields, make your method static. Invocations will be about 15%-20% faster. It's also good practice, because you can tell from the method signature that calling the method can't alter the object's state."
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