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difference between List<Integer> arr and var arr

The following code works fine.
List<Integer> arr = new ArrayList<Integer>();
System.out.println(arr.getClass().getSimpleName()); // output: ArrayList
arr.add(0);
arr.add(1);
arr = arr.subList(0,1);
But if you change the first line to
var arr = new ArrayList<Integer>();
an error will occur:
java: incompatible types: java.util.List<java.lang.Integer> cannot be converted to java.util.ArrayList<java.lang.Integer>
However, even if arr is defined in the second way, its type is still ArrayList, so what is the difference?

When you write
var arr = new ArrayList<Integer>();
the compiler infers the type of the arr variable to be ArrayList<Integer>, so it's equivalent to writing:
ArrayList<Integer> arr = new ArrayList<Integer>();
arr.subList(0,1) returns a List<Integer>, which cannot be assigned to an ArrayList<Integer>, since an ArrayList<Integer> is an implementation of List<Integer>, but not all implementations of List<Integer> are ArrayList<Integer>.
On the other hand, when you declare the variable as List<Integer> arr, you can assign to it any implementation of List<Integer>, which includes the value returned by arr.subList(0,1).
It's important to note that subList does not return an ArrayList.
For example, subList() method of ArrayList returns an instance of an inner class called ArrayList$SubList. Such List cannot be assigned to a variable whose type is ArrayList.

ArrayList's toArray() Method not Working Properly

When looking through ArrayList's methods, I saw a method called toArray(). I tried out this method using the following code:
ArrayList<Integer> a = new ArrayList<>();
// Assigning random elements to the ArrayList
int[] b = a.toArray();
However, this showed the following exception in the compiler:
Incompatible types.
Required: int[]
Found: java.lang.Object[]
The next thing I tried next is down-casting it to int[]
ArrayList<Integer> a = new ArrayList<>();
// Assigning random elements to the ArrayList
int[] b = (int[]) a.toArray();
This showed another error:
Cannot cast java.lang.Object[] to int[]
The last thing I tried is making it an Integer[] instead, and down-casting it to Integer[]
ArrayList<Integer> a = new ArrayList<>();
// Assigning random elements to the ArrayList
Integer[] b = (Integer[]) a.toArray();
This one compiled, but as soon as I ran it it produced ClassCastException. How do I use this toArray() method without errors?

List can only hold reference types (like Integer). Integer is a wrapper type. To convert a List<Integer> to an int[] there is an option using a Stream to map the Integer values to int and then collect to an int[]. Like,
int[] b = a.stream().mapToInt(Integer::intValue).toArray();
System.out.println(Arrays.toString(b));

It's all written in the javadoc:
Integer[] b = a.toArray(new Integer[0]);

Extending the answer of #Matthieu, It seems you need to pass new Integer[]. Attaching an example link given in geeksforgeeks.
Integer[] arr = new Integer[a.size()];
arr = a.toArray(arr);

Defining an array of List of integers in Java

I have an array. For each element of the array, I want to store multiple integers. I know that in C I can make an array of integer pointers, and use that pointer to make a list.
In Java, I can make an array of object 'A', where A has a list of integers. But why can't I do something like this
List<Integer>[] arr = new ArrayList<Integer>[]();
I get:
Type mismatch: cannot convert from ArrayList to List[]

You typically want to avoid mixing collections and arrays together for this very reason; an array is covariant (that is, Integer[] is-an Object[]), but collections (and generics in general) are invariant (that is, a List<Integer> is not a List<Object>).
You can definitely create a list of lists instead, which will ensure type safety and get you around the issue of creating a generic array:
List<List<Integer>> intNestedList = new ArrayList<>();

As stated in Java's own documentation, you cannot create an array of generics.

If you want to create an array which can hold up to ten List<Integer> you must declare the array that way.
List<Integer>[] arr = new ArrayList[10];
following assignment is valid
List<Integer> intList = new ArrayList<>();
arr[0] = intList;
whereas following will fail with an compilation error
List<String> stringList = new ArrayList<>();
arr[0] = stringList;
the compilation fails with
incompatible types: java.util.List<java.lang.String>
cannot be converted to java.util.List<java.lang.Integer>

An ArrayList is a List, but an ArrayList is not a List[]
If you want an Array of Lists that hold integers, I would suggest:
List<Integer>[] xyz; // still writing code will update in a sec
It turns out you can't create arrays of parameterized types, according to the oracle docs.

Unless you know for sure you want a finite array, I suggest you do something like List<List<Integer>> arr = new ArrayList<List<Integer>>();
If you really want an array of Lists then you'll want to see this Java question about ArrayList<Integer>[] x

Creating an array of List is no different than creating an array of any other object. You can do any of the following:
List[] listsArray = new List[3];
listsArray[0] = new ArrayList();
listsArray[1] = new LinkedList();
listsArray[2] = new ArrayList();
Or:
List[] listsArray = new List[]{new ArrayList(), new LinkedList(), new ArrayList()};
Note that you are limited in what you can do with generics on arrays.

Not a very nice solution but you might try it with a cast. Something like this:
List<Integer>[] arr = (List<Integer>[]) new List[SIZE_OF_YOUR_ARRAY];
You will probably get a warning but it should still work.

As i found, you need an array of arrays.
you can do this, to make your inner arrays:
Integer[] array1 = new Integer[];
Integer[] array2 = new Integer[];
and then put them in another array like this:
Integer[][] arrays = new Integer[][] { array1, array2 };
or
Integer[][] arrays = { array1, array2 };
maybe it's better to do it like this:
List<List<Integer>> listOfLists = Lists.newArrayList();
listOfLists.add(Lists.newArrayList("123","456","789"));
after all I recommend you to read this:
How to make an array of arrays in Java

Graph Implementation using Adjacency List depicts the usage of an Array of List.
public class Graph {
int vertex;
LinkedList<Integer> list[];
public Graph(int vertex) {
this.vertex = vertex;
list = new LinkedList[vertex];
for (int i = 0; i <vertex ; i++) {
list[i] = new LinkedList<>();
}
}
}
As you can observe that the constructor of class Graph, is used to define the Array of List.
in the same constructor, Array Of List is initialized too.
Hope It would be Helpful to resolve your problem and requirement !.

ArrayList of Array of Strings

What is the difference between the two data structures defined below?
The second one is an ArrayList, whose elements have type 'String'. But what is the first data structure?
The initializations would also be different. Can anyone give an example here?
ArrayList<String>[] temp1;
ArrayList<String> temp2;

ArrayList<String>[] temp1;: This is an Array of ArrayList's that are containing Strings
ArrayList<String> temp2;: This is an ArrayList containing Strings
If you want an ArrayList of Arrays of Strings, you would have to do a ArrayList<String[]> temp3;. Note the position of the different brackets.
To initialize:
// create an array with 10 uninitialized ArrayList<String>
ArrayList<String>[] temp1 = new ArrayList[10];
// create empty lists that can be filled
for (int i=0; i<temp1.length; i++)
temp1[i] = new ArrayList<String>();
// create an empty list of Strings
ArrayList<String> temp2 = new ArrayList<String>();
// create an empty list of String arrays
ArrayList<String[]> temp3 = new ArrayList<String[]>();

I provide some example to differentiate the Array of ArrayList and ArrayList of String
public class ArrayOfArrayList {
public static void main(String[] args) {
// Declare the Array of ArrayList
List<String>[] arrayOfList = new ArrayList[2];
// Declare the Object of ArrayList
for(int i = 0; i < arrayOfList.length; i++) {
arrayOfList[i] = new ArrayList<>();
arrayOfList[i].add("" + (i + 1));
arrayOfList[i].add("" + (i + 2));
}
// Print out the result
for(List<String> list : arrayOfList) {
for(String str : list) {
System.out.println(str);
}
}
// Declare the Object of ArrayList
List<String> arrayList = new ArrayList<>();
arrayList.add("1");
arrayList.add("2");
// Print out the result
for(String str : arrayList) {
System.out.println(str);
}
}
}

The first data structure is an array of ArrayLists containing string objects

The first is an array of classes of the type ArrayList<String>. The second is simply an ArrayList<String> (ArrayList of Strings.)
In terms of initialisations:
ArrayList<String>[] lists = (ArrayList<String>[])new ArrayList[10];
ArrayList<String> temp2 = new ArrayList<String>();
The first initialisation has to specify a size for the array (note this is not a size for the ArrayList) and this is where the 10 comes from in my example. It can be any size you choose of course, 10 is just an arbitrary example. It will also generate a warning, but, if you really want an array of ArrayList<String> this is AFAIK the only way for now (the reason stems from the fact generics in Java aren't reified, but array types are.)

The second one is an ArrayList, whose elements have type 'String'. But what is the first data structure?
On the surface, it would appear to be an array of lists (containing strings). However arrays and generics don't play very well together. From the article:
Another consequence of the fact that arrays are covariant but generics are not is that you cannot instantiate an array of a generic type (new List<String>[3] is illegal), unless the type argument is an unbounded wildcard (new List<?>[3] is legal). Let's see what would happen if you were allowed to declare arrays of generic types:
List<String>[] lsa = new List<String>[10]; // illegal
Object[] oa = lsa; // OK because List<String> is a subtype of Object
List<Integer> li = new ArrayList<Integer>();
li.add(new Integer(3));
oa[0] = li;
String s = lsa[0].get(0);
The last line will throw a ClassCastException, because you've managed to cram a List<Integer> into what should have been a List<String>. Because array covariance would have allowed you to subvert the type safety of generics, instantiating arrays of generic types (except for types whose type arguments are unbounded wildcards, like List<?>) has been disallowed.

Yes, first is the Array of ArrayList and will have strings value in it.
second statement is only array list of Strings value.

List of Arrays in Java

What is the syntax for making a List of arrays in Java?
I have tried the following:
List<int[]> A = new List<int[]>();
and a lot of other things.
I need to be able to reorder the int arrays, but the elements of the int arrays need not to be changed. If this is not possible, why?
Thank you.

Firstly, you can't do new List(); it is an interface.
To make a list of int Arrays, do something like this :
List<int[]> myList = new ArrayList<int[]>();
P.S. As per the comment, package for List is java.util.List and for ArrayList java.util.ArrayList

List<Integer[]> integerList = new ArrayList<Integer[]>();
Use the object instead of the primitive, unless this is before Java 1.5 as it handles the autoboxing automatically.
As far as the sorting goes:
Collections.sort(integerList); //Sort the entire List
and for each array (probably what you want)
for(Integer[] currentArray : integerList)
{
Arrays.sort(currentArray);
}

List is an interface, not a class. You have to choose what kind of list. In most cases an ArrayList is chosen.
List a = new ArrayList();
You've mentioned that you want to store an int array in it, so you can specify the type that a list contains.
List<int[]> a = new ArrayList<int[]>();
While you can have a collection (such as a list) of "int[]", you cannot have a collection of "int". This is because arrays are objects, but an "int" is a primitive.