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What are the benefits of using Map over ArrayList of costume class

I am learning Java now and I am learning about different kinds of collections, so far I learned about LinkedList, ArrayList and Array[].
Now I've been introduced to Hash types of collections, HashSet and HashMap, and I didn't quite understand why there are useful, because the list of commands that they support is quietly limited, also, they are sorted in a random order and I need to Override the equal and HashKey methods in order to make it work right with class.
Now, what I don't understand is the benefits over the hassle of using these types instead of ArrayList of a costume class.
I mean, what Map is doing is connecting 2 objects as 1, but wouldn't it just be better to create a class that contains this 2 objects as parameters, and have getters to modify and use them?
If the benefit is that this Hash objects can only contain 1 object of the same name, wouldn't it just be easier to make the ArrayList check that the type is not already there before adding it?
So far I learned to choose when to use LinkedList, ArrayList or Array[] by the rule of "if it's really simple, use Array[], if it's a bit more complex use ArrayList (for example to hold collection of certain class), and if the list is dynamic with a lot of objects inside that need to change order according to removing or adding a new one in the middle or go back and forth within the list then use LinkedList.
But I couldn't understand when to prefer HashMap or HashSet, and I would be really glad if you could explain it to me.

Let me help you out here...
Hashed collections are the most efficient to add, search and remove data, since they hash the key (in HashMap) or the element (in HashSet) to find the place where they belong in a single step.
The concept of hashing is really simple. It is the process of representing an object as a number that can work as it´s id.
For example, if you have a string in Java like String name = "Jeremy";, and you print its hashcode: System.out.println(name.hashCode());, you will see a big number there (-2079637766), that was created using that string object values (in this string object, it's characters), that way, that number can be used as an Id for that object.
So the Hashed collections like the ones mentioned above, use this number to use it as an array index to find the elements in no-time. But obviously is too big to use it as an array index for a possible small array. So they need to reduce that number so it fits in the range of the array size. (HashMap and HashSet use arrays to store their elements).
The operation that they use to reduce that number is called hashing, and is something like this: Math.abs(-2079637766 % arrayLength);.
It's not like that exactly, it's a bit more complex, but this is to simplify.
Let's say that arrayLength = 16;
The % operator will reduce that big number to a number smaller than 16, so that it can be fit in the array.
That is why a Hashed collection will not allow duplicate, because if you try to add the same object or an equivalent one (like 2 strings with the same characters), it will produce the same hashcode and will override whatever value is in the result index.
In your question, you mentioned that if you are worried about duplicates items in an ArrayList, we can just check if the item is there before inserting it, so this way we don't need to use a HashSet. But that is not a good idea, because if you call the method list.contains(elem); in an ArrayList, it needs to go one by one comparing the elements to see if it's there. If you have 1 million elements in the ArrayList, and you check if an element is there, but it is not there, the ArrayList iterated over 1 million elements, that is not good. But with a HashSet, it would only hashed the object and go directly where it is supposed to be in the array and check, doing it in just 1 step, instead of 1 million. So you see how efficient a HashSet is compared to an ArrayList.
The same happens with a HashMap of size 1 million, that it will only take 1 single step to check if a key is there, and not 1 million.
The same thing happens when you need to add, find and remove an element, with the hashed collections it will do all that in a single step (constant time, doesn't depend on the size of the map), but that varies for other structures.
That's why it is really efficient and widely used.
Main Difference between an ArrayList and a LinkedList:
If you want to find the element at place 500 in an ArrayList of size 1000, you do: list.get(500); and it will do that in a single step, because an ArrayList is implemented with an array, so with that 500, it goes directly where the element is in the array.
But a LinkedList is not implemented with an array, but with objects pointing to each other. This way, they need to go linearly and counting from 0, one by one until they get to the 500, which is not really efficient compared to the 1 single step of the ArrayList.
But when you need to add and remove elements in an ArrayList, sometimes the Array will need to be recreated so more elements fit in it, increasing the overhead.
But that doesn't happen with the LinkedList, since no array has to be recreated, only the objects (nodes) have to be re-referenced, which is done in a single step.
So an ArrayList is good when you won't be deleting or adding a lot of elements on the structure, but you are going to read a lot from it.
If you are going to add and remove a lot of elements, then is better a linked list since it has less work to do with those operations.
Why you need to implement the equals(), hashCode() methods for user-defined classes when you want to use those objects in HashMaps, and implement Comparable interface when you want to use those objects with TreeMaps?
Based on what I mentioned earlier for HashMaps, is possible that 2 different objects produce the same hash, if that happens, Java will not override the previous one or remove it, but it will keep them both in the same index. That is why you need to implement hashCode(), so you make sure that your objects will not have a really simple hashCode that can be easily duplicated.
And the reason why is recommended to override the equals() method is that if there is a collision (2 or more objects sharing the same hash in a HashMap), then how do you tell them apart? Well, asking the equals() method of those 2 objects if they are the same. So if you ask the map if it contains a certain key, and in that index, it finds 3 elements, it asks the equals() methods of those elements if its equals() to the key that was passed, if so, it returns that one. If you don't override the equals() method properly and specify what things you want to check for equality (like the properties name, age, etc.), then some unwanted overrides inside the HashMap will happen and you will not like it.
If you create your own classes, say, Person, and has properties like name, age, lastName and email, you can use those properties in the equals() method and if 2 different objects are passed but have the same values in your selected properties for equality, then you return true to indicate that they are the same, or false otherwise. Like the class String, that if you do s1.equals(s2); if s1 = new String("John"); and s2 = new String("John");, even though they are different objects in Java Heap Memory, the implementation of String.equals method uses the characters to determine if the objects are equals, and it returns true for this example.
To use a TreeMap with user-defined classes, you need to implement the Comparable interface, since the TreeMap will compare and sort the objects based on some properties, you need to specify by which properties your objects will be sorted. Will your objects be sorted by age? By name? By id? Or by any other property that you would like. Then, when you implement the Comparable interface and override the compareTo(UserDefinedClass o) method, you do your logic and return a positive number if the current object is greater than the o object passed, 0 if they are the same and a negative number if the current object is smaller. That way, the TreeMap will know how to sort them, based on the number returned.

First HashSet. In HashSet, you can easily get whether it contains given element. Let's have a set of people in your class and you want to ask whether a guy is in your class. You can make an array list of strings. And if you want to ask if a guy is in your class, you have to iterate through whole the list until you find him, which might be too slow for longer lists. If you use HashSet instead, the operation is much faster. You calculate the hash of the searched string and then you go directly to the hash, so you don't need to pass so many elements to answer your question. Well, you can also make a workaround to make the ArrayList faster to access for this purpose but this is already prepared.
And now HashMap. Now imagine that you also want to store a score for each person. So now you can use HashMap. You enter the name and you get his score in a short time, without the need of iterating through whole the data structure.
Does it make sense?

Concerning your question:
"But I couldn't understand when to prefer HashMap or HashSet, and I
would be really glad if you could explain it to me"
The HashMap implement the Map interface, to be used for mapping a Key (K) to a value (V) in constant time, and where order doesn't matter, so you can put and retrieve those data efficiently if you now the key.
And HashSet implement the Set interface, but is internanly using and HashMap, its role is to be used as a Set, meaning you're not supposed to retrieve an element, you just check that is in the set or not (mostly).
In HashMap, you can have identical value, while you can't in a Set (because its a property of a Set).
Concerning this question :
If the benefit is that this Hash objects can only contain 1 object of the same name, >wouldn't it just be easier to make the ArrayList check that the type is not already >there before adding it?
When dealing with collection, you have may base you choice of a particular one on the data representation but also on the way you want to access and store those data, how do you access it ? Do you need to sort them ? Because each implemenation may have different complexity (https://en.wikipedia.org/wiki/Time_complexity), it become important.
Using the doc,
For ArrayList:
The add operation runs in amortized constant time, that is, adding n elements requires O(n) time. All of the other operations run in linear time (roughly speaking).
For HashMap:
This implementation provides constant-time performance for the basic operations (get and put), assuming the hash function disperses the elements properly among the buckets. Iteration over collection views requires time proportional to the "capacity" of the HashMap instance (the number of buckets) plus its size (the number of key-value mappings). Thus, it's very important not to set the initial capacity too high (or the load factor too low) if iteration performance is important.
So it's about the time complexity.
You may choose even more untypical collection for certain problems :).

This has little to do with Java specifically, and the choice depends mostly on performance requirements, but there's a fundamental difference that must be highlighted. Conceptually, Lists are types of collections that keep the order of insertion and may have duplicates, Sets are more like bags of items that have no specific order and no duplicates. Of course, different implementations may find a way around it (like a TreeSet).
First, let's check the difference between ArrayList and LinkedList. A linked list is a set of nodes, where each node contains a value and a link to the next and previous nodes. This makes inserting an element to a linked list a matter of appending a node to the end of the list, which is a quick operation since the memory does not have to be contiguous, as long as a node keeps a reference to the next node. On the other side, accessing a specific element requires transversing the entire list until finding it.
An array list, as the name implies, wraps an array. Accessing elements in an array by using its index is direct access, but inserting an element implies resizing the array to include the new element, so the memory it occupies is contiguous, making writes a bit heavier in this case.
A HashMap works like a dictionary, where for each key there's a value. The behavior of the insertion will mostly depend on how the hashCode and equals functions of the object used as a key are implemented. If the hashCode of two keys is the same, there's a hash collision, so equals will be used to understand if it's the same key or not. If equals is the same, then it's the same key, so the value is replaced. If not, the new value is added to the collection. Accessing and Writing values depends mostly on calculating the hash of the key followed by direct access to the value, making both operations really quick, O(1).
A set is pretty much like a hash map, without the "values" part, thus, it follows the same rules regarding the implementation of hashCode and equals operations for the added value.
It might be handy to study a bit about the Big-O notation and complexity of algorithms. If you are starting with Java, I'd strongly recommend the book Effective Java, by Joshua Bloch.
Hope it helps you dig further.

Data Structure with following properties?

Is there a data structure that does the following:
Returns the value given the index
Returns the index given the value
Returns all values sorted by index as List<>
As far as I am aware, a HashMap supports property 2, doesn't support properties 1 and 3.
An ArrayList supports 1 and 3 but not 2.
Is there something that fits my needs?

(1) and (2) describe a bi-directional map; the Guava library provides several implementations of this data structure.
Unfortunately there isn't a SortedBiMap class (presently), however depending on your specific constraints you may be able to address (3) in different ways.
For example, the simplest thing to do would be to create a new wrapping type that contains a BiMap<Integer, V> and a List<V> and ensures the two data structures are kept in sync. This may be inefficient for some use-cases (e.g. removals are O(n) due to the backing list) but may well be all you need.
Alternatively you could try to loosen constraint (3) if you don't really need a List, but just need to be able to iterate in a fixed order, in which case you could probably use Guava's ImmutableBiMap, which is guaranteed to iterate in insertion-order.
Otherwise, you could probably create your own SortedBiMap type modeled after HashBiMap but using TreeMap instead of HashMap. This would allow you to iterate over the keys in order (e.g. 0->n) regardless of their insertion order.

List (Any List including ArrayList) supports all 3 of your requirments. 1 and 3 you already know about, for #2 see method indexOf(). Also see related method lastIndexOf()

Creating a map with a collection as the Key?

Is it possible to create a map where the key is a Collection (any sort of collection)?
If I try it on most common collections I'm told the collection can't be cast to comparable.
I've been trying to write a compareTo function for a custom collection, but I am struggling.
Either I need to write the compareTo, or I need to find a premade Map that accepts collections/Collection accepted by Maps.
How can I use a collection as a key on a map? I've looked over Stack overflow and I've googled this problem several times, but I've never found a solid solution!
The reason I want to do this is that I've written a 'shuffle' simulation in Java that mimic card shuffling. I want to be able to count up the number of times a specific hand (modeled as a collection) comes up. It would look something like this:
H4,C3,D2: 8
H9,D6,S11: 10
......

Is it possible to create a map where the key is a Collection (any sort of collection)?
Yes it is possible, but definitely not recommended. If your collection changes, it is likely that its hashcode will also change and that can lead to surprising behaviour.
See Map's javadoc:
Note: great care must be exercised if mutable objects are used as map keys. The behavior of a map is not specified if the value of an object is changed in a manner that affects equals comparisons while the object is a key in the map.
If I try it on most common collections I'm told the collection can't be cast to comparable.
The key does not need to be comparable, unless you use a sorted map, i.e. TreeMap. Use a simple HashMap and you won't have the issue.
Following your edit, I would create a new immutable Hand class:
class Hand implements Comparable<Hand> {
private final List<Card> cards;
Hand(Card c1, Card c2, Card c3) {
cards = Collections.unmodifiableList(Arrays.asList(c1, c2, c3));
}
//getters, no setters
//implement compareTo
}
and implement compareTo if you want to use it in a TreeSet<Hand, Integer> and sort by hand strength for example.

Yes, you can use any collection as a key. If you want a SortedMap like TreeMap you have to provide a Comparator to determine the order. However if you use any kind of HashMap you don't need.
Map<List<Integer>, String> map = new HashMap<>();
map.put(Arrays.asList(1,2,3), "one to three");
map.put(Arrays.asList(7,8,9), "seven eat nine");
System.out.println(map);
prints
{[1, 2, 3]=one to three, [7, 8, 9]=seven eat nine}

map vs ?? for storing name and score

I used hashmap to store data.
The problem is that I just noticed hashmap can't have more than one same key.
What else should I use to store data which the data looks like this:
Name1 100.0
Name2 99.8
Name3 121.5
...
Other thing I'm trying to do is to show data of one certain person, when I call that key.
So, is there way to store more than one value related to one key? or should I use other type of storage?

A hashmap can have duplicate keys if you store the values within another data structure such as a linked list or a tree at each key index. Then you just have to decide how to handle the collisions.
Edit:
HashMap
["firstKey"] => LinkedList of (3,4,5)
["secondKey"] => null
["thirdKey"] => LinkedList of (3)

To extend on Matthew Coxes answer, you could extend the Hashtable Class so that it automatically manages your lists for you and would give you the appearance of having multiple keys.

The Google guava library contain some collection type that allow for more that one element per key. The Multimap is the first one that come to mind.
http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/collect/Multimap.html
Guava in general contain a lot of very convenient utilities, I think its worth checking out.
If you can't use an external library, you can simply (Like Matthew Cox said) mix a map and a List with Map<K, List<V>>. But that is a bit more inconvenient to work with since you have to initialise a list for every key.

I'd rather go with my own datamodel and store that in a list, or map if you want fast access, e.g.
public class Player {
private String name;
private List<Float> scores;
}
The advantages:
you can easily see, what the structure wants to express
you can easily extend it (e.g. add aliases for the player, or calculate the avarage scor of player 1)

Difference between HashMap and ArrayList in Java?

In Java, ArrayList and HashMap are used as collections. But I couldn't understand in which situations we should use ArrayList and which times to use HashMap. What is the major difference between both of them?

You are asking specifically about ArrayList and HashMap, but I think to fully understand what is going on you have to understand the Collections framework. So an ArrayList implements the List interface and a HashMap implements the Map interface. So the real question is when do you want to use a List and when do you want to use a Map. This is where the Java API documentation helps a lot.
List:
An ordered collection (also known as a
sequence). The user of this interface
has precise control over where in the
list each element is inserted. The
user can access elements by their
integer index (position in the list),
and search for elements in the list.
Map:
An object that maps keys to values. A
map cannot contain duplicate keys;
each key can map to at most one value.
So as other answers have discussed, the list interface (ArrayList) is an ordered collection of objects that you access using an index, much like an array (well in the case of ArrayList, as the name suggests, it is just an array in the background, but a lot of the details of dealing with the array are handled for you). You would use an ArrayList when you want to keep things in sorted order (the order they are added, or indeed the position within the list that you specify when you add the object).
A Map on the other hand takes one object and uses that as a key (index) to another object (the value). So lets say you have objects which have unique IDs, and you know you are going to want to access these objects by ID at some point, the Map will make this very easy on you (and quicker/more efficient). The HashMap implementation uses the hash value of the key object to locate where it is stored, so there is no guarentee of the order of the values anymore. There are however other classes in the Java API that can provide this, e.g. LinkedHashMap, which as well as using a hash table to store the key/value pairs, also maintains a List (LinkedList) of the keys in the order they were added, so you can always access the items again in the order they were added (if needed).

If you use an ArrayList, you have to access the elements with an index (int type). With a HashMap, you can access them by an index of another type (for example, a String)
HashMap<String, Book> books = new HashMap<String, Book>();
// String is the type of the index (the key)
// and Book is the type of the elements (the values)
// Like with an arraylist: ArrayList<Book> books = ...;
// Now you have to store the elements with a string key:
books.put("Harry Potter III", new Book("JK Rownling", 456, "Harry Potter"));
// Now you can access the elements by using a String index
Book book = books.get("Harry Potter III");
This is impossible (or much more difficult) with an ArrayList. The only good way to access elements in an ArrayList is by getting the elements by their index-number.
So, this means that with a HashMap you can use every type of key you want.
Another helpful example is in a game: you have a set of images, and you want to flip them. So, you write a image-flip method, and then store the flipped results:
HashMap<BufferedImage, BufferedImage> flipped = new HashMap<BufferedImage, BufferedImage>();
BufferedImage player = ...; // On this image the player walks to the left.
BufferedImage flippedPlayer = flip(player); // On this image the player walks to the right.
flipped.put(player, flippedPlayer);
// Now you can access the flipped instance by doing this:
flipped.get(player);
You flipped player once, and then store it. You can access a BufferedImage with a BufferedImage as key-type for the HashMap.
I hope you understand my second example.

Not really a Java specific question. It seems you need a "primer" on data structures. Try googling "What data structure should you use"
Try this link http://www.devx.com/tips/Tip/14639
From the link :
Following are some tips for matching the most commonly used data structures with particular needs.
When to use a Hashtable?
A hashtable, or similar data structures, are good candidates if the stored data is to be accessed in the form of key-value pairs. For instance, if you were fetching the name of an employee, the result can be returned in the form of a hashtable as a (name, value) pair. However, if you were to return names of multiple employees, returning a hashtable directly would not be a good idea. Remember that the keys have to be unique or your previous value(s) will get overwritten.
When to use a List or Vector?
This is a good option when you desire sequential or even random access. Also, if data size is unknown initially, and/or is going to grow dynamically, it would be appropriate to use a List or Vector. For instance, to store the results of a JDBC ResultSet, you can use the java.util.LinkedList. Whereas, if you are looking for a resizable array, use the java.util.ArrayList class.
When to use Arrays?
Never underestimate arrays. Most of the time, when we have to use a list of objects, we tend to think about using vectors or lists. However, if the size of collection is already known and is not going to change, an array can be considered as the potential data structure. It's faster to access elements of an array than a vector or a list. That's obvious, because all you need is an index. There's no overhead of an additional get method call.
4.Combinations
Sometimes, it may be best to use a combination of the above approaches. For example, you could use a list of hashtables to suit a particular need.
Set Classes
And from JDK 1.2 onwards, you also have set classes like java.util.TreeSet, which is useful for sorted sets that do not have duplicates. One of the best things about these classes is they all abide by certain interface so that you don't really have to worry about the specifics. For e.g., take a look at the following code.
// ...
List list = new ArrayList();
list.add(

Use a list for an ordered collection of just values. For example, you might have a list of files to process.
Use a map for a (usually unordered) mapping from key to value. For example, you might have a map from a user ID to the details of that user, so you can efficiently find the details given just the ID. (You could implement the Map interface by just storing a list of keys and a list of values, but generally there'll be a more efficient implementation - HashMap uses a hash table internally to get amortised O(1) key lookup, for example.)

A Map vs a List.
In a Map, you have key/value pairs. To access a value you need to know the key. There is a relationship that exists between the key and the value that persists and is not arbitrary. They are related somehow. Example: A persons DNA is unique (the key) and a persons name (the value) or a persons SSN (the key) and a persons name (the value) there is a strong relationship.
In a List, all you have are values (a persons name), and to access it you need to know its position in the list (index) to access it. But there is no permanent relationship between the position of the value in the list and its index, it is arbitrary.