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Matching function name but different arguments

Studying "cracking the coding interview" in Java, on page 51 I came across:
void permutation(String str){
permutation(str,"");
}
void permutation(String str, String prefix){
if(str.length()==0){
System.out.println(prefix);
} else{
for(int i=0;i<str.length();i++){
String rem=str.substring(0,i)+str.substring(i+1);
permutation(rem,prefix+str.charAt(i));
}
}
}
I get that the first permutation function takes a string and calls the second permutation function which does all the work. However, isn't the second permutation a redeclaration of the first permutation function? How will Java recognize and use the first permutation function and not overwrite it?

How will java recognize and use the first permutation function?
When you call the method, Java will see what you're trying pass into it. Based on the arguments you pass, it will decide which 'version' of the method you are trying to use.
Like others have said - this is method overloading

Unlike in Python, in Java these two declarations live side-by-side -- the second doesn't replace the first. In Java, the rule is roughly that when you call a method with multiple definitions (aka an "overloaded" method), Java will look for the one that best matches the arguments you called it with and run that method. So permutation("hi") invokes the first version, and permutation("hi", "") calls the second.
The fundamental difference here is that in Python you can imagine the interpreter reading the definitions one at a time and replacing its overall definition of permutation every time it gets a new definition. In Java, you have to think of it as reading all the definitions of permutation at once, and calling the most appropriate one for any given invocation.
(A consequence of this is that Java also checks at compile-time that every overloaded version of a method is callable: for instance, if you wrote two versions of permutation that both took just a string as their argument, the compiler would give you an error and wouldn't compile your program at all. In python you'd just get the second definition.)

To explain what the semantics are, we need to take a look at how Java methods are differentiated.
In Java, a method is identified by its signature. JLS §8.4.2 specifies that
Two methods have the same signature if they have the same name and argument types.
Important to note is that the return type of a method is not part of a method's signature. Thus if one would write:
public class Foo {
void bar(String baz) {
}
String bar(String baz) {
}
}
Both methods would have the same signature. In Java, this would lead to a compilation error since it is not allowed to have two methods with the same signature in the same class.
The behaviour changes if we take inheritance into the picture:
public class Foo {
void bar(String baz);
}
public class Zoo extends Foo {
#Override
void bar(String baz);
}
In this case, class Zoo overrides method bar(...) of class Foo. Note that the annotation is not responsible for the behaviour and merely a compile-time check to ensure that there is a method void bar(String baz) in at least one parent-class.
The code presented has two method with same name, but different signatures. This is called Overloading in Java. Thus, the method are treated as not "equal". You could rename one of those method and they would not be more or less "equal".
To make things even weirder, if methods are overloaded, the signature for the method to call is made at compile-time. That means that only the static types of parameters can be considered. Let us look at the following code and figure out what the result is:
public class Test {
public static void main(final String... args) {
final String s = "foo";
final Object o = s;
print(s);
print(o);
}
private static void print(final String s) {
System.out.println("Called with String parameter");
}
private static void print(final Object o) {
System.out.println("Called with Object parameter");
}
}
Ideon demo
Now what is the static type of s? It is the type to the left, where s was declared, thus print(final String s) is called and "Called with String parameter" is printed. What is the static type of o? Again, it is the type to the left, where o was declard, and thus print(final Object o) is called and "Called with Object parameter" is printed out. One could argue that in this trivial example, the compiler could figure out that the type of o can only be String, but basing this behaviour on the ability of the compiler to recognize types at compile-time makes it only more confusing.

In java, the whole class is loaded before a method is executed.
This means that the second method is loaded/ready before the first method is executed and the first method is loaded/ready before the second method is executed.
This allows to call a method recursively, and to call a method that will be declared later.
Also, the method is overloaded.
In java, it's possible to create multiple methods with the same name in the same class if the parameters are different. The methods will be treated as different, deoending of the argument that are passed to the method.
In other words, the name alone does not define which method is called but the signature, including the parameters(not the return value)

type conversion at method calling

public class Demo1{
public static void main(String[] args){
show('A','A');
}
public static void show(char c, long a){
System.out.println("long-char");
}
public static void show(char c, int a){
System.out.println("char-int");
}
}
Output : char-int
But when I change the order of parameters in the first show() method (replacing
public static void show(char c, long a){} with public static void show(long a, char c) {}), I get a compilation error.

The compiler says that it is an ambiguous method call, because it is.
The general approach taken for overload resolution is to find the most specific applicable method, given the number and types of the actual parameters.
In the first case, the two methods have char as their first parameter; so it is only down to choosing whether the int or long overload is more specific, given that the actual parameter is a char: it is the int overload which is more specific, because int is narrower than long.
In the second case, one method has char as the first parameter; one method has char as the second parameter. So, given that the actual parameters are both chars, one of the parameters has to be converted (widened) to invoke either of the methods.
The language spec does not define that one is more specific than the other in such a case; they are both considered equally applicable, so the method call is ambiguous, and thus is a compile-time error.

Java varargs method overloading compiler error - ambiguity?

So, today I've been testing Java's overloading techniques and I've come across ambiguity which I can't explain. Basically, when there is a vararg method with primitive and its corresponding wrapper the compiler complains and can't decide which one to choose and I don't understand why? It's easy for human to decide and not for compiler?
Here is the fragment which works for non-vararg parameters:
public static void main(String[] args)
{
int a = 14;
Integer b = new Integer(14);
stuff(a);
stuff(b);
}
static void stuff(Integer arg) { System.out.println("Integer"); }
static void stuff(int arg) { System.out.println("int"); }
And here comes the vararg which complains and cries like a baby:
public static void main(String[] args)
{
int a = 14;
Integer b = new Integer(14);
stuff(a); // Doesn't compile (ambiguity)
stuff(b); // Doesn't compile (ambiguity)
}
static void stuff(int... arg) { System.out.println("varargs int"); }
static void stuff(Integer... arg) { System.out.println("varargs Integer"); }

Consider the following two hypothetical calls to stuff():
int a = 14;
Integer b = new Integer(14);
stuff(a, b);
stuff(b, a);
How does the compiler even know which method should be called here? Because of autoboxing rules, either call could be referring to either overloaded method.
Update:
My answer is logically correct, or at least on the right track, but for a more formal answer we can refer to this SO question:
Why ambiguous error when using varargs overloading with primitive type and wrapper class?
The two varargs method are invoked in loose invocation context. As a result, the compiler will attempt to find the more specific method via JLS 15.12.2.5 Choosing the Most Specific Method. However, since neither int nor Integer are subtypes of one another, the compiler will throw an error.

The problem is:
java is doing behind the scenes bridge methods (you need to verify that is you need deep info)
AND the important part, vargargs means too YOU CAN JUST NOT PASS ANY PARAMETER, so:
static void stuff(int... arg)
and
static void stuff(Integer... arg)
can both being invoked taking no parameters... so that will create some conflict about what method should the JVM invoke

What is the purpose of void?

public class test
{
public static void main(String[] args)
{
int x = 5;
int y = 10;
multiply(x,y);
}
public static void multiply(int x, int y)
{
int z = x*y;
System.out.println(z);
}
}
I am new to programming and I am confused on a few things.
Why is it correct to use void? I thought void is used in order to specify that nothing will be returned but, the multiply method returns z.
Do all programs require that you have exactly "public static void main(String[] args)"? What exactly is the purpose of the main method and what do the parameters "String[] args" mean? Would the program work if the main method was removed?
Thank You!

First, the multiply method does not return anything; it prints the product, but does not return any value.
public static void multiply(int x, int y)
{
int z = x*y;
System.out.println(z); //may look like a return, but actually is a side-effect of the function.
} //there is no return inside this block
Secondly, public static void main provides an entry point into your program. Without it, you cannot run your program. Refer to the Java documentation for more information on the usage of public static void main.
The String[] args here means that it captures the command line arguments and stores it as an array of strings (refer to the same link posted above, in the same section). This array is called args inside your main method (or whatever else you call it. Oracle cites argv as an alternate name)
System.out.print tells the program to print something to the console, while return is the result of the method. For example, if you added print all over your method to debug (a common practice), you are printing things while the program runs, but this does not affect what the program returns, or the result of the program.
Imagine a math problem - every step of the way you are "print"ing your work out onto the paper, but the result - the "answer" - is what you ultimately return.

When a method does not return anything, you specify its return type as "void". Your multiply method is not returning anything. Its last line is a print statement, which simply prints the value of its arguments on the standard output. If the method ended with the line "return z", then you would not be able to compile the program with the "void" return type. You would need to change the method signature to public static int multiply(int x, int y).
All Java programs do require the public static void main(String[] args) if they are to be executable. It is the starting point of any runnable Java program. Here's what it means:
a. public - the main method is callable from any class. main should always be public because it is the method called by the operating system.
b. static - the main method should be static, which means the operating system need not form an object of the class it belongs to. It can call it without making an object.
c. void - the main method does not return anything (although it may throw an Exception which is caught by the operating system)
d. String[] args - when you run the program, you can pass arguments from the command line. For example, if your program is called Run, you can execute the command java Run 3 4. In that case, the arguments would be passed to the program Run in the form of an array of Strings. You would have "3" in args[0] and "4" in args[1].
That said, you could have a Java program without a main, which will not be runnable.
I hope that helps.

Why is it correct to use void? I thought void is used in order to specify that nothing will be returned but, the multiply method returns z.
No
multiply method does not return z. However, you are correct, void is in fact used to specify that nothing will be returned.
Do all programs require that you have exactly "public static void main(String[] args)"? What exactly is the purpose of the main method and what do the parameters "String[] args" mean? Would the program work if the main method was removed?
yes, all programs must have a main function that looks like public static void main(String[] args).

Like others said, the multiply method does NOT return anything. The other answers explained why that is.
However it would also be helpful to mention that when you use void that method can not return anything. In contrast, if you set your method to return anything (not to void) you are required to return that type of value.
For example:
public static void main(String[] args){
int a;
a = returnInt();
}//End Method
public static int returnInt(){
int z = 5;
return z;
}//End Method
The main method does not return anything, which is why we use void. The returnInt method returns an integer. The integer that the method returns is z. In the main method where a = returnInt(); that sets the value of a to the value returned from returnInt(), in this case, a would equal 5.
Tried to keep it simple, hope it makes sense.

public means that the method is visible and can be called from other objects of other types. Other alternatives are private, protected, package and package-private. See here for more details.
static means that the method is associated with the class, not a specific instance (object) of that class. This means that you can call a static method without creating an object of the class.
void means that the method has no return value. If the method returned an int you would write int instead of void.
The combination of all three of these is most commonly seen on the main method which most tutorials will include.
credits to Mark Bayres

The multiply() method in your example does not return the value of z to the calling method, rather it outputs the value of z (e.g., prints it to the screen).
As you said, the void type keyword means that the method will not return a value. Methods like this are intended to "just do something". In the case of main(), the method will not return a value, because there is no calling method to return it to -- that's where your program begins.
OK, technically, that last comment is not accurate; it actually is possible to have your main return a value to the operating system or process that launched the program, but it isn't always necessary to do so -- especially for simpler console-based programs like those you'll write when you're just getting started! :)

Void class is an uninstantiable class that hold a reference to the Class object representing the primitive Java type void.
and The Main method is the method in which execution to any java program begins.
A main method declaration looks like this
public static void main(String args[]){
}
The method is public because it be accessible to the JVM to begin execution of the program.
It is Static because it be available for execution without an object instance. you may know that you need an object instance to invoke any method. So you cannot begin execution of a class without its object if the main method was not static.
It returns only a void because, once the main method execution is over, the program terminates. So there can be no data that can be returned by the Main method
The last parameter is String args[]. This is used to signify that the user may opt to enter parameters to the java program at command line. We can use both String[] args or String args[]. The Java compiler would accept both forms.

Why is it correct to use void? I thought void is used in order to
specify that nothing will be returned but, the multiply method returns
z.
Your multiply method is correct to have void since it is returning nothing, it is just printing to the console.
Returning something means gives out a result to the programm for further computation.
For example your methode with return of the result would look like this:
public static int multiply(int x, int y)
{
int z = x*y; //multipling x and y
System.out.println(z); //printing the restult to the console
return z; //returning the result to the programm
}
this "new" method can be used like this for example:
public static void main(String[] args)
{
int x = 5;
int y = 10;
int result = multiply(x,y); //storing the returnen value of multiply in result
int a = result + 2; //adding 2 to the result and storing it in a
System.out.println(a); //printing a to the console
}
Output:
50
52
Do all programs require that you have exactly "public static void
main(String[] args)"? What exactly is the purpose of the main method
and what do the parameters "String[] args" mean? Would the program
work if the main method was removed?
This mehtod seves a the etry point for your programm. This meas the first thing that is executet of your programm is this mehtod, removing it would make the programm unrunneable.
String[] args stands for the commandline arguments you can give to you programm befor starting over the OS (OS = Windows for example)
The exact purpose of all of the words is very well explained in the other answers here.

Polymorphism and method overloading

I have a quick and straighforward question:
I have this simple class:
public class A
{
public void m(Object o)
{
System.out.println("m with Object called");
}
public void m(Number n)
{
System.out.println("m with Number called");
}
public static void main(String[] args)
{
A a = new A();
// why will m(Number) be called?
a.m(null);
}
}
UPDATE: actually is method with Number actually being called. Sorry about the confusion.
If I call a.m(null) it calls method with Number parameter.
My question is: why is this? where in the java language specification is this specified?

First of all, it actually calls m(Number).
It happens because both methods are applicable, but m(Number) is the most specific method, since any argument of m(Number) can be passed to m(Object), but not vice versa.
If you replace m(Object) by m(String) (or add another method such as m(Date)), compiler would report ambiguity, since the most specific method can't be identified.
See the section Choosing the Most Specific Method in the Java Specification.

This is not polymorphism or overriding. This is method overloading.
I tested this and specific method is being called (not the m(Object)) and according to the spec the specific method is always called. Which overload will get selected for null in Java?

another related question for you to think about:
public static void main(String[] args)
{
A a = new A();
Object n = new Integer(1);
a.m(n); // which method will be called?
}

My 2 cents. Method with Number argument is the one that is called, Because Number extends Object. I had a similar situation in the past, I did override a method and put Component instead of JComponent (by mistake). It took me one week to find out the reason why my method was never called. I figure it out, that if there are some inheritance relationship between the overloaded methods, the JVM matches first the deeper one in the class hierarchy.

Object is the default type in Java. If you refactor your m(Object o) method to m(String o) you'll have a compile time error saying that the call m(null) is ambiguous because Java cannot determine which class between String and Number defaults to null
Other than that, between m(Object o) and m(Number o), calling m(null) will call m(Number o) because it's the most specialized method. You would need to cast null into an Object (or anything not an instance of Number) otherwise.
a.m((String) null);