Can a class have no constructor?

It is not required to explicitly define a constructor; however, all classes must have a constructor, and a default empty constructor will be generated if you don't provide any:

public Maze() {
}

See Default Constructor.

If you don't write the constructor explicitly, compiler will generate a no-args constructor by default.

public Maze(){

}    

the above will be included If you don't write the constructor explicitly, compiler will generate a no-args constructor by default.

public Maze(){

}    

the above will be included by the compiler.

for Example check the Byte code for this class:

public class ABC {

}

BYTE CODE:

public class sorting/ABC {

  // compiled from: ABC.java

  // access flags 0x1
  public <init>()V         //Default no-args constructor included by the compiler
   L0
    LINENUMBER 7 L0
    ALOAD 0
    INVOKESPECIAL java/lang/Object.<init>()V
    RETURN
   L1
    LOCALVARIABLE this Lsorting/ABC; L0 L1 0
    MAXSTACK = 1
    MAXLOCALS = 1
}

To be more accurate, the compiler automatically provides a no-args constructor for a class that doesn't have a constructor, this constructor calls the no-args constructor of the superclass, if the superclass doesn't have a no-args constructor, it's an error, if it does, that's fine.

If your class has no explicit superclass, then it has an implicit superclass (Object), which does have a no-args constructor.