difference between equals() and hashCode()

public boolean equals(Object obj)

This method checks if some other object passed to it as an argument is equal to the object on which this method is invoked. The default implementation of this method in Object class simply checks if two object references x and y refer to the same object. i.e. It checks if x == y. This particular comparison is also known as "shallow comparison". However, the classes providing their own implementations of the equals method are supposed to perform a "deep comparison"; by actually comparing the relevant data members. Since Object class has no data members that define its state, it simply performs shallow comparison.

The equals method implements an equivalence relation:
-It is reflexive: for any reference value x, x.equals(x) should return true.
-It is symmetric: for any reference values x and y, x.equals(y) should return true if and only if y.equals(x) returns true.
-It is transitive: for any reference values x, y, and z, if x.equals(y) returns true and y.equals(z) returns true, then x.equals(z) should return true.
-It is consistent: for any reference values x and y, multiple invocations of x.equals(y) consistently return true or consistently return false, provided no information used in equals comparisons on the object is modified.
For any non-null reference value x, x.equals(null) should return false.

public int hashCode()

The general contract of hashCode is:
-Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.

-If two objects are equal according to the equals(Object) method, then calling the hashCode method on each of the two objects must produce the same integer result.
-It is not required that if two objects are unequal according to the equals(java.lang.Object) method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hashtables.

Hashcode example

public class HashCodeString {
public static void main(String args[]) {
Integer j = new Integer(4);
Long k = new Long(4);
Integer v = new Integer(3);
System.out.println("false is returned: " + j.equals(k)); // Result - false
System.out.println("Hash code of number 4 is: " + j.hashCode() //Result 4
+ "\nHash code of number 4 is: " + k.hashCode()); // 4
System.out.println("Method returns three: " + v.hashCode()); // 3
String baadshah = "latter in time there will be my empire every where";
System.out.println("Corresponding hash code value returned is: "
+ baadshah.hashCode()); // Result 342564105
}

}

==, .equals(), compareTo(), and compare()

==
Compares references, not values. The use of == with object references is generally limited to the following:
Comparing to see if a reference is null.
Comparing two enum values. This works because there is only one object for each enum constant.
You want to know if two references are to the same object

equals()
Compares values for equality. Because this method is defined in the Object class, from which all other classes are derived, it's automatically defined for every class. However, it doesn't perform an intelligent comparison for most classes unless the class overrides it. It has been defined in a meaningful way for most Java core classes. If it's not defined for a (user) class, it behaves the same as ==.

It turns out that defining equals() isn't trivial; in fact it's moderately hard to get it right, especially in the case of subclasses. The best treatment of the issues is in Horstmann's Core Java Vol 1. [TODO: Add explanation and example]

compareTo()
Comparable interface. Compares values and returns an int which tells if the values compare less than, equal, or greater than. If your class objects have a natural order, implement the Comparable interface and define this method. All Java classes that have a natural ordering implement this (String, Double, BigInteger, ...).

compare()
omparator interface. Compares values of two objects. This is implemented as part of the Comparator interface, and the typical use is to define one or more small utility classes that implement this, to pass to methods such as sort() or for use by sorting data structures such as TreeMap and TreeSet. You might want to create a Comparator object for the following.

Multiple comparisions. To provide several different ways to sort somthing. For example, you might want to sort a Person class by name, ID, age, height, ... You would define a Comparator for each of these to pass to the sort() method.
System class. To provide comparison methods for classes that you have no control over. For example, you could define a Comparator for Strings that compared them by length.
Strategy pattern. To implement a Strategey pattern, which is a situation where you want to represent an algorithm as an object that you can pass as a parameter, save in a data structure, etc.

If your class objects have one natural sorting order, you may not need this.