java.util

## Interface Comparator<T>

- Type Parameters:
    `T` - the type of objects that may be compared by this comparator
  All Known Implementing Classes:
    Collator, RuleBasedCollator

      public interface Comparator<T>

  A comparison function, which imposes a total ordering on some collection of objects. Comparators can be passed to a sort method (such as `Collections.sort` or `Arrays.sort`) to allow precise control over the sort order. Comparators can also be used to control the order of certain data structures (such as `sorted sets` or `sorted maps`), or to provide an ordering for collections of objects that don't have a `natural ordering`.

  The ordering imposed by a comparator `c` on a set of elements `S` is said to be consistent with equals if and only if `c.compare(e1, e2)==0` has the same boolean value as `e1.equals(e2)` for every `e1` and `e2` in `S`.

  Caution should be exercised when using a comparator capable of imposing an ordering inconsistent with equals to order a sorted set (or sorted map). Suppose a sorted set (or sorted map) with an explicit comparator `c` is used with elements (or keys) drawn from a set `S`. If the ordering imposed by `c` on `S` is inconsistent with equals, the sorted set (or sorted map) will behave "strangely." In particular the sorted set (or sorted map) will violate the general contract for set (or map), which is defined in terms of `equals`.

  For example, suppose one adds two elements `a` and `b` such that `(a.equals(b) && c.compare(a, b) != 0)` to an empty `TreeSet` with comparator `c`. The second `add` operation will return true (and the size of the tree set will increase) because `a` and `b` are not equivalent from the tree set's perspective, even though this is contrary to the specification of the `Set.add` method.

  Note: It is generally a good idea for comparators to also implement `java.io.Serializable`, as they may be used as ordering methods in serializable data structures (like `TreeSet`, `TreeMap`). In order for the data structure to serialize successfully, the comparator (if provided) must implement `Serializable`.

  For the mathematically inclined, the relation that defines the imposed ordering that a given comparator `c` imposes on a given set of objects `S` is:

             {(x, y) such that c.compare(x, y) <= 0}.

  The quotient for this total order is:

             {(x, y) such that c.compare(x, y) == 0}.

  It follows immediately from the contract for `compare` that the quotient is an equivalence relation on `S`, and that the imposed ordering is a total order on `S`. When we say that the ordering imposed by `c` on `S` is consistent with equals, we mean that the quotient for the ordering is the equivalence relation defined by the objects' `equals(Object)` method(s):

           {(x, y) such that x.equals(y)}.

  This interface is a member of the Java Collections Framework.

  Since:
    1.2
  See Also:
    `Comparable`, `Serializable`

- - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `int` | `compare(T o1, T o2)` Compares its two arguments for order.
    `boolean` | `equals(Object obj)` Indicates whether some other object is "equal to" this comparator.

- - ### Method Detail

    - #### compare

          int compare(T o1,
                    T o2)

      Compares its two arguments for order. Returns a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.

      In the foregoing description, the notation `sgn(`expression`)` designates the mathematical signum function, which is defined to return one of `-1`, `0`, or `1` according to whether the value of expression is negative, zero or positive.

      The implementor must ensure that `sgn(compare(x, y)) == -sgn(compare(y, x))` for all `x` and `y`. (This implies that `compare(x, y)` must throw an exception if and only if `compare(y, x)` throws an exception.)

      The implementor must also ensure that the relation is transitive: `((compare(x, y)>0) && (compare(y, z)>0))` implies `compare(x, z)>0`.

      Finally, the implementor must ensure that `compare(x, y)==0` implies that `sgn(compare(x, z))==sgn(compare(y, z))` for all `z`.

      It is generally the case, but not strictly required that `(compare(x, y)==0) == (x.equals(y))`. Generally speaking, any comparator that violates this condition should clearly indicate this fact. The recommended language is "Note: this comparator imposes orderings that are inconsistent with equals."

      Parameters:
        `o1` - the first object to be compared.
        `o2` - the second object to be compared.
      Returns:
        a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.
      Throws:
        `ClassCastException` - if the arguments' types prevent them from being compared by this comparator.

    - #### equals

          boolean equals(Object obj)

      Indicates whether some other object is "equal to" this comparator. This method must obey the general contract of `Object.equals(Object)`. Additionally, this method can return `true` only if the specified object is also a comparator and it imposes the same ordering as this comparator. Thus, `comp1.equals(comp2)` implies that `sgn(comp1.compare(o1, o2))==sgn(comp2.compare(o1, o2))` for every object reference `o1` and `o2`.

      Note that it is always safe not to override `Object.equals(Object)`. However, overriding this method may, in some cases, improve performance by allowing programs to determine that two distinct comparators impose the same order.

      Overrides:
        `equals` in class `Object`
      Parameters:
        `obj` - the reference object with which to compare.
      Returns:
        `true` only if the specified object is also a comparator and it imposes the same ordering as this comparator.
      See Also:
        `Object.equals(Object)`, `Object.hashCode()`

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